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JOURNAL OF SEMANTICS Volume 17 Number

2

CONTENTS Special Issue on Dialogue (Part II) Guest Editors: Henk Zeevat and Robert van Rooy

ANDREAS HERZIG AND DoMINIQUE LoNGIN

Belief Dynamics in Cooperative Dialogues

91

RoBERT VAN Rooy

Permission to Change

II9

(end of Special Issue)

Regular Articles

JEAN-PIERRE KoENIG AND NurrANART MuANSUWAN How to End Without Ever Finishing: Thai Semi-Perfectivity

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Belief Dynamics in Cooperative Dialogues A N D RE AS HERZIG and D OMI NIQUE LO NGI N Institut de Recherche en Informatique de Toulouse

Abstract We investigate how belief change in cooperative dialogues can be handled within a modal logic of action, belief, and intention. We first review the main approaches of the literature, and point out some of their shortcomings. We then propose a new framework for belief change. Our basic notion is that of a contextual topic: we suppose that we can associate a set of

the agents' belief states after a speech act. We illustrate our theory by a running example.

1 INTRO D U C T I O N Participants i n task-oriented dialogues have a common goal, to achieve the task under consideration. Each of the participants has some information necessary to achieve the goal, but none of them can achieve it alone. Consider e.g. a system delivering train tickets to users. The system cannot do that without user input about destination and transport class. The other way round, the user needs the system to get his ticket. Each of the participants is supposed to be cooperative. This is a fundamental and useful hypothesis. Informally, a person is cooperative with regard to another one if the former helps the latter to achieve his goals (c£ Grice's cooperation principles, as well as his conversation maxims (Grice 1 975)). For example, if the system learns that user wants a train ticket, then the system will intend to give it to him. The other way round, if the system asks for some piece of information it needs to print the ticket, then the user answers the questions asked by the system. Each participant is supposed to be sincere: his utterances faithfully mirror his mental state. If a participant says 'the sky is blue', then he indeed believes that the sky is blue. Such a hypothesis means that contradictions berween the presuppositions of a speech act and the hearer's beliefs about the speaker cannot be explained in terms of lies. Note that our sinceriry assumption is much weaker than in other approaches, where sinceriry is sometimes viewed as the criterion of input adoption (Cohen & Levesque 199oc). Under these hypotheses, how should the mental state of a rational agent participating in a conversation evolve? In the sequel we call belief change the process leading an agent from a mental state to a new one.

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topics with every agent, speech act, and formula. This allows us to talk about an agent's competence, belief adoption, and belief preservation. Based on these principles we analyse

92 Belief Dynamics in Cooperative Dialogues

The following dialogue is our running example to highlight different problems and our solutions. There are only two agents, the systems and the user u:

s1: u 1: S2: U2: s3: u3: s4:

100 €

by

This illustrates that in a conversation agents might change their mind, make mistakes, understand wrongly, etc. Since by our cooperation hypothesis the agents interact with each other in order to achieve the dialogue goal, they are the victims of such phenomena. They must consequently be taken into account when modelling the evolution of mental states. In our example, the system o o

o

o o

accepts some information (e.g. information about destination and class­ c£ U1); derives supplementary information not directly contained in the utter­ ance by using laws about the world (e.g. to derive the price if the user informs about his destination and class-c£ s2); sometimes accepts information contradicting its own beliefs, in par­ ticular when the user changes his mind (e.g. switching from a first-class ticket to a second-class ticket-c£ u2); preserves some information it believed before the utterance (e.g. the system preserves the destination even when the class changes-c£ u2); may refuse to take over some information, in particular if the user tries to inform the system about facts the user isn't competent at (e.g. prices of train tickets-c£ s4).

To sum up, s has two complementary tasks: (1) dealing with contradictions between his mental state and consequences of the input, and (z) preserving his old beliefs that do not contradict this input. We consider each participant to be a rational agent having mental states represented by different mental attitudes such as belief, choice, goal, intention, etc. Belief change takes place within a formal rational balance theory and a formal rational interaction theory a Ia Cohen & Levesque (199oa,

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Hello. What do you want? A first class train ticket to Paris, please. 150 €, please. Ouups! A second-class train ticket, please. 1 oo €, please. Can I pay the So € by credit card? The price isn't So €. The price is 100 €. Yes, you can pay the credit card.

Andreas Herzig and Dominique Longin 93

I990c). These approaches analyse linguistic activity within a theory of actions: this is the base of so-called BDI-architectures (for Belief, Desire, and Intention). Each utterance is represented by a (set of) speech act(s) (Austin I962; Searle I969), in a way similar to Sadek (2ooo).1 Belief change triggered by these speech acts is analysed in terms of consequences of these speech acts. From an objective point of view, a dialogue is a sequence of sets of speech an ) , where each ak + I mapS a State Sk tO a neW State sk+I; aCtS ( a . I l

· · l

1

We use 'set of speech acts' rather than 'a speech act', because a Qiteral) speech act may entail

indirect speech acts. We develop this question in Herzig

et a/. (2000).

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So is the initial state (before the dialogue starts). Given Sk and ak+�> our task iS tO COnstruCt the neW State Sk+I• The background of our work is an effective generic real-time coopera­ tive dialogue system that has been specified and developed by the France Telecom R&D Center. This approach consists in first describing the system's behaviour within a logical theory of rational interaction (Sadek I99I, 2ooo, I992), and second implementing this theory within an inference system called ARTIMIS (Bretier & Sadek I997; Sadek et al. I996, I997)· For a fixed set of domains, this system is able to accept nearly unconstrained spontaneous language as input, and react in a cooperative way. The activities of the dialogue system are twofold: to take into account the speaker's utterances, and to generate appropriate reactions. The latter reactive part is completely defined in the current state of both the theory and the implementation. On the other hand, the acceptance of an utterance is handled only partially, in particular its belief change part. In our approach, building on previous work in Farinas del Cerro et al. (I998), we implement belief change by an axiom of belief adoption and one of beliefpreservation. Both of them are based on our key concept of topic of information. We refine our previous work by contextualizing topics by mental attitudes of the agents. We aim at a logic having both a complete axiomatization and proof procedure, and an effective implementation. This has motivated several choices, in particular a Sahlqvist-type modal logic (for which general completeness results exist) that is monotonic (contrarily to many approaches in the literature) and which has a notion of intention that is primitive (contrarily to the complex constructions in the literature). In the next section we discuss the failure of the existing approaches to correctly handle belief change (section 2). Then we present an original

94 Belief Dynamics in Cooperative Dialogues

approach based on topics (section 3). This is embedded in a BDI framework (section 4). Finally we illustrate the approach by a complete treatment of our running example (section s). 2 EXISTI N G APPROACHES

+-+

2. r

Cohen

&

Levesque

Cohen & Levesque (1990a, 1 99oc) have defined a formal theory of rational interaction where an agent may accept new pieces of information ('inputs' 2

W e view S as not closed under logical consequence. Therefore it can be confused with the

conjunction of its elements. Just like Katsuno & Mendelzon operator mapping the formulas S and A to a formula.

3

(1992),

we view

o

as a (metalanguage)

Nevertheless, it is known in the belief revision literature that the AGM revision postulates must

be considerably weakened if the language contains modalities (Fuhrmann's impossibility theorem (Fuhrmann

1989),

(Hansson

1999:

section

5.1)).

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The most prominent formal analysis of belief change has been done in the AGM (Alchourr6n et al. 1985) and the KM (Katsuno & Mendelzon 1992) frameworks. There, a belief change operator o is used to define the new state So A from the previous state S and the input A.2 There are two difficulties if we want to use such a framework. First, until now, update operators have only been studied for classical propositional logic, and not for epistemic or doxastic logic.3 But an appropriate theory of dialogues should precisely be about the change of beliefs about other agents' beliefs: an agent i believing that p and that another agent j believes p must be able to switch to believing that j believes •p, while maintaining his belief that p. Nothing is said about that in the current theories of revision and updates. The second difficulty is that both revision and update have several common properties that must be refined or rejected. For example, the postulate (So A) ___, A (input A has always priority) is problematic: in some approaches the new information may be rejected (as in Sadek's); in our approach, the new information is always accepted, but not all its consequences. We reject the postulate (So A) S if S ___, A because it neglects the over-informing nature of some information: our agents may have different behaviour in the cases of over-information. In the rest of this section we review the logical analyses of belief change in dialogues that have been proposed in the literature. Due to the above difficulties to formalize belief change within the existing frameworks for revision or update, belief change is integrated into a formal theory of rational behaviour.

Andreas Herzig and Dominique Longin 95

2.2

Perrault

Perrault's system is based on Reiter's default logic (Reiter 1980). A=?- B denotes a normal default. Doa, 1T means that action o: is performed at time t, observe1,1A means that agent j observes A at time t, and (Assert;, i P ) means that agent i communicates propositional content P to agent j. The main axioms and default rules of Perrault's approach are as follows:

(I) (2) (3)

memory: Bel;, 1A-+ Bel;, 1+1 Bel;,1A persistence: Bel;, 1+1Bel;, 1A-+ Bel;, 1+1A observability: Doa, 1T 1\ Observej ,1Doa,1T-+ Be� ,t+1 Doa, 1T, where o: is performed by the agent i

(4) belief transfer: Bel;, 1BelJ, t A =?- Bel;, 1A

(s) assertion rule: Do(Assert; . 1 A), tT =?- Bel;, t A Moreover there is a default schema saying that if A =?- B is a default then Bel;, 1A =?- Bel;,1B is also a default, for every agent i and timepoint t. Here sincerity is not required in order to admit an act (as illustrated by axiom (3)). But an agent consumes its effects only if he doesn't yet believe the converse of this effect (in terms of defaults: if the effect is consistent with his current beliefs, c£ (s)). Thus the speaker does not have the right to lie, to

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for short). In this approach, the input corresponds to the speaker's intention to obtain some effect rather than to the speech act itself The hearer's belief adoption is conditioned by the speaker's sincerity. Their theory allows the agent both to change his beliefs and to reject the input (if the speaker is believed to be insincere). However, as Sadek notes (Sadek 1 99 1), even lies might generate some effects (for example, the hearer adds to his beliefs that the speaker is insincere). Thus even if the input is rejected, the mental state of the hearer evolves. Finally, in Cohen & Levesque's approach beliefs not undermined by the act are never preserved from the preceding mental state to the new one (c£ the frame problem in Artificial Intelligence (McCarthy & Hayes 1969)). Thus inconsistency of the newly acquired beliefs with old ones is never the case, simply because old beliefs are given up by the agent. (Such a behaviour corresponds to what has been called the trivial belief change operation in the AGM and KM literature.)

96 Belief Dynamics in Cooperative Dialogues

But as he notes himself, in this case there are always two extensions: one where the agent preserves his (old) beliefs and then adopts the input if it is consistent with these beliefs, and another one where the agent adopts the input and then preserves those old beliefs that are consistent with the new information. But there seems to be no way of determining which choice the agent should make. Perrault's approach has some other problems that we do not discuss here (for example, if the speaker ignores whether A is the case, then he starts to believe it as soon as he utters that A, c£ Appelt & Konolige ( r 989)). 2.3

Sadek

Sadek defines a theory of rationality similar to Cohen & Levesque's, enriching it with two new mental attitudes, uncertainty and need (Sadek 1 991, 1 992). In his belief reconstruction (Sadek 1 994), he presents an alternative to Perrault's approach. He enriches the latter's theory by an axiom of admission, and orders the application of his axioms of memory, admission, effects acceptance, and preservation. His axiom of admission describes the behaviours that can be adopted by an agent, but it does not specify the way the agent chooses between different possible behaviours. In particular he enables the hearer to reject an act. The latter point seems problematic to us, given that hearers do not reject an act that has been performed, but rather (hypothetically) accept it in order to conclude that it was not this one that has been performed. 2.4

Rao

&

Georgejf

In several papers, Rao & Georgeff have proposed theories and architectures for rational agents (Rao & Georgeff 1 991). Such a theory can in principle be

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make mistakes or to change his mind; otherwise the effect of his act will never be consumed (in technical terms, the default will be blocked). This is at the origin of an even more radical behaviour: as highlighted in Appelt & Konolige (r989), Perrault's agents never question old beliefs, but only expand their mental state (in the sense of the AGM framework). Indeed, it follows from axioms ( r ) and (2) that Bel;, 1A-+ Bel;, 1+,A. Consequently if a belief stemming from memory conflicts with a belief stemming from the act, then the default ( s) will never been applied, and the effect will never be consumed. Perrault is aware of that and suggests to achieve persistence by a default rule: (6) Persistence (his): Bel;, 1+,Bel;, 1A ::::;>Be/;, 1+,A

Andreas Herzig and Dominique Longin 97

applied to dialogues. In Rao & Georgeff ( 1992 ), in a way similar to STRIPS, actions and plans are represented by their preconditions together with add­ and delete-lists. The latter lists are restricted to sets of atomic formulas. In such a framework, one can a priori neither represent non deterministic actions nor actions with indirect effects (obtained through integrity constraints). Even more importantly, actions can only have effects that are factual: this excludes the handling of speech acts, whose effects are epistemic, and are typically represented by means of nested intensional operators (such as intentions to bring about mutual belief ). Recently, they have defmed a tableau proof procedure for their logic {Rao & Georgeff 1998).

Appelt

&

Konolige

Appelt & Konolige highlight the problems of Perrault's approach (Appelt & Konolige 1989). They propose to use hierarchic auto-epistemic logic {HAEL) as a framework. Basically, what one gains from this is that application of default rules can be ordered in a hierarchy. This can be used to fine-tune default application and thus avoid unwanted extensions. Apart from the relatively complex HAEL technology, it appears that Appelt & Konolige's belief adoption criterion encounters problems similar to Perrault's. Suppose the hearer has no opinion about p. Now if the speaker informs the hearer that p, then under otherwise favourable circumstances the hearer adopts p. But if the speaker informs the hearer that the hearer believes p (or that he believes the hearer believes p), then it is clearly at odds with our intuitions that the hearer should accept such an assertion about his mental state. The only means to avoid the latter behaviour is to shift the hearer's ignorance about p to the level of the HAEL hierarchy that has priority (level o). But in this case the acceptation of the assertion that p would be blocked as well.

3

TOPIC-BASED B ELIEF CHANGE 3.1

The modal language

Like the previously cited authors, we work in a multimodal framework, with modal operators of belief, mutual belief, intention, and action. Our language is that of first-order multimodal logic without equality and without function symbols {Chellas 1980; Hughes & Cresswell 1972;

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2. 5

98 Belief Dynamics

in

Cooperative Dialogues

Bel5Done( lnlorm.,,Bei.Bel,p) Bel5Belu Bel5•p is a formula. 3 .2

The problem of belief change

In our approach, unlike Sadek's, we always accept5 speech acts, but we proceed in two steps: the agent accepts the indirect and intentional effects, but only adopts the speaker's beliefs if he believes the speaker to be competent at these beliefs. Thus, speaker competence is our criterion to determine which part of the input must be accepted by the hearer and which part must be rejected. For example, s accepts input about the new 4 5

Done0A et Feasible0A are just (o:-1)A and (o:) A of dynamic logic (Hare! as

'Accepting' an act means that we admit that it has been performed.

1984).

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Popkorn 1 994). We suppose that /\, •, T and V are primitive, and that V, --+, l_ and 3 are defined as abbreviations in the usual way. Let ACT be the set of agents. For i,j E ACT, the belief operators Bel; and Bel;, J respectively stand for 'the agent i believes that' and 'it is mutual belief of i and j that'. For each i E ACT, the intention operator Intend; stands for 'the agent i intends that'. In our running example, we use two particular agents, s and u, which stand for the system and the user. Speech acts are represented by tuples of the form (FORCE;,j A ) where FORCE is the illocutionary force of the act, i, j E ACT, and A is the propositional content of the act. For example (Inform u ,s Dest(Paris) ) represents a declarative utterance of the user informing the system that the destination of his ticket is Paris. Let ACT be the set of all speech acts. With every speech act a E ACT we associate two modal operators Doneo: and Feasibleo:. Doneo:A is read 'speech act a has just been performed, before which A was true'; Feasibleo:A is read 'speech act a is feasible, after which A will be true'.4 In particular, Doneo:T and Feasibleo:T are respectively read 'a has just been performed' and ' a is feasible' (or 'can be performed'). Using the Doneo: operator, the beliefs of the system at the state Sk can be kept in memory at state Sk + 1: if B is the conjunction of all beliefs of the agent i at the (mental) state k, and a has just been done, then Bel;Doneo:B is the memory of i in the state k + 1. T o express temporal properties, we define the Always operator, and its dual operator Sometimes. Always A means 'A always holds' and Sometimes A means 'A sometimes holds'. The operator Always will enable us in particular to preserve the domain laws in all states. Formally, acts and formulas are defined by mutual recursion. This enables speech acts where the propositional contents is a non -classical formula. For example:

Andreas Herzig and Dominique Longin 99

3·3

Topic structures

The concept of topic has been investigated both in linguistics and philo­ sophical logic. For example, in Biiring (1995) a semantical value related to the topics is associated with each English sentence. Van Kuppevelt has developed a notion of topic based on questions and has applied it to phenomena of intonation (van Kuppevelt 1991, 1995). In Ginzburg (1995), some sets of topics play a decisive role in the coherence of dialogues. Several approaches to the notion of topic exist in the philosophical logic literature, in particular those of Lewis (1972) and Goodman (r961). Goodman's notion of 'absolute aboutness' is defined purely extensionally. Hence for him logically equivalent formulas are about the same topics, while this is not the case for us. Moreover, as he focuses on the 'informative aspect' of propositions, the subject of a tautology is the empty set. Epstein's (1990) notion is quite different from Lewis's and Goodman's. He defines the relatedness relation R as a primitive relation between propositions because 'the subject matter of a proposition isn't so much a property of it as a relationship it has to other propositions' (Epstein I 990: 62). Thus, he does not represent topics explicitly. Then he defines the subject matter of a proposition A as s(A) = { {A, B} : R(A, B) }. More precisely, sis called the subject matter set-assignment associated with R (Epstein 1990: 68). Epstein shows that we can also define s as primitive, and that we can then

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class (after uJ but rejects input about the price (after u 3 ), the reason being that he considers u to be competent at classes but not at ticket prices. Which beliefs of the hearer can be preserved after the performance of a speech act? Our key concept here is that of the influence of a speech act on beliefs. If there exists a relation of influence between the speech act and a belief, this belief cannot be preserved in the new state. In our example, the old transport class cannot be preserved through u2, because the act of informing about classes influences the hearer's beliefs about classes. How can we determine the competence of an agent at beliefs and the influence of a speech acts on beliefs? The foundation of both notions will be provided by the concept of a topic: we start from the idea that with every agent, speech act, and formula some set of topics can be associated. Thus, an agent i is competent at a formula A if and only if the set of topics associated with A is a subset of the set of topics associated with i-the set of topics at which i is competent. And a formula A is preserved after the performance of a speech act a if A and a have no common topic, i.e. occurring both in the set of topics associated with A and in the set of topics associated with a. We give the formal apparatus in the rest of the section.

1 00

Belief Dynamics

in

Cooperative Dialogues

define two propositions as being related if they have some subject matter in common. Our subject function can be seen as an extension of this function to a multi-modal language. For us, topics are themes in context, where the set of themes is an arbitrary set and contexts correspond to mental attitudes of agents. We define three functions associating topics to formulas, agents, and speech acts. 3. 3. r Themes, contexts, and topics

Definition 1 Let i E ACT. Then ma; is called an atomic context. A context is

a possibly empty sequence of atomic contexts. The empty context is noted .>.. C is the set of all contexts. ma; stands for 'the mental attitude of agent i '.

Definition 2 A topic of information (or contextual thematic structure) is a theme together with a context, denoted by c:t, where t E T and c E C.

For example, mau : price is a topic consisting in the user's mental attitude at prices, and ma5 : mau : price is a topic consisting in the system's mental attitude at the user's mental attitude at prices. For the empty context A, we have

(7)

A

:c

=

c:

A

=

c.

By convention, we identify introspection, we postulate (8)

ma;: ma;

=

A

: t with t. In order to take into account

ma;.

Given a set of themes and a set of agents we note lf the associated set of topics. lfn is the set of topics whose contexts have length at most n. As we have identified A : t with t, lr0 is the set of themes. In this paper, for reasons of representational economy we shall suppose that the length of each context is at most 2. Hence we restrict lf to lf2.6 Note that we have overloaded the operator : '. As we only use A, c, '

6

We did not fmd examples requiring length J. Nevertheless, this restriction

can

be relaxed easily.

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A theme is what something is about. For example, information on the destination is about the destination but not about the transport class. Let T =/= 0 be a set that we call the set of themes. In our running example, we suppose that T contains destinations, classes, prices, and payment.

Andreas Herzig and Dominique Longin

ma;, . . . for contexts and only t, t 1,

.

.

•

101

for themes, there should be no

confusion.

3.3.2 The subject of a formula

Definition

3 The subject of a formula A is a set of topics associated with A (the topics A is about). This notion is formalised by a function subject mapping every formula to a set of topics from 1L

We give the following axioms. 1

subjed(p) �

T

and subjed(p) f. 0 where p is atomic.

intuition that might be helpful is to think of the subject of p as the predicate name of p. An

Axiom 2 subject(T)

=

0.

Note that this slightly differs from Epstein's account.7

Axiom 3 subject( •A) = subject(A). Axiom 4 subject(A 1\ B) = subject(A) U subject(B). Axiom s subject(Bel; A) = { ma; : c : t I c : t E subject(A) }. Note that example:

c

might be the empty context here. Thus, in our running

subject(Class ( I st) ) = {class} subject(Dest(Paris) ) = {destination} subject(Bel5BeluPrice( 8o €) 1\ Bel5Price( 100 €)) = {mas : mau : price} U { ma5 : price} .

Axiom 6 subject(Bel; ,JA)

=

subject(Bei;A) U subject(Be�A) U subject(Bel;Bel; ,JA) U subject(Be�Be/; ,1A ) .

Axiom 7 subject(lntend;A) = subject(Bel;A). 7

Indeed, Epstein stipulates that R(A, A) for every formula A. O n the contrary, the present axiom

makes that not(R(T, T) ) . More generally, we have R(A, A) iff the set of atoms of A is nonempty. Due to the logical operators T and ..l in the language we had to modify that.

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Axiom

1 02

Belief Dynamics

Axiom

8

in

Cooperative Dialogues

subject(DoneaA)

propositional content of

8 a.

=

subjed(A) U subjed(A') where A' 1s the

=

Axiom 9 subjed(VxA) subject(A). Axiom 10 subjed(A[t/x]) � subject(A), where A[t/x] resulting from the substitution of the variable x by the term t.

is

the formula

=

subject(BeluBeluPrice(Iso€)) {mau :price} , and subject(BeluBel5BelkPrice( 1 so €) ) { mau :ma5 :price}, for any agent k. =

3 · 3· 3 The competence of an agent

Definition 4 The competence of an agent i is a set of topics associated with i

(the competence of i). This notion isformalised by a Junction competence mapping every agent to a set of topics from lr. We assume every agent is competent at his mental states.

Axiom

II

competence(i) 2 {rna;: tIt E T}.

An agent may be competent at some facts. For example, competence( u ) contains destinations and classes, but not prices.9 Competence will allow us to formulate in the next section our belief adoption axiom which basically says: 'an agent j adopts the belief of another agent i about a formula A if j considers that i is competent at the subject of

A'.w

3 . 3 ·4 The scope of an act

Definition

5 The scope of a speech act a is a set of topics associated with a (the scope of a). This notion isformalised by a Junction scope mapping every speech act to a set of topics from lr.

8 Another choice would have been subject{Done0A) = subject(A) U scope{ a). But this would tOQ much mix up the reading of the subject function of 'being about something' with that of the scope function of 'modifying the truth value'. 9 Note that an agent might be competent at mental attirudes of some other agent. This means that

the former agent controls the latter. We do not exploit this further here. 10 Hence competence should be a 2-argument function. As we only have two participants in our examples, we have dropped the second argument for the sake of simpliciry.

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This expresses that if an instance of A is about some topic, then A is about that topic as well. Due to our restriction to contexts of length 2 we suppose that contexts of the form ma; :ma 1 :c are reduced to rna; :ma 1. The corresponding subject function can be obtained by first simplifying the topics by (7), (8), and the above equation ,\ :t = t; and then by reducing those of length greater than 2 to topics of length 2. For example,

Andreas Herzig and Dominique Longin 103

Axiom

12 scope((FORCE;,JA)) 2 { maJ : rna; :t I t E subject(A) }, for every illocutionary force FORCE.

For example, consider the speech act where the user informs the system about the ticket price. This speech act influences the system's belief about the user's belief about prices. Now consider the case where a is a request act. We postulate that the type of mental attitudes maJ : ma; :t is the only one that is in the scope of a.

Axiom

13

scope((Request;,JA)) � {maJ : rna; :t l t E T } .

3·3·5 Topic structures

We have thus defined three functions mappmg the different types of expressions in our language to topics.

Definition 6 Given a set of themes and a set ofagents, a topic structure consists

of the associated set of topics lr together with the subject, scope, and competence functions. Is there an interaction between these functions? Consider the speech act ( l nf orm u s Class(2 nd) ) . It follows from the axiom we gave for the scope function that mas :mau :class E scope( a ) . Given that the user is

a=

,

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Suppose the user informs the system about his destination. As the user is competent at destinations, this speech act influences the system's factual beliefs about the destination. It also influences its beliefs about prices, because a destination change possibly entails a price change. Hence scope( (Inform u,s Dest(Paris) ) ) contains the topics destination, price, mas : destination and mas :price. The scope of a speech act determines which mental attitudes of an agent might be changed by this act. In the formalization of speech acts the illocutionary force determines a set of formula schemes (the preconditions and the effects of the act) instantiated by the propositional content. The scope of a speech act is the set of topics associated with this act, and must depend on its illocutionary force and its propositional content. Roughly speaking, the themes of a speech act are determined by its propositional content, and the context by its illocutionary force. Thus, contexts tell us which mental attitudes might change. We propose some axioms in order to compute the scope of a speech act. The performance of a speech act always influences some mental attitudes of the hearer. In particular:

104

Belief Dynamics

in

Cooperative Dialogues

competent at classes, a also influences s's factual beliefs about the class, i.e. mas : class E scope(a). We propose the following constraint for acts of the informative type.

If A contains no modal operator, a= ( lnform;,jA }, and t is a theme such that t E subject(A) n competence(;) then t E scope(a) and ma1: t E scope(a).

Axiom 14

3·4

Axioms for belief change

Our axioms for belief change are based on a given topic structure. The first one allows one to preserve beliefs: Axiom Schema of Belief Preservation

DoneaA

--t

A if

{ scope(a)

subject(A)= 0 and A contains no Done13 operator, for any (J. n

The restriction to formulas without Done13 operators is necessary because our reading of Done13 is that (J has just been performed (and not at some arbitrary time point in the past). The second axiom schema allows one to adopt beliefs� Axiom Schema of Belief Adoption

Bel;A ---> A if subject(A) � competence(;) The schema expresses that if agent i both believes that A and is competent at A, then A is true. For example the formula BelsBelu Dest (Paris) ---> Bels Dest(Paris) can be proved from the instance Belu Dest(Paris) Dest(Paris) of the belief --->

adoption axiom. Indeed, the belief adoption axiom applies because

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Note that if this axiom is violated, then the mental state of the hearer might become inconsistent: suppose mas : class ¢scope(a). Then Bels•Class( 2nd) would be preserved after a, while the indirect effect BelsBeluClass(2nd) of a would entail BelsClass(2nd) by the belief adoption ax1om. A given topic structure will allow us to compute the new state by means of two principles: belief adoption and preservation. In the next section we shall present these principles.

Andreas Herzig and Dominique Longin ros

subjed(Dest(Paris)) � competence( u ) , and we can then use the standard modal necessitation and K-principles for Bels. On the contrary, BeluPrice( So €) -> Price( So €) is not an instance of our axiom schema, because subject(Price( So €)) Cl competence( u ) .11

3. 5

Discussion

11

In our preceding approach (Farinas del Cerro

eta/. 1998)

we used non-contextualized topics to

formulate axioms for belief change. This turned out to be too weak. Suppose the system believes p.

and believes that the user believes p: Bel, p 1\ Bei,Bel. p. Now suppose the user informs the system that

he does not know whether p. Then the belief Bei,Bel. p should go away, while

Bel, p can

be expected

to be preserved. Hence the scope of this speech act should contain the system's attitudes towards the user's attitudes towards p. but not the system's attitudes towards p. We were not able to distinguish

that before. 12

Note also that this is the reason why we did not state, as is usually done

abbreviates p V language.

..., p.

'

for some p , and instead added T to the primitive operators

in 1\

textbooks

'T

and ..., of our

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Our subject function is not extensional: logically equivalent formulas may have different topics. In particular, subject( p V •p) =/= subject(T). Indeed, p V •p being an abbreviation of •( •p 1\ ••p) , we have subject( p V •p) = subject( p) =/= 0, while subject(T) = 0.12 It follows from our axioms that the subject of an arbitrary formula is completely determined by the subjects of its atomic formulas. This is representationally interesting, but it is certainly a debatable choice. Notwithstanding, the way we use the subject function is sound: suppose e.g. subject(p) = {t}, subject(q) = {t '}, and scope(a) = {t '}. Hence p and p 1\ ( q V -, q) do not have the same subject, and Done0 p -> p is an instance of the preservation axiom, while Done0( p 1\ (q V • q))-. ( p 1\ ( q V -, q) ) is not. But the latter formula can nevertheless be deduced from the former by standard modal logic principles: as p +--+ p 1\ ( q V -, q) we have Done0p +--+ Done0(p 1\ (q V-, q) ) . Hence the theorem Done0p-> p enables us to deduce Done0(p 1\ (q V • q) )-+ ( p 1\ (q V • q)). W e did not formulate such strong compositionality axioms for the scope function. The reason is that a speech act might influence more than the topics of its propositional contents. For example, the scope of (lnformu, sClass(rst)) contains not only mau: mas : class but also mau : mas : price. Our hypothesis here is that the scope of a speech act is determined by the subject of its propositional contents together with the integrity constraints (for example, linking destinations, classes, and prices). This is subject of ongoing research. Finally, as we have mentioned, competence can be generalised in order to involve an agent j believing i to be competent at some topic. Then

106 Belief Dynatnics in Cooperative Dialogues

our axiom

schema

would

take the

subject(A) � competence(}, i).

form Be�(Bel;A --t A)

if

4 THE MULT I MODAL FRAMEWORK 4· r

Axiomatics

Bel;A

( KBe1 )

Bel;A 1\ Bel;(A

(DBei)

Bel;A

---+

-.Bel;-.A

( 4Bel)

Bel;A

---+

Bel;Bel;A

(SBel)

-.Bel;A---+ Bel;-.Bel;A

---+

B)

---+

Bel;B

The rule schema of necessitation (RNBel) and the axiom schema (KBe1) are in every normal modal logic, (DBe i) is the 'axiom of rationality' (if i believes A then he does not believe -.A), (4Bei) is the axiom of positive introspection (if i believes A then he believes that he believes A), and (SBei) is the axiom of negative introspection (if i does not believe A then he believes that he does not believe A). With each operator of mutual belief we associate the normal modal logic KD45, whose logical axioms are similar to these of belief operators. We suppose that mutual belief of i and j implies belief of both i and j, i.e. we have the logical axiom (9) Bel;,J A---+ (Bel;A 1\ Be�A) To keep things simple we suppose that the logic of each operator of intention is the normal modal logic KD. (The inference rule (RNincend ) and the axioms (Kincend ) and (Dincend ) are just as (RNBel), (KBe1) , and (DBel).) Obviously, our notions of mutual belief and intention are oversimplified: first, our condition (9), linking belief and mutual belief, is weaker than usual, where mutual belief Bel;,JA is identified with the infinite formula

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In this section we give the logical axiom and inference rule schemas. They are those of a normal modal logic of the Sahlqvist type (Sahlqvist 1975), for which general completeness results exist. Just as in Cohen & Levesque (199ob), Perrault (1990), and Sadek (1991), with each belief operator we associate the (normal) modal logic KD45 (Halpern & Moses 1985). Thus we have the following schemas: A (RNBei)

Andreas Herzig and Dominique Longin 107

Bel;A 1\ Be�A 1\ Bel;Be�A 1\ Be�Bel;A 1\ . . . We argue that such an induc­

(RNDone)

•A

( KDone) (RNFeasible) (KFeasible)

•FeasibleaA ( •FeasibleaA

1\ FeasibleaB ) ---+ Feasiblea ( •A 1\ B )

For example, the first rule means 'it is never the case that inconsistent formulas hold before action o:'. We suppose speech acts to be deterministic: their performance should lead to a single state. This is expressed by the converse (DC) of the modal axiom (D).14 (DCDone)

Done0A ---+ •Donea•A

(DCFeasible)

FeasibleaA ---+ •Feasiblea•A

For example, the last axiom says that there is only one way of executing a (and not one where A holds afterwards, and another one where •A holds afterwards). The following conversion axioms (Van Benthem 1991) account for the interaction between the Donea and Feasiblea operators: (10) Feasiblea•DoneaA ---+ •A

( I I) Done0 •Feasible0A ---+ •A 13

However, one can define intention operators in a minimal models semantics a Ia Chellas (1980:

Ch. 7). This has heen undertaken in Herzig & Longin (zooob) & Herzig et al. (zooo). 14 We recall that Done0 and Feasib/e0 are modal operators of type 'possible' (and not 'necessary').

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tive construction is not necessary at least in a first approach: like, Cohen & Levesque, we suppose that mutual belief directly comes as the indirect effect of a speech act. (This is different e.g. from Perrault's view, where mutual belief is constructed via default rules. See Traum (1999, section 7.2.1) for a discussion of these issues.) Second, we offer no particular principle for intentions. We did this because the existing analyses of intention vary a lot, and the systems that have been put forward in the literature are rather complex. A normal modal logic for intention is too strong: for example, (Klncend) is not a theorem of Cohen & Levesque's logic (and neither is its converse).13 All Donea and Feasiblea operators obey the principles of the (normal) modal logic K. As they are modal operators of 'possible' type, the rule of necessitation and the K-axiom take the form:

ro8 Belief Dynamics in Cooperative Dialogues

The logic of the Always operator is the normal modal logic KT4· (KTime) and (4Time) are just as (KBe1) and (4Be!). (TTime ) AlwaysA --+ A The dual to Always is Sometimes:

(Defsometimes ) SometimesA � •Always•A In order to describe some interactions between the different mental attitudes (Cohen & Levesque 199ob), we propose the following logical a.xtoms. (12) Intend;A --+ Intend;Bel;A

(14) Bel;•lntend;A +-+ •lntend;A (15) Intend;Belj A --+ Bel;A V Intend;Bel;A (16) Bel;Done( FORCE ;, J A ) T

+-+

Done ( FORCE;, J A ) T

The semantics of each of these logical axioms is given in Longin (1999) and Herzig & Longin (2ooob). 4.2

Laws

Laws are non-logical axioms. We suppose that laws cannot be modified by the belief change process in a dialogue. We use the Always operator to preserve them in every state. We note laws the set of all laws (which might also be called our non-logical theory). There are three kinds of laws: static laws (alias domain laws, similar to integrity constraints in data bases); laws governing speech acts (to describe the different preconditions and effects of the speech acts); reactive laws (to describe some reactive behaviours generating intentioru). 4.2. 1 S tatic laws

Some of the static laws are believed only by the system, such as those relating destinations, classes, and ticket prices: (17) AlwaysBels(Dest(Paris) 1\ Class( 1St) ---+ Price(I so €) )

(1 8} AlwaysBel5(Dest(Paris) 1\ Class ( 2 nd) ---+ Price ( 10o € ) )

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( 13 ) Bel;Intend;A +-+ Intend;A

Andreas Herzig and Dominique Longin

109

Some static laws are known both by the system and the user. More precisely, they are mutual beliefs: (19) AlwaysBel;, j ' (Class(ISt) 1\ Class ( 2nd) ) (2o) AlwaysBel;, j ' ( Dest (Paris) 1\ Dest(New-York) ) (There is only one class for a particular ticket, etc.)

Following Sadek (2ooo), we associate with each speech act • • • •

a precondition; an indirect effect (the persistence of preconditions after the performance of the speech act); an intentional effect (in the Gricean sense (Grice 1967)); a perlocutionary effect (expected effect).

take the form AlwaysBelk •Donea •A' where A' is a precondition of a, and k an agent. Note that there is no constraint on k: k may be the speaker or some hearer (mutual belief ). For example the precondition of an informative act is:

Preconditions

AlwaysBelk •Done (lntorm ;.J A) --, (Bel;A 1\ •Bel;Be�•Bel;A 1\ where Belijj A is an abbreviation of Be�A V Be�•A. 1 5 (Preconditions and effects of our speech acts follow from (Sadek 1992, 2000).) The precondition means: •

• •

15

the agent i believes A; i doesn't believe that j believes that he doesn't believe A (sincerity condition);1 6 i doesn't believe that j knows if A holds or not; If we suppose that

p must be

either true or false (in the real world), and if Belljjp holds, then j

knows necessarily what is rrue in the real world (hut

Then, BelijjA is read

we do not

knows whether

p

is rrue or false).

'j knows if A is rrue or not'. In KD4 5, Be�BelijjA is equivalent to BelijjA. In (21),

we keep Be� Be/Ijj because the precondition is a simplification of an infinite conjunction in the original precondition (Sadek 2000). 16

The second term is an abbreviation of Sadek's infinite conjunction:

•Bel;Be�•Bel;A II •Bel;Be�Bel;•Bel;A II •Bel;Be�Bel; Beli •Bel;A II . . .

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4.2.2 Laws governing s peech acts

I Io •

Belief Dynamics in Cooperative Dialogues

i doesn't believe that j believes that j knows if A holds or not (condition of context relevance). 1 7

From this law and the standard principles of normal modal logics we can prove formulas of the form AlwaysBeh(Done01 T - Done01A1), where A' is a precondition of a. For informative acts we have:

AlwaysBe/k(Done( lntorm; , j A ) T

�

Done ( lntorm; , j A ) (Bel;A 1\

-.Bel;Be�·Bel;A 1\ •Bel;Bellj}A) ) Suppose the user informs the system he wants a first class ticket. Then we have:

The formulas 2 and 4 are what we call presuppositions: immediately after a speech act a its observers believe that the preconditions of a were true just before the performance of this act. As illustrated by 4, the speaker is also viewed as an observer of his act. In this case, presuppositions are part of his memory (he remembers what he believed just before the performance of the speech act). is the preservation of preconditions, and must be derived from presuppositions (c£ 2nd and 4th items in the above example) by formulas of the form AlwaysBeh(Done01A1 - A') where A' is a precondition of a: this will follow from our axiom schema of belief preservation (c£ section 3.4). 18

The indirect effect

is always accepted by the hearer and corresponds to the hearer's recognition of the speaker's intention (in Grice's sense).

The intentional effect 17

The second term is an abbreviation of Sadek's infinite conjunction:

•Bel;Be&BelljjA II •Bel;BeljBel;BelljjA II •Bel;Be&Bel;Be&BelljjA II . . . 18

While the presetvation of sincerity preconditions seems to be intuitively correct, it seems that the

presetvation of context relevance preconditions is an a priori choice of the agent, supposing that his

act failed. In Herzig & Longin (2ooob) we have proposed introducing a transient state of ignorance to

overcome that.

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I . Bel5Done ( lntorm , , ,class ( m) ) T (s believes the act has just been performed); 2. Bel5Done ( lntorm,,,Ciass (m) ) (BeluClass( 1St) 1\ •BeluBels •Belu Class( 1St) 1\ •BeluBel.ifsClass( 1st) ) (from 1, (22) with k = j = s, i = u, and principles of normal modal logics); 3· BeluDone( lntorm, ,Ciass( m)) T (u believes the act has just been performed); 4· BeluDone( lnform, ,,, Ciass ( m)) (Bel., Class( I st) 1\ •BeluBels •Belu Class( I st) 1\ •BeluBel.ifsClass( 1st) ) (from 3, (22) with k = i = u, J = s, and principles of normal modal logics).

Andreas Herzig and Dominique Longin I I I

The acceptance of this effect is expressed by formulas of the form a. For an informative speech act the instance of this schema is:

AlwaysBelk(Doneo. T _, A" ), where A " is the intentional effect of (23) AlwaysBelk(Done ( lnform; , j A ) T

--+

Intend;BeVntend;Be�A)

does not obtain systematically: our agents being autonomous, the expected effect of an act does not obtain system­ atically. Hence the propositional content is not necessarily added to the hearer's belief state. In the case where the new state (obtained by the admission of a speech act and the acceptance of its indirect and intentional effects) entails the perlocutionary effect, we say that the latter has been accepted.

The perlocutionary effect

The reactive laws allow us to generate some intentions:

(24) AlwaysBel;(A 1\ Be�..., A

--+

Intend;Be� A)

(25) AlwaysBel;(A 1\ Done ( lntorm j ,; A ) Bef; -,A --+ Intend;Be� Bel;A) (26) AlwaysBel;(Donea (Done1 T 1\ Bel;Done{3 T) --+

Intend;Be� Bel;DoneaDone1 T)

For example, (24) is used for the first part of the utterance s4 in our running example: the system invalidates the price of 8o€, and informs the user that the price is 100€. Formally: ·

r . Bels Price( r oo € )

2. 3· 4· 5· 6. 7·

BelsBeluPrice(8o €) Bels,u...., (Price( 100 € ) 1\ Price( So € ) ) Bels...., Price( 8o € ) IntendsBelu...., Price( 8o € ) BelsBelu...., Price( r oo € ) IntendsBeluPrice( roo € )

(hypothesis) (hypothesis) (static law) (by r and 3) (by (24), 4 and 2) (by 2 and 3) (by (24), r and 6)

(We didn't give the logical axioms we use; s and u are the agents i and j in the law (24), respectively.) The intentions in 5 and 7 are associated with a denying speech act (the price isn't 8o €) and an informative act (the price is roo €), respectively.

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4.2.3 Reactive laws

I I 2 Belief Dynamics in Cooperative Dialogues

5

EXAMPLE

We illustrate our analysis of the belief change process by means of our running example. To each utterance we associate a speech act (for example, au, corresponds to utterance u;). We describe parts of the different states Ss, during our example. These parts correspond to the mental state of the system after the different speech acts of the user. The set of themes is T = {class, destination, price, payment }. The speech acts are:

au, = (l nform u,sClass( I St)

/\

Dest(Paris ) )

au3 = (1 nform u,sPrice(8o €)) au, = ( Req l nfo rm l f u sPayment( crediLcard ) ) ,

.

The subjects of the atomic formulas are the predicate name, e.g. subjcct(Class( I st)) = {class}. The scopes of the speech acts are: • • •

•

au , SCOlJC au , SCOlJC au3 SCOlJC au, SCOlJC

= = = =

{mas {mas {mas {mas

: : : :

maut, mas : t, t I t E {class, destination, price}; maut, mas : t, t I t E {class, price}; mau : price}; mau : payment}.

The competence of the user and the system is: • •

comvctcncc( u ) = { mau : t I t E T} U {destination, class}; comvctcncc(s) = {mas : t I t E T} u { price,payment}.

We use the following abbreviations: • •

C1 and C2 are Class( I st) and Class(2 nd ), respectively; PI , P2 and P3 are Price( I so €) , Price(wo €) and Price(8o €), respectively;

We have simplified the preconditions of the speech acts.

au, has the following effects. I. performance of the act: EelsDonea. , T 2. presuppositions: EelsDonea. , (Eelu ( C1 1\ Dest(Paris ) ) 1\ •EeluEel!fs ( CI 1\ Dest (Paris ) ) ) 3. indirect effect: EelsEelu ( C I 1\ Dest (Paris) ) 1\ Eels•EeluEel!fs ( C1 1\ Dest(Paris ) ) 4· intentional effect: EeUntenduEelsintenduEels (CI 1\ Dest(Paris ) )

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au, = (lnform u,sClass(2 nd ) )

Andreas Herzig and Dominique Longin I I 3

S· reduction of intention:19 EeUntendu Eels(CI t\ Dest(Paris ) ) 6. adoption: Eels( C I t\ Dest( Paris ) ) 7· application of static laws: EelsPI au,

has the following effects.

au1 has the following effects.

I. performance of the act: EelsDone0" J T 2. memory: EelsDone0• 1 (Dest(Paris ) t\ C2 t\ P2 t\ Donea., (Dest(Paris ) t\ CI /\ PI t\ . . . ) t\ . . . ) 3· presuppositions: EelsDone0• 1 (Eelu P3 t\ •EeluEellfsP3 ) 4· indirect effect: EelsEeluP3 t\ Eels•EeluEellfsP3 S · intentional effect: EeUntendu EeUntendu EelsP3 6. reduction of intention: EeUntendu EelsP3 7· preservation: EelsEeluC2 t\ Eels •EeluEellfsC2 t\ EeUntendu EeUntendu EelsC2 t\ EelJntendu EelsC2 t\ Eels Eelu Dest (Paris) t\ EeUntendu Eels Intendu Eels Dest ( Paris ) t\ Ee/intenduEels Dest(Paris ) t\ Eels Dest(Paris ) t\ EelsC2 8. application of static laws: EelsP2 9· application of reactive laws: IntendsEelu •P3 t\ IntendsEelu P2 au. has the following effects. 1 . performance of the act: EelsDonea •• T 2. memory: EelsDonea • • (Dest(Paris ) t\ C2 t\ P2 t\ . . . ) 3· presuppositions: EelsDonea •• ( •Eellf,.Payment( crediLcard) t\ Eelu •lntendsDone(lnformlf,,.Payment(crediu:ard)) T ) 4· indirect effect: Eels •Eellf,.Payment( crediLcard) t\ EelsEelu •lntendsDone (lnformlf,.• Payment(crediu:ard)) T 19

This law is due to Sadek (1 992), and has been reformulated in Longin (1 999) � Bel;A where subject(A) = {maj : c : t l c E C, 1 E T}.

Bel;lntendjBel;A

as

follows:

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1. performance of the act: EelsDonea., T 2. memory: EelsDonea., (EelsCI t\ Eels Dest(Paris ) t\ . . . ) 3· presuppositions: EelsDonea., (EeluC2 t\ •EeluEellfsC2) 4· indirect effect: EelsEelu C2 t\ Eels •EeluEellfsC2 S· intentional effect: Eelslntendu EelslntenduEelsC2 6. reduction of intention: EeUntenduEelsC2 7· preservation: EelsEelu Dest(Paris ) t\ EeUntendu EeUntendu Eels Dest(Paris) t\ EelJntendu Eels Dest(Paris) t\ Eels Dest(Paris) 8. adoption: EelsC2 9· application of static laws: EelsP2

1 1 4 Belief Dynamics in Cooperative Dialogues

5. intentional effect: Bel5Intendu Bel5IntenduDone( I nform II ,,.Payment (credit-card}} T 6. reduction of intention: BelJntenduDone(lntormlt ,,.Payment(crediuard ) }T 7 · preservation: Dest ( Paris ) 1\ C2 1\ P2 1\ . . . 8. application of reactive laws: IntendsDone( intormlt,,.Payment (credit..card)} T

6 D I S CU S S I O N

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We have sketched a theory of change in the context of dialogues. Our framework is based on the notion of topic of information, which is exploited through topic-based axioms of belief adoption and preservation. We think that our concepts are natural and appealing. It is intuitively clear that these two mechanisms permit to implement all possible evolutions of belie£ The framework can be augmented by other concepts such as that of sincerity can be added. The latter could be implemented in a way similar to competence. Beyond the example dialogue given in the paper, we have tested our approach on a list of toy dialogues provided by France Telecom R&D Center. In our running example, the propositional contents of the speech acts is rather simple. However, in Sadek (1991) and Longin (1999) there have been defined laws permitting to treat more complex propositional contents. Note that in some applications it might be necessary to revise part of the competence of an agent. This happens in particular when it turns out that an agent has forgotten information he is competent at. Suppose for example, in u4 the user says 'Hum, finally I'll pay cash that first-class ticket'. If we do not modify the c oml)dence function this case is handled as if u changed his mind about the train class: as u is competent at classes, s starts to believe that he now wants a first-class ticket again. What is needed here is to dynamically modify the competence function during the dialogue. This is possible in our framework. (As competence is a parameter of our logic, it amounts to modifying the logic.) Perrault and Appelt & Konolige have argued that defaults are crucial elements in a theory of speech acts because they allow the transformation of absence of knowledge into knowledge. In a sense, what we do is to transfer that task to the metalinguistic relations of competence and scope. This permits to keep a monotonic framework, whose behaviour is considerably simpler and predictable than the nonmonotonic approaches of the literature. We note that a possible worlds semantics for our multimodal logic can

Andreas Herzig and Dominique Longin I I s

Acknowledgements This work has been supported by the France Telecom R&D Center, scientific area 'Intelligent Interactions and Dialogue', in the framework of contract 97 IB 046. Thanks to Renata Wassermann, David Sadek, and Jerome Lang for relevant discussions. The detailed comments and suggestions of an anonymous referee of Amstelogue'99 and of the reviewers of the present special issue have (hopefully) contributed to improve the paper both in form and contents. Received: o 1 .09. I 999

ANDREAS HERZIG and DOMINIQUE LONGIN

Institut de Recherche en Informatique de Toulouse {IRIT) Universite Paul Sabatier 1 18 Route de Narbonne, F-31062 Toulouse Cedex 4 France e-mail: Andreas.Herzig@iritfr, Dominique.Longin@iritfr http://www. iritfr/A CTIVITES/LILaC/

Final version received: 2 I .07.2ooo

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Journal ofSemantics

17: 1 1 9- 1 4 5

© Oxford University Press 2000

Permission to Change R OB E RT VAN R O OY University of Amsterdam

Abstract In this paper I discuss how to account for the performative effects of imperatives, and concentrate mainly on permission sentences. In the first part of the paper I argue that the performative effects of permission sentences should be accounted for in terms of a context change theory by making use of contraction defined in terms of an ordering relation, and show also how this ordering relation evolves from permission to permission. In the second sentences. I develop rwo ways to solve this problem. First, I suggest that this problem is due to the wrong way of accounting for contraction, and propose an alternative way in which contraction can be defined that accounts for the performative effects of conjunctive permissions in a more satisfactory way. Although the analysis is appealing, I will argue that we should account for the problem by means of a rype-shift analysis.

1 I NTRO D U C T I O N According to Austin's (1962) speech act analysis, by using sentences we perform certain linguistic acts. The traditional problem for speech act analyses was to find interesting types of speech acts, and to find necessary and sufficient conditions for the successful performance of the act. In later theories of context change the emphasis was on the essential effects of speech acts. In Stalnaker's (1978) classical analysis of assertions, for instance, the essential effect of an assertion is said to be the change it brings about in what is commonly assumed; the context that represents what is commonly assumed is incremented with the content of the assertion. More recently, the essential effects of other speech acts, like questions and denials, have been analyzed in terms of context change, too. The goal of this paper is to follow up some classical papers of Kamp and Lewis to characterize in a context change theory the essential effects of imperatives, normally stated in terms of command and permission sentences of the form You must/may do A. In sections 2 and 3 , I will discuss whether we can account for the performative effects of command/obligation and permission sentences by treating them assertorically, or whether we should treat them as explicit performatives. I will argue for the latter option. This gives rise to the question in what way command and permission sentences change the context. In the third section I will show how we can account for the

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part a problem for this analysis is discussed, i.e. the problem of conjunctive permission

1 20 Permission to Change

2 PERF ORMATIVE E FFECT I N TERMS O F ASSERT I O N

According to Austin's classical analysis of speech acts, sentences of the form You must/may do A are not used to describe a states of affairs. In terms of the language game between master and slave as described by Lewis (1970/79), they are typically used by one person, the master, to command or permit another person, the slave, to do certain things. How should we account for these so-called peiformative effects of the sentences used by the master? One proposal might be to say that command and permission sentences are assertorically used, but that the performative effect is accounted for in an indirect way, due to the fact that we learn, or realize, more about the world (Kamp 1979). One of the things one might learn about the world is what is demanded and permitted. A truth conditional analysis of what is demanded and permitted is given in deontic logic. Standard deontic logic (SDL) was based on the same principles as classical modal logic.1 Where normal modal logic has the operators 0 and <> standing for necessity and possibility, SDL has the two operators 0 and P, standing for ought or obliged and for permission, respectively. Just like D 1

There are other truth conditional analysis of deontic concepts, of course. The analyses of

Hansson (1990) and Meyer ( 1993) certainly belong to the most interesting ones. Other approaches

claim that to talk about deontic discourse, we should also take the notion of tense seriously. Although

these approaches all have something interesting to say, I will not discuss them here, but I should note that they go some (but not the whole) way in solving the problems we will discuss in this paper. For a discussion of a number of approaches towards the closely related analysis of bouletic concepts like 'desire' and 'intention', see van Rooy ( 1 999).

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change when we represent the prior information state by a preference order, and how in terms of this change we can predict most intuitions about coordination connectives and quantificational determiners. In section 4, I discuss the problem how imperatives determine the preference order of the posterior information state, relate the account of the third section with Veltman's analysis of defaults in update semantics, and with analyses of iterated revision. In the sections that follow it, I will concentrate on a particular problem for our analysis that was noted first by Merin (1992): the problem of conjunctive permissions. First, I will show how the standard analysis of contraction used for the analysis of permission sentences gives rise to this problem, and in the last two sections I will discuss some ways in which the problem can be solved when we give up the assumption that all that counts are the propositions that are expressed by the embedded clauses of permission sentences.

Robert Van Rooy 1 2 1

and 0 are duals of each other, also P is defined in terms of 0 as follows: P(A) 0 ( A ) for any proposition A. In model theory, we define O(A) to be true in w iff in all ideal worlds accessible from w, A is true, and P(A) to be true iff A is consistent with this set of all ideal worlds, i.e. if there is at least one ideal world accessible from w in which A is true.2 The set of ideal worlds in w will be denoted by P(w) , and is known as the permissibility set. According to the standard theories of context change for assertions (Stalnaker 1 978), the effect of the successful assertion that A is the case is that the context, K, which represents what is commonly assumed by the participants of the conversation, changes from K to { w E K I w makes A true} .3 Note that according to the truth conditional analysis used in SDL, what the agent is obliged and permitted to do is a fact about the world, represented by the world-dependence of the permissibility set. What is permitted in different worlds might be different; i.e. P(w) need not be the same as P( w ' ) for any two worlds w and w ' in K. If we now learn that John is permitted to make A true, we learn something about the world. As in standard context change theory this can be accounted for by eliminating those worlds from K whose permissibility set contains no A-worlds. Thus, if Upd(A, K ) denotes the update of information state K with A, we define Upd(P(A) , K ) as {w E K: P(w) n A :f: 0}. We might now propose that the performative effect of command and permission sentences is due to the fact that only after a command or permission sentence is used by the master, the slave knows that he is obliged/permitted to do something, and acts accordingly. This assertoric analysis seems appropriate for some uses of command and permission sentences, but there are serious problems for the analysis too. First, a truth conditional analysis of imperatives gives rise to the expectation that command and permission sentences can be iterated, or embedded into one another, which in fact seems impossible.4 Second, it is rather questionable whether the performative effect of all permission sentences should be accounted for in the epistemic way sketched above. Consider the following sentences: _

•

•

2 In this paper I will use capitals for both sentential clauses and the propositions expressed by them. I hope this will never lead to confusion. 3 If we forget about introspection, and consider only monotone updates. 4 I should note, though, that also the standard truth conditional analysis can account for the

intuition that the formula

0( O(A ) )

;

should mean the same as O(A ) j ust assume that the accessibility

relation is both transitive and dense. A deontic accessibility relation is dense if every deontic alternative is a deontic alternative to a deontic alternative.

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( 1) a. You may take an apple, b. You may take a pear, c. You may take an apple or take a pear.

1 22

Permission to Change

According to SDL, (1c) follows from both (1a) and (1b), and neither (1a) nor (1b) follows from (1c). Normally, however, if we make a disjunctive permission, both disjuncts are also permitted. The most straightforward way to account for this strong reading of disjunctive permissions would be to add the Free Choice Permission, FCP P(A V B) => P(A) 1\ P(B) as an axiom to the formal theory. Unfortunately, if we assume that FCP is a theorem of the logic, we can derive in our deontic logic that everything was allowed. Because in normal deontic logic we can derive O(A V B) from O(A), and because P(A V B) follows by our above definition of P from O(A V B), the assumption that FCP would be a theorem of deontic logic has the consequence that from O(A) we could derive P(B) for any A and B. But this has the unwanted result that by demanding or allowing something, you permit everything else. Suppose, for instance, that you are allowed to walk in the park, P(A). By logic, this means that you are also allowed to walk in the park or kill the king, P(A V B). If FCP were valid, this would mean that allowing you to walk in the park, also allows you to kill the king. Thus, already for logical reasons alone, our analysis should not obey disjunction elimination, i.e. FCP. But the assumption of disjunction elimination is empirically wrong, too. As Kamp ( 1 979) observed, there is nothing problematic with the assertion of the following permission sentence: =

We can conclude that we should not make FCP valid by stipulation. An assertoric analysis of permission sentences based on standard deontic logic indeed does not allow for disjunction elimination. It remains mysterious, however, how such an analysis can account for the fact that normally we conclude from a permission of a disjunction to the permission of its disjuncts.5 There is another phenomenon that the SDL-truth conditional analysis cannot explain. This is the fact that quantificational determiners are not interpreted in the same way in permission sentences on the one hand and in obligation/command sentences on the other. Note that permission sen­ tences obey existential weakening, i.e. we are allowed to infer (3b) from (3a): 5 But see Kamp (IQ7Q) for some proposals bv using Gricean conversational implicatures. and Merin (I 992) for a �ri,ti�ai discussion. For ; very in�eresti�g proposal that I came acros; only recently, see Higginbotham (I 99 I). He claims that by assuming that (i) or is shon for either/or, (ii) is scopally ambiguous, and (iii) that either is systematically ambiguous between a negative polariry item (an existential) and a 'free-choice' item (a universal), we can explain why disjunctive pennissions can be interpreted conjunctively within a truth conditional analysis. As he admits himself, however, such a truth conditional analysis leaves unresolved the problem why a disjunction under a deontic adjective of pennission gives rise to a conjunctive interpretation, while this need not be the case for a disjunction under the metaphysical adjective possible.

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(2) You may take an apple or a pear, but I don't know which.

Robert Van Rooy 1 2 3

(3) a. You may eat three apples. b. You may eat an apple.

3 THE PERFORMATIVE A NALYSIS OF I MPERATIVES The natural alternative to the assertoric analysis of obligation and permission sentences is the peiformative one. According to the performative analyses of Lewis (1970/79), Stalnaker (MS), and Kamp (1973), command and permission sentences are not primarily used to make true assertions about the world, but rather to change that what the slave is obliged/ permitted to do.6 With some feeling for Amsterdam rhetorics, we might say that according to the performative analysis, we know the meaning of an imperative sentence when we know how imperatives change permissibility sets.7 According to this Lewis/Kamp/Stalnaker account, if the master com­ mands John to do A by saying You must do A, or allows John to do A by saying You may do A, it is typically not yet the case that the proposition expressed by A is respectively a superset of, or consistent with, John's permissibility set, P.8 However, the performative effect of the command/ permission will be such that in the new context what is commanded is a superset of, and what is permitted is consistent with, the new permissibility set. Thus, in case the command or permission is not used vacuously, the permissibility set, P ' , of the new context will be different from P, so that the obligation/permission sentence will be satisfied. 6

Although

Lewis ( 1 970/79) and Kamp ( 1 973) account for

the effect of permission sentences in

rather different ways, both might be called performative analyses

in the sense

that their effect is to

change the permissibility set 7

8

c£ Tan & Van der Torre (1 997).

From now on I will assume in most of this paper that there is only one (global) permissibility set

around.

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Indeed, this is predicted by the standard truth conditional account, because permissions are predicted to be closed under logical implication. But what this account cannot predict is why quantifiers under the scope of may get the 'at most' reading, while in the scope of must they get the 'at least' reading. Intuitively, after (Ja) is said by the master, the slave is allowed to eat none, one, two, or three apples, but not more. But if the master says that you must eat three apples, it is still possible that you may eat more than three apples. On the standard truth conditional account, however, this cannot be explained, because quantifiers always get the same 'at least' interpretation.

I 24 Permission to Change

9

What if the new command is incompatible with one or more of the earlier ones? In that case

we might make use of change by revision to be discussed below. 1 0 A relation R is reflexive if for all w: R( w, w) , it is transitive if for all w, v and u ,

u:

if R( w, v) and

then R(w, u ) , and it is connected if for all w and v, R(w, v) or R(v, w) or w = v. 1 1 Van Fraassen ( 197 3) and Kratzer ( 1981) use a different way to determine the preference relation. They say that u �o v iff {A E Ol v E A} � {A E O l u E A}. In this way, �0 determines a partial ordering, but not a total one. Not all worlds have to be connected with each other.

R(v,

)

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But if knowing the meaning of an imperative means that you have to know how the imperative changes the permissibility set, our problem is to say how command and permission sentences govern the change from the prior permissibility set, P, to the posterior one, P ' . For commands this problem seems to have an easy solution. If the command You must do A is given by the master, the new, or posterior, set of permissible futures for John, P ' , is simply P n A.9 However, things are more complicated for permission sentences. It is clear that if A is allowed, P ' should be a superset of P such that P ' n A =/= 0. It is not clear, however, which A -worlds should be added to P. Obviously, we cannot simply say that P ' = P U A. By that suggestion, an allowance for A would allow everything compatible with A, which is certainly not what we want. But how then should the change from P to P ' be determined if a permission is made? This is Lewis's problem about permissions. Stalnaker (MS) suggested that Lewis's problem about permissions can be solved when we know not only what the best, or ideal, worlds are, but also assume that some of the non-ideal worlds are better than others. Thus, to account for the performative effects of commands and permissions, we need not only a set of ideal worlds, but rather a whole preference, or reprehensibility, ordering, ::;, on the set of all possible worlds. On the interpretation that u ::; v iff v is at least as reprehensible as u, it is natural to assume that this relation should be reflexive, transitive, and connected.10 We might assume a primitive preference relation among worlds, but we can also follow Harper (I 976) and determine an ordering relation on worlds by looking at the number of obligatory propositions that worlds make true. Van Fraassen (1973) and Kratzer (1981) have argued that to account for moral deliberation we should not rule out the possibility that the command-sentences that determine what should be done might be mutually inconsistent. Let 0 be the set of propositions that John is obliged to make true. Then we say that u is at least as desirable as v with respect to 0, u ::;0 v, iff the set of commands in 0 that v makes true, I {A E Ol v E A } 1. is smaller than or equal to the set of commands in 0 that u makes true, I {A E Ol u E A} I, where I S I is the cardinality of S.1 1 In terms of this preference order on possible worlds, we can determine the set of worlds that make as much as possible commands true; the minimal

Robert Van Rooy 1 2 5

elements of the relation :::; 0. Thus, if we call this set of minimal elements P, P can be defmed as follows: def

def

{ u E A I \fv E A: u :::; v} It turns out that our revision function ' * ' will satisfy the following constraints on minimal change for any set of worlds K (c£ Harper 1975), so in particular for P: (K* 1 ) For any proposition A, K� � A (K*2) If A =/= 0, then K� =/= 0 (K* 3 ) If K n A =/= 0, then K� K n A (K*4) If K� n B =/= 0, then K� 11 8 = K� n B

P�

=

The first condition demands that the new state should contain the new information. The second requires that changing with new consistent information results in a new consistent information state. The third and fourth condition demand that the change is conservative; if A is consistent with K, K� is simply K to which A is added, and if B is consistent with K�, then receiving the information B after the information that A has the same 12 13

Note that if the propositions in 0 are mutually consistent, P is just n 0. For instance, A is obligatory iff P � A. Notice that in terms of our preference order we also

might go for various other analyses of obligation. Just to mention one, we could say that the slave is

obliged to make A true iff V(v, w) E ::;: : if w E A ,

then

v E A. Notice that this analysis of

obligation, unlike the standard one, does not predict that obligations are closed under logical implication.

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{ v E w I \fu : v :::; 0 u f2 In terms of this set of ideal worlds we can, as before, determine of course whether according to the present state A is obliged or permitted.13 But this ordering relation contains more information than just what the set P of ideal worlds is, and in terms of this extra information we can determine the new permissibility set P'. If the master permits the slave to make A true, we can assume that P contains no A -worlds, i.e. none of the A -worlds is ideal. But some A -worlds are still better than other A -worlds. Stalnaker proposes that the effect of allowing A is that the best A -worlds are added to the old permissibility set to figure as the new permissibility set. In modern terminology (c£ Gardenfors 1 988), we might say that the change from P to P' due to a permission sentence is accounted for in terms of contraction, the rational retracting of information from an earlier informa­ tion state, where contraction is governed by a reprehensibility ordering :::; 0 , which I will denote by :::; from now on. I will define contraction in terms of revision, and the revision of P by any proposition A can be defined in terms of the relation :::; as follows: p

!26 Permission to Change

Upd(Must(}ohn, A) , P) = P n A P�A = P U P� Note first that if change by permission is governed by the reprehensibility ordering, the absence of the 'at least' interpretation of the quantificational determiners used in the embedded sentences is immediately explained. If according to the prior state John was not even allowed to take one single apple, one might assume that worlds where he takes only one apple are 'closer' to the worlds in P, than worlds where he takes more. So, after the permission that he may take an apple, the new permission set, P', can be expected to contain only worlds where he takes at most one apple.17 Note that by our analysis it is also predicted that the quantificational determiners in command sentences get the usual 'at least' reading, just as desired. Thus, our performative analysis of command and permission sentences can predict and explain certain intuitions about the behavior of quantificational determiners which the standard truth conditional, or assertoric, analysis cannot. Note that according to our performative account it does not follow that for a permission sentence of the form You may do A or B the slave can infer Upd(May(}ohn, A) , P)

14

=

Alchour6n, Gardenfors, & Makinson

(r985). See Gaardenfors (1988) for a general overview of

theories of belief revision. 1 5 By representing information states as sets of possible worlds, the contraction come down to rhe following (K- 1 ) - (K-G):

8

AGM-postulates for

(r t )K <;; K.4 , (r 2)K � A '* KA" = K, (r3)k f T '* K.4 � A. (r 4 )K <;; A '* KA" n A <;; K, (r s )K.411 8 <;; KA" U KiJ, (K-6)K.411 8 � A '* KA" <;; K.411 8.

16 This analysis of permission sentences, and thus of contraction, was assumed by Kamp and Merin (1992) in their discussions of the performative analysis of permissions.

(1979)

17 Rohrbaugh (1996) wrongly claimed that the possible world framework as such always predicts the at least readings for quantified permission sentences like (3a) and (3 b).

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effect as receiving the information A and B together. These rules are the analogues of the familiar AGM-postulates for revision, 14 when it is assumed that information states and propositions are modeled by sets of possible worlds. If we now define the contraction of K by A, KA, via the Harper identity as K U K� A ' it follows that also the usual AGM-postulates for contraction will be satisfied.15 To implement Stalnaker's suggestion, we can say that the change induced by the permission You may do A is that the new permission set, P', results from P by contracting •A: P' = P�A , which is P U P� .16 Thus, according to this proposal, command and permission sentences change a context of interpretation as follows (where I assume that John is the relevant agent, and P his permission state):

Robert Van Rooy

1 27

=

20

18

The epistemic variant of this ordering relation between propositions is called the epistemic entrenchment relation. 19 Where A -< B iff A ::$ B, but not B ::$ A. 20 But this doesn't always seem to be the case; as noted by Kamp {I 97J), even for the performative analysis of permission sentences the arbitrarily interpretation can be cancelled: You may pick a flower, but don't pick a rose, or You may do A or B, but don't do the dangerous one. However, as mentioned by Kamp (I 979), and stressed by Zimmermann {I 999). for epistemic uses of may, it seems that the choice effect cannot be cancelled. That is, it seems that from (i) John might be in Amsterdam or in Utrecht we can derive both (ii)john might be in Amsterdam, and (iii)john might be in Utrecht, and we cannot follow (i) by saying but Iforget which. These facts are difficult to explain when a truth-conditional analysis of disjunction is assumed together with any treatment where epistemic might is analyzed as a consistency check such as in Veltman (I 997). But now suppose that epistemic might is rypically used to bring certain possibilities to the attention of the audience, as was considered by Kamp ( I 979: 28 I ). In that case, it seems not unreasonable to analyze epistemic might in similar ways as we analyze permission sentences in this paper, i.e. by means of contraction of an information state. Thus, might(A) analyzed with respect to epistemic state K does not check whether A is consistent with K, but rather adds to K worlds that make A true. This does not yet guarantee a choice reading of a sentence like Might(A V B), but it does when we assume that K is not yet consistent with A V B, and that our disjunctive epistemic sentence can only be appropriately uttered when •A and •B are equally strong entrenched in K. It is perhaps asking a lot to assume that A V B is inconsistent with what is implicitly presupposed, but we can also imagine a model where K represents what is explicitly presupposed, i.e. where it represents that part of the common ground of which all participants are fully aware.

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that according to the new permissibility set he is allowed to do any of the disjuncts, nor is the arbitrary interpretation of indefinites guaranteed. Still, the performative analysis can give an explanation why indefinites and disjuncts are normally interpreted in this 'free-choice' way. To do this, let me first define a deontic preference relation between propositions in terms of our reprehensibility relation between worlds, :::; . We can say that although both A and B are incompatible with the set of ideal worlds, A is still deontically preferred to B, A ::5 B, iff the best A -worlds are closer to the ideal worlds than the best B-worlds, 3v E A and Vu E B : v :::; u.18 Then we can say that with respect to :::; , A and B are equally strongly reprehensible, A � B, iff A ::5 B and B ::5 A. Because we defmed contraction via the Harper identity in terms of revision, and because any revision function that obeys (K* r ) - (K* 4) satisfies the following factoring condition: K� v B = K� if A -< B,19 K� v B = K� if B -< A, and K� v B K� U K� if A � B, we can now explain why normally disjunction elimination is allowed for permission sentences. For simple disjunctive permission sentences like You may do A or B, it is not unreasonable to assume that by Gricean, or strategic, reasoning we can conclude (perhaps after accommodation) that when performatively used the master has no strict preference for the one above the other. This does not mean that this reasoning can be accounted for in a straightforward way. It would be nice to explain the strong reading completely in terms of conversational implicatures. Kamp (1 979) shows, however, that by the way conversational implicatures are normally

128

Permission to Change

understood, as inferences that take as one of their arguments the proposition expressed by sentences, these implicatures can be of no help to explain the strong reading of disjunctive permissions. The problem is that these strong readings should also be predicted in case disjunctive permissions are embedded in larger sentences such that the proposition expressed by this larger sentence does not entail the proposition expressed by the embedded disjunctive permission sentence. The following example is g1ven: (4) Usually you may only take an apple. So if you may take an apple or take a pear, you should bloody well be pleased.

21

Zimmermann (1999) has recently argued that this condition does not count as an appro­ priateness condition for disjunction, but is part of the semantic meaning. 22 This is exactly what Stalnaker (1975) proposes to be the acceptability conditions for disjunctive sentences. 23 Notice that according to this entailment relation we do not predict that we can infer May(A V B) from May(A ) , and thus that Ross's paradox does not arise. 24 See also Stalnaker (1975) for his notion of reasonable inference.

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To account for the strong reading of performatively used disjunctive permissions it seems that we have to build the implicature into the meaning of or, that is, we have to assume that the relevant implicature is not a conversational one, but a conventional one instead. But then, how should we account for this conventional implicature? We might propose that disjunctions of the form P V Q can only be appropriately interpreted in contexts K such that P n •Q n K; v Q =I= 0 and -,p n Q n K; v Q =I= 0.21 As a result, it is predicted that a normal sentence of the form A or B can only be appropriately asserted in a context K that is compatible with both A 1\ •B and •A 1\ B/2 and that a permission sentence like You may do A or B can only be said appropriately by the master to John iff he is indi.fforent between A and B, A � B. Kamp (1973) argued that just as we can define an inference relation between propositions, we might also define an inference relation between performatively used permission sentences, which he called 'p-entailment'. In terms of our framework, he proposes that permission sentence May(B) is p-entailed by permission sentence May(A), iff for every appropriate initial permissibility ordering �. no new worlds would be added to the set of ideal worlds through the use of May(B) after the initial permissibility set was 'updated' through the use of May(A). On the assumption that � can only be an appropriate initial permissibility ordering for the performatively used May(A V B) iff A � B, we can conclude that both (�a) and (1b) are p-entailed by (1c)?3 Some readers will see that Kamp's notion of p-entailment is rather close to Veltman's (1996) fixed-point notion of entailment between speech acts.24

Robert Van Rooy 1 29 4

C HAN G I N G PRE FERE NCES

Veltman's update semantics can be used to account for the performative effect of normal commands or obligations, but it also seems to be the natural framework to account for conditional obligations like Ifjesse robbed the bank, he ought to confess. In the standard analyses of Hansson ( 1 969), Lewis (1973), Spohn (197 5), and Kratzer (1978), conditional obligations are treated solely in terms of our ordering relation �. Just like a standard obligation to do A is satisfied in the traditional truth-conditional analysis when the best worlds according to � are all A-worlds, they say that an obligation to do A on the condition that C is satisfied when the best C-worlds according to the ordering relation are all A -worlds. Notice that the analyses of conditional obligations by the above authors are all static; they only say when a conditional obligation is true, not what the performative effect is of the use of a conditional obligation sentence. Fortunately, this performative effect can be easily accounted for in terms of the framework Veltman (1996) uses for the analysis of rules of exception. To account for rules of exception in update semantics, Veltman no longer represents an information state by a pair like (K, �), where � orders the worlds in W (and thus in K), but rather by a pair like (K, 1r) , where is a 1r

25

This use of Veltman's update semantics for the analysis of commands

Tan & Van der Torre ( 1 997).

was

actually proposed by

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Lewis (1979) complained that an account in terms of reprehensibility­ gradings of worlds might handle single cases of permissions, but leaves undetermined how the comparative permissibility relation evolves from permission to permission. Actually, the problem exists already for the case of commands. But here the problem can be solved almost straightforwardly in a way made familiar to us by the analysis of defaults in update semantics by Veltman {1996). According to one version ofVeltman's system, an information state, (K, � ) . consists of two parts: (i) a set of possible worlds, K, which represents the factual knowledge we assume, and (ii) our reflexive and transitive ordering relation, �. on worlds. Until now we have assumed that for the analysis of the command You must do A we only need to look at the best worlds according to �. and we only gave a partial description of the resulting state; we only defined what the best worlds are in the new information state, not what the whole new ordering relation will be. But given Veltman's analysis of 'normally', it is quite straightforward to say how the new ordering relation after the update with the command should look like: Upd (Must (A ) , (K , � ) ) = (K, { (v, w) E � I if w E A, then v E A})25

1 30 Permission to Change

function taking as argument a proposition, A, and has as value an ordering relation �A restricted to the A -worlds. On the assumption that conditional obligations state rules of exception, the natural thing to say is that the information state (K, 1r) accepts the conditional obligation 'Must(B), if A' iff the best worlds according to the ordering relation 1r(A) are all B-worlds. Now we can also account for the performative effect of conditional obligations as follows: =

Upd( (ifA , Must(B) ) , (K, 1r) ) (K, 1r') , where 7r' is such that (i) VC =/= A : 1r1( C) 1r( C) , and (ii) 1r1(A) { (v, w) E 1r (A ) I if w E B, then v E B} =

=

26 Notice that in this way we treat the conditional connective and the obligation operator in IfA, then Must(B) separately. Something like this was first proposed, as far as I know, by Mott (1 973), and defended recently also by Frank (1997).

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Although this analysis of conditional obligations is somewhat different from the traditional Hansson/Lewis/Spohn/Kratzer one, it shares with it an unwanted consequence. Note that both according to the traditional approach, and according to the analysis above, it is predicted that conditional obligations of the form If A, then Must(A) should be tautologically true. But that does not seem to be the case; the conditional obligation If you rob banks, you should rob banks is not trivially acceptable. Hansson (1969) already noted this prediction, but argued (somewhat mysteriously) that it is not really problematic. Spohn (1975) was not so confident about this anymore, and, in a more recent discussion, Frank (1997) argued that this prediction shows that the traditional analysis of conditional obligations must be on the wrong track. If the traditional analysis of conditional obligations must be rejected because of the predicted validity of sentences of the form If A, then Must(A) , our analysis of conditional obligations must be rejected, too. But in distinction with the traditional approach towards conditional obligations, we can easily change the formal analysis such that the problematic prediction disappears. Note that in the above analysis we have assumed, just like Veltman (1996) did for the analysis of default rules, that the ordering relation 1r(A) only orders the A -worlds. This has the result that the best worlds in 1r(A) are by necessity all A -worlds. But, as we just saw, this is exactly what gives rise to the unwanted prediction that If A, then Must(A) must always be accepted. This suggests that our problem can simply be solved if we give up the assumption that for any A, 1r(A) only orders the worlds in A; we simply assume that for all A, 1r(A ) orders the set of all worlds, W.26 This doesn't mean that thus the condition has no effect anymore; it still might be the case that for different propositions A and B,

Roben Van Rooy

131

z7

For another, and perhaps more popular, analysis of iterated revision, see Spohn ( 1 987).

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the best worlds according to rr(A) are different from the best worlds according to rr(B) . Then we might say that for the analysis of some conditional obligations we should only consider worlds that satisfy the antecedent, while for others we should not restrict the ordering relation in such a way. We have seen that in terms of Veltman's update semantics we can determine not only how the set of best worlds evolves through the making of a (conditional) command, but even how the (set of) ordering relation(s) change(s). Although this is a stimulating result, it is still not clear how the ordering relation should evolve through the use of a permission sentence. The reason behind it is that the above analysis of the performative effects of (conditional) obligation sentences is essentially eliminative; through these sentences certain elements of the ordering relation that help to represent the information state are thrown away. The problem with permission sentences is that it does not seem to be possible to account for their performative effect in an eliminative way. It follows that we need an account that determines what the ordering relation looks like in the posterior information state, even if the change cannot be accounted for by eliminating possibilities. Notice that the problem we face is similar to the problem how to account for iterated belief revision. According to the standard analyses of belief revision, a prior information state is represented by an ordering relation like our �- If we revise this state with A, it is said that the posterior information state will be the set of best A-worlds according to �- But notice the difference in kind between prior and posterior information states; prior information states are ordering relations, while posterior information states are just sets of worlds. Because of this difference, the traditional approaches of revision can only account for so-called 'one-shot' revisions, but leave undetermined how iterated revisions should be accounted for. But this means that Lewis's problem as stated in the beginning of this section can still not be solved. Meanwhile, however, there are several accounts of iterated revision around that can represent a posterior information state as an ordering relation, too. Using any of those approaches towards iterated revision, we could analyze permission sentences as functions from one comparative permissibility relation to another. In the remainder of this section we will show how Lewis's problem can be solved when we make use of the first analysis of iterated revision due to Harper ( I 976).27 Suppose that P is a set of possible worlds denoting a permission set. Then it seems reasonable to assume with Harper that only propositions decided by

1 3 2 Permission to Change

P determine the ordering relation in terms of which revisions of P should be defined. If we assume that S is an arbitrary set of propositions, and x and u are worlds, we can define the set of P-decided propositions in S on which X and u differ, s:P, as follows: s:P = {A E S: (P � A or P � •A) and ( (x E A &

u

� A ) or ( x � A &

u

E A )) }

28 The simplest way is to let this set of designated propositions be the set of atomic propositions, but one might also take any other set of arbitrary subsets of W. See Harper (1976) for details. 29

This set is contextually determined, and stays constant

and slave.

during the 'discourse' between master

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Now we define a relational measure of reprehensibility based on the assumption that only the propositions that are decided by P determine this measure. How is that done? We can say that v is at least as reprehensible as u, iff for any world w in P, the cardinality of the P-decided designated propositions on which u differs from w is less than or equal to the cardinality of the P-decided designated propositions on which v differs from w. More formally, we can define relative reprehensibility in the following way: u �P v iff I Suwpl is smaller than or equal to I SvwPj, for any w E P, where S is the set of designated propositions that potentially determine reprehensibility.28 From this definition it follows that the ordering relation �P is reflexive, transitive, and connected. In terms of this ordering relation we can define the revision of P by A, P�, as usual: P� � { u E A I Vv E A: u �P v}. Because the ordering relation is reflexive, transitive and connected, it should' be clear that the revision function satisfies (K * I ) - (K * 4 ) , just like the revision function we defined in the previous section. Thus, given a set, S, of propositions that potentially determine reprehensibility, 29 we can determine for each permissibility set P a corresponding ordering relation �P that determines the result of the revision of P by A. In the previous section we have determined the change of the permissibility set due to a given permission in terms of contraction. This contraction, in turn, was defined in terms of revision, and thus indirectly in terms of the ordering relation. But this means that we can determine, via Harper's method, not only how the permissibility set changes due to a permission, but also how the reprehensibility relation evolves from permission to permission, and thus solving Lewis's problem as stated in the beginning of this section.

Robert Van Rooy 1 3 3

s

C O NJUNCTIVE PERM I S S I O N SENTE NCES

=

30 This problem was not discussed by Kamp, although in Kamp (1973) he did discuss the closely related problem of accounting for permissions like You may take {any flower/every flower/all flowers] growing in the garden. Because I take this latter problem to be similar to the one to be discussed in this paper, I will not deal with such permissions separately. 31 To a great extend, the problem is due to the validity of the recovery-postulate for standard contraction. Let me explain: By defining contraction in terms of revision by means of the Harper identity, it follows that if K <;; A, K;i n A K, i.e. after contracting K with A, you can recover the original state K by learning A. In particular, this means that P�(A I\ B) n ..,(A 1\ B) P. For the analysis of conjunctive permission sentences, standard contraction does normally not add enough worlds to the prior information state, because it seems that we want it to be the case that normally after contracting P with -,(A 1\ B) we need not come back to our original state P when it is commanded that ..,(A 1\ B). =

=

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In the discussion of Kamp (1979) the main concern was to account for the problematic disjunctive permission sentences. The above discussed analysis in terms of contraction goes a long way in solving this problem. But as noticed by Merin (1992), this analysis also gives rise to a new problem: the problem of how to account for the performative effect of the use of conjunctive permission sentences.30 In the original Stalnaker account it is predicted that a conjunctive permission sentence You may take an apple and a pear has semantically the package deal effect: take either none or both. The reason is that P� 1\ B is a subset of the proposition expressed by A 1\ B, and thus that the only worlds in P�(A I\ B) (which is P U P� I\ B) where either A or B are true, are worlds where both are true, if P n (A V B) 0.31 For some conjunctive permissions this is exactly what we want; in some circumstances my conjunctive permission You may take an apple and a pear is paraphrasable as You may take an apple provided that you also take a pear, and vice versa. In these circumstances the conjunctive permission can be thought of as a (bi)conditional offer. Some conjunctive permission sentences are indeed naturally interpreted as conditional offers; if I say You may take that car and payfor it, for instance, I only allow you to take that car provided that you pay for it. Something similar holds when his mother tells John You may give a party and clean the house afterwards. But, as argued by Merin { 1992), the 'package deal' interpretation is empirically a rare special case, and usually requires that one of the conjuncts be interpreted as a countervailing demand. Indeed, for the majority of the conjunctive permission sentences this package-deal prediction is empirically wrong, since these other conjunctive permissions allow also for the conjuncts to be done separately. That is, the prediction conflicts with the intuition that conjunctive permissions normally permit free choice among four options: both conjuncts, the first, the second, or either conjunct. If I say, for example, You may take an apple and take a pear, or You may walk and talk, you normally do not have to

1 3 4 Permission to Change

=

Notice that for any propositions A and B such that A � B it will be the case that B :S A. Because both A and B follow from A 1\ B, it is predicted that if it is allowed that A 1\ B, also A and B alone are allowed, which seems just what we wanted. Now it appears as if our new analysis goes wrong exactly where the original Stalnakerian analysis makes the correct predictions. Suppose that his mother allows John to give a party and clean the house afterwards. Allowing John to give a party and clean, A 1\ B, entails according to our analysis allowing John to give a party, A. But, then, his mother does not allow John simply to give a party, but only if he cleans afterwards. Fortunately, our analysis immediately accounts for this apparent problem. If his mother allows John to give a party, only the 'best' party-worlds are added to the set according to the reprehensibility ordering. It is natural to assume that in the given circumstances the best party-worlds (according to his mother) are only worlds where John gives a party and cleans the house 32 What I will give up, however, is that the only thing that counts is the propositional content detennined by the embedded clause of the permission sentence. In this sense I agree with Gazdar (I 98 I) and others that for different speech act types, different types of denotations might be involved. Remember that according to almost any modern analysis of questions, for instance, the denotations involved are not simply propositions. 33 Because for any A, it will always be the case that T ::S A, and that for any P, P-TP we do not have to defme the resulting state in terms of the revised state united with the original state anymore. =

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fear my punishment if you only take an apple, or only walk, respectively. Merin (1992) concludes that we should thus give up the analysis of permission sentences in terms of reprehensibility orderings, and that permission sentences stand in the way of Boolean and other lattice­ theoretic semantics. In the rest of this paper I will take up the challenge to improve on the Stalnaker analysis, without giving up the assumption that the performative effect of permissions should be accounted for in terms of contraction.32 Can we get rid of the package-deal effect, and still analyze the effects of permissions in terms of contraction? And can we do this without even giving up a Boolean, or latice-theoretic, analysis of what is denoted by the embedded clause? At first appearance there seems to be an easy solution, based on a very simple intuition. Normally if the master allows you to do something, you can count on it that it is the 'worst' �hing for him that he allows you to do. This seems to mean that when he allows you to do A, he also allows you anything that is less bad for him; i.e. he implicitly also allows you to make true any proposition B such that B j A. This suggests that we should analyze permission sentences in the following way: Upd(May(]ohn, A) , P) U {P;I B j AP 3

Robert Van Rooy 1 3 5

Upd(May(}ohn, A) , P)

=

U {P=;B IB � A & A f-t B}

' f-t '

is some kind of relevant entailment relation. Notice that by our where reasoning above it holds that when our relevant entailment relation is stronger than the classical entailment relation, the analysis comes down to the following: Upd(May(]ohn, A), P) U {P�B I A f-t BP6 =

Our problem now seems to come down to finding a suitable entailment34 Notice that if we defined the contraction of P by -.A by U {P; I B j A}, this contraction function would satisfy all AGM-posulates for contraction, except for {K - 4 ) , the one responsible for recovery. From this observation, and the fact that the contraction function that we will actually use for the analysis of permission sentences in this section will be 'stronger' than this contraction function, it follows that also our contraction function to be defmed below will satisfy all these AGM­ postulates for contractiolL 35 For a nice discussion of the need for 'relevance contraction', see Canrwell ( 1 999). His proposed analysis for relevant contraction is, however, different from mine, and will not help with our problem to account for conjunctive permission sentences. 36 Where P�8 is P U P; , as before. In the informal discussion in the main text, I did not call this function the actual contraction function anymore, but rather meant with the contraction from P with ...., A the whole set U {P�8 I A >--> B}. It is perhaps good to note that if '>--> ' is stronger than

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afterwards. Thus, no world is added where he gives a party and does not clean, which shows that the apparent problem is not a real one. However, the above suggested solution must be given up for another reason. It wrongly predicts that after the allowance ofA 1\ B, not only A and B are allowed, but also everything else that is less reprehensible than A 1\ B, such as (A 1\ B) V C. Thus, if a proposition C that is not allowed in the prior context and is totally unrelated to A, but less reprehensible than A, the above interpretation rule would have the unwanted effect that the allowance of A also allows the agent to do C. We have seen that by analyzing permission sentences in terms of the standard contraction function, not enough worlds are added to the permissibility set after the permission to do A 1\ B, while analyzing permission sentences in terms of our second contraction function would have the result that too much worlds are added. If we want to analyze permission sentences in terms of contraction, it seems that we need to define contraction such that the result of contracting P by •A is somewhere in between P U P� and U {P; I B � A}.34 What seems to be missing is a notion of relevance, i.e. if we are allowed to do A, not all worlds are allowed that are at least as good as the best A -worlds, but only the B-worlds that are at least as good as the best A-worlds for any proposition B that is relevantly entailed by A.35 Thus, it seems we should analyze permission sentences as follows:

r 36

Permission to Change

relation that does the job. We have seen already that the ordinary entailment-relation is too weak. Is there any stronger notion of entailment around that does our job? Given our informal talk about 'relevance', it seems that we should take a look at Anderson & Belnap's (1962) relevance logic. But that would be wrong, for their relevance logic, just like classical logic, predicts that for any propositions A and B it follows that A entails A V B. We have seen already that this has the unwanted result that allowing A might allow the slave also to do C, for a C that is totally unrelated with A. Still there exists a semantics for the logic of tautological entailment that suggests a way to define our sought after inference relation ·�·.

Until now we have assumed that propositions are the basic building blocks of meaning, and that 'and' and 'or' should always be treated as intersection and union, respectively. Others have been more radical, and proposed that we should look at different kinds of primitives. A motivation for us might be that it seems that permission sentences take mainly eventive clauses as complements that are denoted by to-infinitives (c£ Rohrbaugh (1996) and Portner (1997)). Rohrbaugh argued, for instance, that for the analysis of permission sentences we need something like situation semantics, because we need a notion similar to, although not identical with, Kratzer's (1989) notion of lumping. He does not, however, give a formal definition of such a notion, but I will show how this can be done. Proponents of this more radical solution typically take situations, facts, or events as primitives. Let us therefore look at one of the earliest analyses of such entities: van Fraassen's (1969) analysis of events or facts to give a semantics for the above-mentioned 'tautological entailment' relation. Let us assume that an event-type is a set of events, and that an event itself is a set of urelements. We will say that each eventive clause will denote an event-type. The model determines, as always, which event-type is denoted by atomic eventive clauses, and we might, but need not, assume that atomic eventive clauses denote sets that contain only one set of urelements. Let us ,..a,.., m � Jcp thP � 11(:<:Pl 1 1 'l n "l<:<:nrnnt"1nn th "l t urirh P..-.rh "l tnt"'n ; r sP.nt-P.nrP. .r + associate the 'urelements' p J (p) and p = r ( p ) , whose occurrence in a world would make p minimally true and false, respectively. Defining I;t (p) to be { {p}}, if p holds in w, and 0 otherwise, and something _,...-.........._

.....-.........

.._ .,. _._....., ..,... ..,.... ...,........ ._

r ._.a._.a..o.

.....v... _......_...

._....IW.. ._

w w .a. ....&..&.

.._. ......_. . .......

IU.'-'toJ.&..a..&..&.....

'lv.&.l.'-'-'.1..1.........

..,

,.,TP. YV 'Iv

'-'

.1..1.

=

entailment, it still holds that U { P�8 J A t-> B} n A P;. Thus, even if the contraction function does not satisfy the recovery postulate, the revision with A is still equal to adding A to the contraction of •A (known as the Levi-identity in the belief revision literature). =

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6 EVENTS

Robert Van Rooy 1 3 7

def

def

It turns out that the first condition comes down to tautological entailment in the sense of Anderson & Belnap (1962). This means that if B does not classically follow from A, clause (i) assures that it will also not be the case that A � B. Although clause (i) assures already that our notion of entailment is stronger than classical entailment, it still predicts for any B that we can derive A V B from A. This inference is ruled out, however, by our clause (ii). 37 Note that in distinction with Kratzer's situation-theoretic approach, but like Barwise & Perry's, we have conjunctive situations/events, but no disjunctive ones. 38 It is worth observing that van Fraassen's analysis of events is closely related with Peleg's (1 987) analysis of actions in his Concurrent Dynamic Logic. In this logic, actions denote relations berween worlds and sets of worlds. Assuming that action a denotes D0 and that action f3 denotes Df3, in his semanticsthe denotation of action a V (3, Da v f3• is D0 U Df3 as in ordinary dynamic logic, and the denoation of the concurrent action a 1\ {3, De. l\f3• is defined as follows: Da l\ {3 �{ ( w, e U e' ) I ( w, e) E Da and ( w, e ' ) E Df3}. As far as these connectives are concerned, we can conclude that we could have given our analysis also in terms ofPeleg's variant of dynamic logic. 39 The classical notion of a proposition can obviously be defined in terms of the events: [[A]] = {w E Wl 3e E I; (A)}, at least, if for each world w and atomic sentence p. either 1,;- (p) = { {p} }, or 1.,- (p) = { {p} } . Propositions, of course, behave Boolean, but what is, perhaps, remarkable to see is that [[A]] n [[B]] = {w E W l 3e E I.,+ (A 1\ B) } , and [[A]] U [[B]] = {w E W l 3e E [w+ (A V B)}. This is interesting because it shows that if we want to give a uniform meaning to the conjunctive coordinator and in sentential and eventive clauses, we do not have to assume that and denotes Boolean intersection; we simply do not calculate primarily at the Boolean leveL

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similar for I;; (p) , we can define I: (•A) I;; (A) and I;; (•A) 1;- (A) in the way familiar from partial logic. When the two eventive clauses A and B in w positively denote 1;- (A) and 1;- (B), respectively, the disjunctive eventive clause A V B will denote 1;- (A) U 1;- (B), while the conjunctive eventive clause A 1\ B will denote 1;-(A) X 1;- (B). The set S x T is the def product of S and T determined as follows: S X T { e U e ' l e E S and e ' E T}.37,3s Our purpose of using eventives was to be able to defme a consequence relation, ·�·. that is stronger than ordinary entailment between propositions.39 According to Rohrbaugh the consequence relation that we need for the analysis of permission sentences should also be closely related to Kratzer's notion of lumping. If we say that pw+ (A) � {e ' l 3e E Iw+ (A) : e � e ' }, the set of events forced by Iw+(A), we can define Kratzer's notion of lumping as follows: A lumps B in w iff pw+ (A) � pw+ (B) . Now we can finally define our sought after inference relation, �. as follows: iff (i) Vw : A lumps B in w, and (ii) Vw E [[A]] : Ve ' E 1;- (B) : 3e E 1;- (A) : e ' � e

r38

Permission to Change

Now we can use this consequence relation for the analysis of permission sentences. As expected, the new permission set after the allowance to do A will now be defined as U {P�B I A B } . In this way the allowance to do A and B will always allow you to do both separately.40 As mentioned above, also Rohrbaugh (1996) used events to account for the effect of permission sentences. He argues that a permission to do A or B will always also give rise to the permission to do A and to do B. This is different from the way we have used eventives to analyze the effect of permission sentences ourselves, but we could, if we wanted, account for this intuition, too. Just say that the permissibility set changes after the allowance to do A from P to U {P�n i 3C E IA : C B } , where IA {D i V'w E [[A]] : D E Jw+ (A ) } . �

�

7

SCOPE B Y L I F T I N G

Although in many cases both the disjunctive permission You may do A or B and the conjunctive permission You may do A and B have the effect that you are allowed to do A and B separately, we have already discussed examples where this prediction seems to be wrong. A disjunctive permission does not have the free choice reading when we add a phrase like but I don't know which, like in (2) repeated here as (s): (s) You may take an apple or a pear, but I don't know which. A conjunctive permission, on the other hand, can sometimes really have the 'package deal' reading when it can naturally be interpreted as a conditional offer, like in

(6) You may give a party and clean the house afterwards. Our event-semantics allows us technically to account for the non free­ choice readings of disjunctive permission sentences, but it is not clear whether it could account for the intuition why (s) has such a reading. Even more problematic is the fact that the 'package deal' interpretation of (6) cannot be accounted for. At this point it seems that we should account for the different readings of coordinated permissions in terms of a notion of scope. Normally the disjunction in disjunctive permission sentences has narrow scope with respect to the speech act operator May, resulting in the free choice reading, but sometimes it takes wide scope, as for instance in a sentence like (s) . For 40 Similarly, the problem of section 3, that You may eat three apples does not allow you to eat one or two apples, is resolved.

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=

Robert Van Rooy

1 39

4 1 See also Gazdar (r98o) and von Stechow (1974).

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conjunctive permission sentences something similar happens, but then the other way around; normally the conjunction has wide scope, resulting in the reading where both conjuncts are allowed to be done separately, but sometimes the conjunction has narrow scope, as in (6), resulting in the package-deal reading. Notice that when we accounted for the non package-deal reading of conjunctive permission sentences in terms of scope, we would not have to give up the assumption that we could account for the performative effect of permissions in terms of ordinary contraction. Although our problems seem to disappear when we allow the disjunction and conjunction to have scope over the speech act operator, there are a number of worries that such a proposal has to deal with. The first thing to note is that we have. to allow connectives to take scope over speech act operators, which is very unusual. Second, and more seriously, an analysis that accounts for the non free-choice reading of disjunctive permission sentences, and for the non package-deal reading of conjunc­ tive permissions, by assuming that the relevant connective has in the logical form syntactically wider scope than the speech act operator seems very unnatural (c£ Kamp 1 979), and contradicts the ceteris paribus preferred assumption of direct surface compositionality, the assumption that we do not need a mediating level of logical form for our semantics, i.e. that our compositional semantics directly assigns to each surface expression a model-theoretic interpretation. It turns out, fortunately, that we can account for the intuition that the above-discussed 'scope-analysis' alludes to, without contradicting surface compositionality, if we make use of our best known type-shift: lifting. The type-shift operator of lifting is the operator from expressions of type T to expressions of type ( ( T , t) , t), for any type T. This type-shift operator has been used by Partee & Rooth (1983), for instance, to enable expressions of type T to conjoin with expressions of type ( ( T, t) , t) .41 Following Montague (1973), Keenan & Faltz (1985) propose that proper names, just like other NPs, should be analyzed as being of such a higher type from the very beginning. They notice that expressions of type ( ( T, t) , t), are special in the sense that all denotations of this type can be thought of as Boolean combinations of the principle filters generated by the expressions of type T. The principle filter generated by the name John, for instance, can be denoted by { C � p(D) I {john E C } , where D is our set of urelements. Notice that on a Boolean analysis of conjunction, the sentence john and Mary danced is predicted to be true if and only if John danced and Mary danced. That is, the sentence can be true although John and Mary did not

140 Permission to Change

dance together, and {john} n {Mary} = 0, i.e. it matters when to apply Boolean intersection; application at the higher type results in a 'wide-scope' reading to 'and', but application at the lower type does not.42 Keenan & Faltz notice that for that-clauses, whether-clauses, and to-infinitives, too, it seems to make a difference when the relevant operator is applied if the clause is coordinated; the (a)- and (b)-sentences below can have a different interpretation (for instance when John only wants his mother to leave in case Mary comes):43 John John John John

hopes that Mary comes and that his mother leaves. hopes that Mary comes and his mother leaves. knows whether Fred left or whether Mary left. knows whether Fred or Mary left.

Keenan & Faltz propose to account for this difference between (7a) and (7b), for instance, by assuming that the that-clauses do not denote propositions of type (s, t) that function as arguments of what John hopes (or Mary believes), but rather that these clauses denote entities of type ( ( (s, t) , t) , t) , i.e. sets of sets of propositions, which take as arguments that which is denoted by john hopes' (the set of propositions that John hopes), or 'Mary believes' (the set of propositions that Mary believes).44 If we now assume that the word ' that' is a type-shifting operator that shifts a proposition, A, of type (s, t) into the principle filter generated by A, { C � p(W) I A E C}, of type ( ( (s, t) , t) , t), it will make a difference whether we apply the Boolean operations before or after the type-shift. Applying the operation before the type-shift results in a narrow scope reading of the operator, but when it is applied after the type shift (which is the case in the (a)-sentences), a wide-scope reading of the Boolean operator results. Keenan & Faltz furthermore assume that natural language users can be rather sloppy, and sometimes use (7b) when they really mean (7a). Thus, due to our laziness, the (b)-sentences, but not the corresponding (a)-sentences, are in fact ambiguous. Partee & Rooth (1983) allow for type-shift only in case of type-mismatch. Type-mismatch might occur, for instance, when we want to coordinate two expressions with different types. By restricting the use of type-shift in this wav thev �predict that when an operator of tvoe ( ( T., t) . t) wants to take as � argume�t an expression of type ( T, t) , wh�;e thls ��p �ession involves a

42 Here, and in the rest of this section, 'wide scope' reading means only the reading that intuitively corresponds with the reading where the coordinator actually had wide scope with regard to the permission operator in the syntactic tree according to an explicit scope analysis. 43 See also Groenendijk & Stokhof (1989) for type-shifts and interrogatives. « Keenan & Faltz note that in this way they can also account for sentences like That Fred Jailed surprised John and annoyed Bill without making use of old-fashioned conjunction reduction.

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(7) a. b. (8) a. b.

Robert Van Rooy

141

.

mm (X 45

46

) def { =

e E X I -de 1 E X: e 1

See also Groenendijk & Stokhof

C

(1989)

occurs

e} , for this liberal theory of type-shift.

in the embedded clause of a permission sentence, this negation has typically a 'wide-scope' reading, and it is not easy to see how to account for this for the reasons I discussed earlier. This does not mean that our performative analysis allows for a straightforward account of sentences of the form You may not do A. Notice that when a negation

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coordinative connective, this coordinative connective can never have wide scope with respect to the operator. We have seen above that Keenan & Faltz, instead, allow operators like John hopes and Mary believes to be outscoped by coordinative connectives occurring in the relevant embedded clauses, and that, indeed, this seems to predict correctly. However, Keenan & Faltz assume that shifts of expressions from type (r, t) to type ( ( (r, t) , t) , t) should be induced by an explicit type-shift operator like that. This latter assumption, however, seems rather unnatural. Hendriks (1987), on the other hand, allows for free type-shifting at any level, and in this way is able to account for the scope ambiguities of a sentence like Every man and woman walks by applying the conjunction before (narrow scope) or after (wide scope) the (optional) type-shift of the nouns man and woman.45 Notice that when we adopt Hendriks' free type-shift analysis, so that type­ shift is possible even though not triggered by type-mismatch or explicit expressions, we do not have to assume that the ambiguity of (7b) and (8b) is due to our laziness of using the word that; ambiguity is simply almost always around when Boolean operators are used and type-shift is possible. Suppose now that the speech act operator May in sentences like You may A and/or B takes as arguments expressions of type ( ( T, t) , t), although the coordinates A and B might also denote entities of type T. This means that the interpretation of the embedded clause should involve a type-shift, and as a result it will be the case that also for permission sentences the Boolean operators can apply either before or after the type shift. Let us also assume that the relevant type-shift is one from propositions to sets of sets of propositions, and that if A denotes a proposition, s (A ) has as its denotation its type-shifted counterpart. If we now would give a standard truth­ conditional analysis of permission sentences, this would immediately result in a narrow- and a wide-scope reading of the Boolean operator, just like in the case of (7a)-(7b).46 However, we have argued above that to account for the perforrnative effect, our analysis should not be truth­ conditional, but should rather be perforrnative, by changing the permissi­ bility set. The question now is whether and how we can use the type-shift to account for the performative effect of conjunctive permission sentences. I will propose using the type-shift by making use of the standard rninirnality operator:

r 42 Permission to Change

and by defining the update of P with May(John, E), where E is of type (((s, t) , t) , t), as follows:

Upd(May(}ohn, E) , P)

def

u {P�B I::JC E min(E) : B E C}

.

(9) You may take an apple or a pear, but I don't know which. 47

-18

If A and

B

are atomic.

Although conjunctive permission sentences do not always give rise to the package-deal effect,

we have seen in section 6 that some conjunctive permissions do in fact have a package-deal reading.

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Suppose now that the embedded clause is conjunctive in nature and involves A and B. In that case the embedded clause is either of the form 's(A) 1\ s(B)' and denotes { C � p(W) I A E C} n { C � p(W) I B E C}, or is of the form 's(A I\ B)' and will denote {C � p(W) I (A n B) E C}. Notice that both the first and the second object contains only one minimal element.47 However, these minimal elements are not the same. In the first case the minimal element itself contains two propositions, A and B, but in the second case the minimal element contains only one proposition, the proposition denoted by A 1\ B. By our definition of the update-operator, this means for the second case that only worlds are added that make both A and B true, and the package-deal is predicted just like before.48 When conjunction is applied after the type-shift, however, it is predicted due to our definition of the update function that both A 1\ -.B worlds and B 1\ -.A -worlds might be added to the permissibility set, because the minimal element of the denotation of 's(A) 1\ s(B)' contains both the proposition A and the proposition B. As a result, the new permissibility set might contain possibly some A 1\ -.B-worlds and some -.A 1\ B-worlds, just like we wanted. It is worth observing that our above analysis also has an interesting consequence for disjunctive permission sentences. First, consider the case where the disjunction of the embedded clause has narrow scope with respect to the lifting operator, May(s(A V B) ) . In that case, disjunctive permissions have the same reading as in the original Stalnaker approach; the best A V B­ worlds are added to the permissibility set. But now suppose that the disjunction has wide scope with respect to the lifting operator, May(s(A) V s(B) ) Now it will be the case, due to our definition of the update by permission sentences, that May(s(A) V s(B) ) has the same effect on the permissibility set as its corresponding conjunctive May(s(A) 1\ s(B) ) , if A and B are atomic. This means that in distinction with the corres­ ponding conjunctive case, the application of disjunction after type-shift does not really result in a wide scope reading for disjunction. But this seems to be wrong, given disjunctive permission sentences like (2), repeated below as (9):

Robert Van Rooy

143

that do not give rise to the free-choice reading. In (9), the disjunction intuitively has widest scope, representing the episternic ignorance of the master about what is actually allowed. However, I don't think this is a problem for our analysis, because {9) seems to be used assertorically, and not performatively. If it had been used performatively, it would have violated the felicity condition of the speech act whose intended success conditions the speaker knows.

8 CONCLUS I O N

Acknowledgements This paper was written while I was working on the 'Sources and Streams of Information' Project, sponsored by the Dutch Organization for Scientific Research (NWO), and presented during the third Tbilisi Symposium on Language, Logic and Computation in

1999. I would like to

thank Frank Veltman, Henk Zeevat, Ede Zimmermann, the audience

at the third Tbilisi Symposium, and some anonymous reviewer, for stimulating remarks and discussion. Received: o 1 .09. 1 999

ROBERT VAN ROOY

ILLC/University of Amsterdam Nieuwe Doelenstraat 15 1 o 12 CP Amsterdam The Netherlands [email protected]

Final version received:

23.07.2000

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Robert Van Rooy 145 Spohn, Wolgang ( 1987), 'Ordinal condi­ tional functions: a dynamic theory of epistemic states', in W. L. Harper & B. Skyrms (eds), Causation in Decision, Belief Change, and Statistics Vol. z, Reidel, Dordrecht, 105-34. Stalnaker, Robert C. ( 1 975), 'Indicative con­ ditionals', Philosophia, ), 269-86. Stalnaker, Robert C. ( I 978), 'Assertion', in P. Cole (ed.), Syntax and Semantics, Vol. g: Pragmatics, New York: Academic Press, 3 I 5-J2. Stalnaker, Robert C. (MS.), 'Comments on Lewis's problem about pertnission'. Stechow, Arnim von ( 1 974), 'E - ,\ kon­ textfreie Sprachen: Eine Beitrag zu einer natiirlichen formalen Semantik', Linguistische Berichte, 34, r -JJ. Tan, Yao-Hua & Torre, Leen van der ( 1 997), 'Obligations in update semantics', in K. van Marcke & W. Daelemans (eds), Proceedings of the Ninth Dutch Conference of Artificial Intelligence, University of Antwerp, 249-53. Veltman, Frank ( I996), 'Defaults in update semantics�, Journal of Philosophical Logic, 2), 22I-6I. Zimmermann, Ede ( I 999), 'Free choice disjunction and episternic possibility', Preprint on Logic in Philosophy, nr. 31, Konstanz.

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on Grammar and Semantics, Dordrecht: Reidel, pp. 22 I -242. Mott, Peter ( 197 3 ), 'On Chisholm's paradox', Journal ofPhilosophical Logic, 2, I 97-2 I 1 . Partee, Barbara & Rooth, Mats ( I 983), 'Generalized Conjunction and Type Ambiguity', in R Bauerle et al. (eds), Meaning, Use, and Interpretation of Language, Berlin: W. de Gruyter. Peleg, David ( 1 987), 'Concurtent dynamic logic', Journal of the Association for Computing Machinery, 2, 45o-79. Portner, Paul ( 1997), 'The semantics of mood, complementation, and conversa­ tional force', Natural Longuage Semantics, s. I 67-2I 2. Rohrbaugh, Gene ( 1 996), 'An event-based semantics for deontic utterances', in P. Dekker & M Stokhof (eds), Proceedings ofthe 1oth Amsterdam Coloquium, Amster­ dam. Rooy, Robert van ( 1 997), 'Attitudes and changing contexts', Ph.D. dissertation, University of Stuttgart. Rooy, Robert van ( I999), 'Some analyses of pro-attitudes', in H. de Swart (ed.), Logic, Game theory and Social choice, Tilburg University Press, Tilburg. Spohn, Wolfgang ( 1975 ), 'An analysis of Hansson's dyadic deontic logic', Journal of Philosophical Logic, 4, 237-52.

Journal of&manrics

IT

© Oxford University Press

147- 1 84

2000

How to End Without Ever Finishing: Thai Semi-perfectivity J E A N - P IERRE K O E N I G and N U TTANART MUANSUWAN University at Buffalo, State University cif New York

Abstract

Perfectivity is often assumed to entail the completion of the event described by event-denoting stems and their arguments (see Herweg 1 991, 1 991b for an explicit expression of this assumption). In particular, if the stem belongs to the accomplishment Aktionsart class, perfectivity-which we informally define for now as the requirement that the event that the sentence describes is bounded-entails that the accomplishment's resulting state holds at the reference time interval. Some scholars, such as Binnick (199 1) and Smith (1997), have noted that perfective markers do not always entail completion of the event denoted by 1

1

Following Smith

(1 997), we call the combination of a verb and its arguments, to the exclusion of

tense or aspect marking, a verb constellation. We assume that Aktionsart classes are defined, as in

(1 979), via statements of the following kind: a is a specified quantity (in the sense of Verkuyl I 99 3), then, if P(a ) true at interval J, it is not true at all subintervals of I (adapted from . Dowty 1979 p. 1 66).

Dowty

i. If P is an accomplishment and is

Since this paper is only concerned with sentences in which accomplishment predicates combine with arguments that are specified quantities, we use the term accomplishment verb/stem to mean a verb/stem whose meaning includes an accomplishment predicate

P combining with arguments that

are specified quantities. We also sometimes refer to verb constellations, clauses, or sentences whose main verb stems belong to the accomplishment class as

sentences.

accompliJhment verb constellations, clauses, or

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Perfectivity is often assumed to entail the completion of the event described by event­ denoting stems and their arguments. Although some scholars have noted that perfective markers do not always entail completion, their formal definitions contradict their informal descriptions. We show that these traditional models of perfective aspect cannot account for the aspectual system of Thai. In Thai, perfective markers do not entail that the event was completed: the resulting state of sentences that are in appareance telic in their 'inner aspect' need not have been reached. We call these non-completive perfective markers semi­ perfectives. We propose a formal model of semi-perfectivity within Discourse Representa­ tion Theory that relies on the inclusion of an imperfective operator in the lexical meaning of Thai accomplishment verbs as well as the notion of maximal event relative to an event description. We show that this latter notion is strictly weaker than the traditional notion of telicity, thus demonstrating that (a)telicity is not the sole property of event descriptions relevant to the semantics of grammatical aspect.

148 How to End Without Ever Finishing: Thai Semi-perfectivity

I ASPE CTS O F T I ME

Because the literature on aspect ascribes different meanings to the same theoretical constructs, we begin with a few terminological pointers. First, we distinguish between the semantic properties that underlie (im)perfective or what we later call semi-perfective sentences and the grarrm1atical markers, which, in some languages, insure the presence of these properties. Thus, we call (im)perfectivity or semi-perfectivity semantic properties of sentences and reserve the term (im)perfective or semi-perfective markers to their putative grammatical causes. As Zucchi (I999) emphasizes, the assignment of (im)perfective or semi-perfective semantic effects to par­ ticular markers is quite indirect and also depends on the semantic

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the sentence of which they are part; however, their formal definitions contradict their informal descriptions. In this paper, we show that traditional models of perfective aspect cannot account for the aspectual system of Thai. In Thai, markers traditionally called perfective (see Thepkanjana I 986) do not entail that the event was completed: the resulting state of sentences that are telic in their 'inner aspect' (in the sense of Verkuyl I 993) need not have been reached. We call these non­ completive perfective markers semi-perfective. Our fundamental insight is that the non-completive character of sentences that contain the Thai semi­ perfective marker results from the fact that, by contrast to English, aspectually unmarked accomplishment clauses in Thai never describe completed eventualities; rather they describe (non-necessarily proper) subparts of inherently bounded eventualities. We argue that a formal model of semi-perfectivity requires the recognition of a weaker property of event descriptions than telicity, what we call maximality. Whereas aspectual distinctions in English and many other languages revolve around the former notion, Thai aspect involves only the latter. More generally, our formal account of Thai aspect grounds the informal claims of Smith (I997) or Depraetere (I 995) regarding the need to recognize notions such as arbitrary boundaries or boundedness aside from telicity proper. The paper is organized as follows. Section I discusses various current accounts of aspect and shows that their formal definitions, implicitly or explicitly, assume that perfectivity is always completive in character. Section 2 presents a subset of the Thai aspect system which reveals that this assumption is incorrect. Section 3 presents a model of the subset of the Thai aspect system described in section 2 within Discourse Representation Theory.

Jean-Pierre Koenig and Nuttanart Muansuwan 1 49

(I) Patsy wrote a letter. More precisely, in Herweg's treatment of perfective aspect, sentences such as (2) denote sets of events once the simple past tense marker is left aside (that is, once the verb constellation is extracted). The past tense marker indicates that the time at which any member of that set of events occurred precedes the time of utterance, as shown in (2). (e* denotes the speech event and (e) the time at which e occurred). 7

(2) a. Peter put the book on the table. b. Ae (PETER-PUT-THE-BOOK-ON-THE-TABLE(e)

1\

PAST(e*, T(e)))

The (im)perfectivity of sentences in the simple past, in this account, follows from the semantic type of the verb constellation they contain. If the constellation is stative, the overall sentence is imperfective (it characterizes a state, understood by Herweg, following Galton I 984, as a property of time). If the constellation is eventive, the overall sentence is perfective. As de Swart (I998) puts it, the English past tense is aspectually transparent. By contrast to perfectivity which is. built in the past tense transparency to the event or state status of the verb constellation, progressive markers are treated as operators that map events onto states. Thus, in Herweg's analysis, the perfectivity of (I) or (2a) does not require a semantic representation or definition. It follows from the definition of the English simple past. The representation of the semantics of (2a) in (2b), which does not include any term, predicate, or operator referring to the perfective aspect, makes this clear. More importantly, if a sentence is perfective, an event of the type that the verb describes must have occurred (or will occur). In particular, if the

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contributions of other subsentential elements. One should therefore not read too much in our use of the expression (im)perftctive or semi-perftctive marker. We only mean to convey by this expression that these markers are a salient determinant of the (im)perfectivity or semi-perfectivity of the sentences in which they occur. Second, the word telic is often used to describe inner aspect properties or properties of verb constellations. But it is also used in the tradition of Krifka (I989, I 998) more generally to describe properties of event descriptions. If one takes outer or grammatical aspect operators to be functions from event descriptions to event descriptions (see de Swart I 998 ), event description properties, such as telicity and atelicity, can be assessed for both verb constellations and verb constellations that are modified by outer aspect operators. It is in this latter sense that we use the words telic and atelic in this paper. In Herweg's (I99Ia, I99Ib) analysis of aspect, perfectivity is a property of events (in opposition to states). Thus, sentences that describe events, such as ( 1 ) , are perfective in Herweg's sense.

I so

How to End Without Ever Finishing: Thai Semi-perfectivity

verb corresponds to Vendler's ( 1967) accomplishment class, as is the case for (2a), perfectivity entails the completion of the event: the book ends up on the table.2 A similar point can be made for languages that explicitly mark perfectivity or whose past tenses are sensitive to the inner aspect properties of the verb constellations over which they have scope. The Spanish perfective past can, for instance, combine with both telic and atelic verb constellations, as shown in the sentences in (3). But, crucially, when the perfective past combines with a verb constellation that belongs to the accomplishment class, the completion of the action is entailed (the lawn is mowed in (3a)).

As we show in this paper, the kind of perfective sentences that Herweg analyzes and that is exemplified in (2a) and (3a) is only one kind of perfectivity. Not all perfective sentences entail the completion of events whose corresponding verb falls into Vendler's accomplishment class. We call completive peifectives perfective sentences that do entail the completion of telic events. 3 By contrast to Herweg's description of perfective sentences, many treatments of English tense and aspect in the formal semantics literature do not explicitly mention perfectivity at all and merely discuss the temporal aspect of past tenses such as the English preterite. Aspectual considerations arise only when discussing the progressive and the perfect. This is the case in Hornstein ( 1990), but also in Steedman's ( 1997) recent summary, and many others. This omission is prompted, we believe, by the correlation between past tense and completive perfective aspect in English and the assumption articulated by Michaelis ( 1 998) that perfectivity is the default grammatical aspect for events. The same omission is true of Dowty's ( 1979) treatment of the progressive and tense marking. Here again, English simple past tense only contribu tes ten..se information_ Thus, (4a) is given the 2 Herweg is not alone in equating perfectivity and occurrence of an instance of the event-type associated with the sentence's verb constellation. For example, when describing the conceptual basis of perfectivity and imperfectivity, Michaelis (1998) (citing Langacker 1991) talks of event boundaries and changes vs constancy and open-endedness and assumes that the boundaries of perfective sentences built around accomplishment verbs match the 'natural' boundaries of telic events. 3 The notions of non-completive (semi-perfective) and completive perfective sentences parallel the distinction between ending and finishing discussed in ter Meulen (1995).

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(3) a. Mario corto el cesped Mario mow.PFVE.PST the lawn 'Mario mowed the lawn.' b. Mario estuvo enfermo Mario be.PFVE.PST sick 'Mario was sick.'

Jean-Pierre Koenig and Nuttanart Muansuwan

I5I

semantic representation in (4b). The progressive, of course, receives a different treatment, in terms of a PROG operator. (4) a. Joan left. b. 3t (PAST(t)

1\

AT(t, leave'(})))

4 Talmy {199 1 , zooo) discuss the same phenomenon in Chinese, although not in the context of perfective markers. See below for details.

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This kind of treatment easily extends to languages like Spanish whose past tenses mark aspectual information or are aspectually sensitive. Verb constellations that belong to Vendler's accomplishment or achievement class and that are in the perfective past entail the realization of the state associated with the accomplishment, as sentence (3a) illustrates, while for verb constellations that describe states or activities the perfective past merely entails the cessation of the state or activity. Even though the Spanish perfective past leads to an aspectual shift in the case of atelic verbs, its aspectual import for telic verbs is null, as the English simply past is. Informally speaking, the event boundary that was reached in (3a) was that which is encoded by the verb and its arguments, namely the state of the lawn being mowed. Both the English simple past and Spanish perfective past are aspectually transparent to the 'natural' boundary encoded in telic verbs. The perfectivity of simple and perfective past sentences reduces to the semantic properties of telic verbs, namely to the fact that they describe events with 'natural' boundaries. Transparent treatments of the perfectivity of telic verbs, such as Dowty's, Herweg's, or Hornstein's are unproblematic in all languages (such as English or Spanish) in which perfective sentences are completive. The semantic information that the described event is bounded easily reduces to the semantic properties of telic verbs, since the fact that the 'natural' boundary of a telic event is (or will be) reached is inferable from the fact that a non-progressively marked accomplishment verb constellation is instantiated in the past (or future). But several scholars have noted that perfectivity is not always completive; in those languages, the perfectivity of sentences containing telic verbs whose arguments are specified quantities cannot be equated with the 'natural' boundary characteristic of telicity. Binnick (1991), Smith (1997), and Singh (199 1), in particular,4 explicitly note this when discussing Slavic, Chinese, and Hindi perfective markers, respectively. For expository purposes, we discuss Chinese -le in this section. Smith provides the following sentence as evidence that Chinese -le is non completive: even when the event-type described by a verb constellation belongs to Vendler's accomplishment

1 52

How to End Without Ever Finishing: Thai Semi-perfectivity

e = [I wrote a letter to Zhangsan yesterday] write (x, y, z) e E Accomplishment Viewpoint (1 1 , e) = Perfective t; E / 1 ,J t; = I( e), t1 = F(e)

t E 1 1 - t � t;, t s t) t2 = yesterday (3 = (2 r2 < r,

x=l letter (y) z = Zhangsan

Figure

I A

Smith-style

DRS

for sentence (6)

class, the inclusion of -le does not guarantee that the 'natural' end-point associated with the event (in this case, the end of the letter) is reached. We call the kind of perfectivity sentence (s) exhibits semi-perfectivity.

( s) Wo zuotian xie-le

gei Zhangsan de xin, keshi mei xie-wan I yesterday write-LE to Zhangsan DE -letter, but not write-finish 'I wrote a letter to Zhangsan yesterday, but I didn't finish it.'

Despite the fact that they note that perfectivity does not always entail completion of the events described by telic verbs, the formal descriptions of perfectivity that Binnick and Smith propose do not seem properly to model semi-perfectivity. Smith's formal account of aspect marking is couched within Discourse Representation Theory (hereafter DRT). To illustrate, consider her formal representation of the English sentence in (6), shown in Figure r .5 (6) I wrote a letter to Zhangsan yesterday. The first line of the Discourse Representation Structure (hereafter DRs) in Figure 1 lists a set of discourse markers which are interpreted semantically as denoting individuals in the model's domain. The second line indicates that the event e is the type of event in which the speaker writes a letter to 5 For ease of exposition, we assume that write is a three-place predicate relating a writer, a written object, and a recipient.

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/1 at r3

Jean-Pierre Koenig and Nuttanart Muansuwan

153

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Zhangsan. The third and fourth lines state that the event is an accomplish­ ment viewed under the perfective aspect. Lines five through seven indicate that the reference interval of time 11 includes the initial and fmal boundaries of e. Lines eight through eleven indicate that the reference interval is located at an interval of time that is equal to the denotation of the deictic yesterday and is located prior to speech time, namely t;. Finally, lines twelve through fourteen constrain the interpretations of the discourse markers x, y, and z. Without entering into the details of this particular representation of the semantic contribution of (6), its major drawback is that it de facto forces perfective marking to be always completive. The conventional interpretation of (verifying) embedding functions for DRS such as Figure I is that the domain of the model for their interpretation must include individuals for each discourse marker and that, furthermore, these individuals must satisfy the denotata of the predicative conditions listed below the list of discourse markers. Thus, an embedding function that verifies the DRS in Figure I must map the discourse marker y onto an individual in the domain which belongs to the set of individuals which are letters (per the predicative condition on line thirteen). Similarly, a verifying embedding function must also map the discourse marker e onto an individual of the domain which satisfies each predicative condition which includes e as one of its arguments. In particular, e must respect its situation-type condition, as it is encoded on line two. But this amounts to saying that e is an event of the speaker writing a letter to Zhangsan. Although this representation is adequate for the English sentence in (6), it will not do for the Chinese example in (s ). since the latter does not entail that the letter was finished. Smith's informal description of the semantic difference between the English and Chinese perfectives involves the distinction between 'natural' and 'arbitrary' boundaries for events. The final boundary that is indicated by English-style completive perfective markers is the 'natural' boundary, in case the event has one, whereas Chinese-style non-completive perfective markers only indicate that the event has a final 'arbitrary' boundary. To model this informal description of the difference between English and Chinese, we could explicitly represent the nature of the final boundary in the DRS in Figure I and add, for English-style perfective markers, the condition: culminate( e, � ), where the predicate culminate is interpreted to mean that the eventuality e culminated at � (following Parsons 1990). Including this condition does not affect the interpretation of the DRS for the corresponding Chinese sentence, though. To prevent the erroneous entail­ ment that an event e in which the speaker has written a letter to Zhangsan occurred, we must include a condition for Chinese-style perfective markers that would explicitly preclude tj from being the time at which e culminates.

1 54

How to End Without Ever Finishing: Thai Semi-perfectivity

(7)

¢ is true relative to a time interval i and a world relative to i and w. COMP

w

iff ¢ is true

Clearly, such a definition makes the perfective always be completive, an assumption which the Chinese example in (s ) and the Thai data presented in the next section contradict. More generally, no formal account of aspect of which we are aware properly models instances in which perfectivity does not entail the completion of telic events. Our own analysis of the Thai aspectual system solves this problem, as we show in section 3 · But, before presenting our model, we must describe in detail the relevant parts of the Thai aspect system.

2

THE THAI ASPECT SYSTEM

Thai's aspect system is particularly rich, too rich for us to be able to discuss it in its entirety in this paper. We merely outline its overall features and 6 The only other alternative of which we can think is to assume that line two does not denote the set of events in which the speaker wrote a letter to Zhangsan. This set of events would only be described by taking together several predicative conditions, including those of lines two through four. Unfortnn�rely, the meaning of the predicative condition on line two is now unclear: what constraint on the value of e does it encode? 7 We say seem, because Binnick's description of the formal semantics of tense and aspect is more a literature review than a new proposal. It is therefore difficult to know what Binnick's own formal definition of the perfective would be. But he seems to favor the formal approach ofJohnson (1981) on p. JOO, where he says the following (PERF stands for perfect operators, IMPFVE for imperfective operators, and PFVE for perfective operators): 'A successful universal set of truth conditions for the operators PERF, IMPF, and COMP (alias PERF, IMPVE, and PFVE) along the lines of Johnson's (1981) proposals . . . seems feasible.' We therefore discuss only Johnson's formal treatment.

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But this would not do either. Chinese is simply vague on the issue of whether tj is or is not the 'natural' boundary of the event. In fact, the nature of embedding functions on DRS makes any additional condition similarly incapable of preventing the Chinese DRS corresponding to Figure I from having a model-theoretic interpretation that entails the completion of e. Any verifying embedding function must map discourse markers such as e to individuals in the domain and the second line of the DRS in Figure I , which the corresponding Chinese DRS must also include, forces this denoted event to be one in which the speaker has written a letter to Zhangsan.6 Binnick (I99 I) formal definition of perfective marking does not seem to fare better.7 Adopting Johnson's (I98 I) analysis of the Kikuyu completive marker, he proposes the following definition of the perfective marker COMP (the formulation is simplified in irrelevant respects, ¢ stands for any verb constellation).

Jean-Pierre Koenig and Nuttanart Muansuwan

r55

s

�

NP

VP

I

�

Surii

VP

�

v

NP

tEEIJ

khm

I

Figure

2

I

yma.x

I

kh um

The syntactic structure of Thai aspectual serial verb construction

do work Surii FROG 'Surii is in the process of working.' h khm k llin (9) Surii tceu Surii compose poem ascend 'Surii composed a/the poem (perfective)'

The syntactic structure of sentence (9) is shown in simplified tree form in max Figure 2. The notation y is meant to indicate that the constituent can either be a single word or a phrase. Muansuwan (1999) argues on the basis of adverb placement and the so-called do so test that serial verb construc­ max tions are recursively adjoined to a y constituent. Since the syntactic details of Thai serial verb constructions are orthogonal to our concerns, we will simply assume this analysis without arguing for it (see Thepkanjana 1 986 for a different syntactic analysis of Thai serial verb constructions). The set of Thai verbs that can occur as serial verbs and encode aspectual information is comparatively large. It includes the verbs listed in Table 1 .8 8 The expression relic events in the second column is only used mnemonically. Tests of telicity of the kind mentioned in fn. I do not apply to the corresponding Thai verbs, as our description of the aspect system of Thai will make clear. Since providing an exact characterization of the set of verbs

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discuss in detail the aspectual markers on which this paper focuses. Thai aspect can be marked with auxiliaries in pre-main verb position (see sentence (8)) or by serial verbs in post VP position, as illustrated in sentence (9). We do not discuss pre-verbal aspectual auxiliaries in this paper. We are only concerned with the more pervasive way of marking aspect in Thai, namely through the use of a serial verb construction, which sentence (9) illustrates. (The English translation of (9) is inadequate, as we discuss shortly. We provide it as an approximation of the semantics of the perfective marker kh rim. A similar caveat applies to most of the translations of Thai aspect markers.) (8) Surii kamlall!J tham uaan

I 56

How to End Without Ever Finishing: Thai Semi-perfectivity

Table

I

Thai serial aspectual verbs

Encoded aspect

Aktionsart of the initial verb

Perfective

Telic events

Imperfective Perfect

Activity Any

First serial verb

Second serial verb

khWm 'ascend',

paj 'go

loiJ 'descend', ?:Uk 'exit' khaw 'enter'

'

paj 'go' maa 'come

'

Surii kill bird three CLASS ascend 'Surii killed three birds' (intended reading) ( I I ) a. B;}d ra?-b;J;}d happen explosion 'There was an explosion/There used to be explosions.' b. k;J;}d ra?-b;J;}d kh wn happen explosion ascend 'There was an explosion.'

By contrast, the serial verb lov 'descend' mostly combines with verbs of destruction and is therefore felicitously used in combination with khaa 'kill', as sentence ( 1 2) illustrates. ( u) Surii khaa nok siam tua lou Surii kill bird three CLASS descend 'Surii killed three birds'

The perfective marker f?J:Jk 'exit' encodes the same aspectual information as k\ im, but seems to add a presupposition that the act was difficult to accomplish. Thus, sentence ( I 3 ) has the same aspectual characteristics as (9), but adds the presupposition that writing the poem was hard for Surii.

(I 3) Surii teeij

Surii compose poem exit 'Surii composed a poem.'

Table with

I

describes the aspect encoded by k\ im, lov, or

f?J:Jk

as perfective.

which each aspect marker combines is not our focus, we do not discuss the issue further in this paper.

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This paper concentrates on the perfective markers kh cim 'ascend' is restricted in its occurrence; it mainly combines with verbs of creation, as the contrast between sentences (9) and (ro) illustrates. But k\ im can also combine with achievement verbs, as sentence ( I I ) shows. (ro) *Surii khaa nok siam tua khtim

Jean-Pierre Koenig and Nuttanart Muansuwan

1 57

But the notion of perfectivity involved parallels the one that Chinese -le encodes, namely what we call semi -perfectivity, as sentences (I 4) and (I s) illustrate. The inclusion of kh r.im or loiJ marks that the activity of writing (in (I 4)) or eating (in (I s)) must have stopped. But the poem need not be completed in ( I4), nor the rice (in the amount of three bowls) be finished in (I s), even though it is a frequent implicature of sentences such as (I 4) or (I S ) Like Chinese -le, Thai kh r.im appears to be a semi-perfective marker. h kb:m k wn ti:c jal) mij sed (I 4) Surii ti:CI) .9

The fact that sentence (I4) does not entail that the poem was completed, but merely that the writing stopped, is unlikely to be due to a property of the direct object. The same absence of completion is observed when the NP is a specified quantity, as in (I6a), when it is modified by a deictic determiner (I6b), or even when it is a pronoun (I6c). h (I6) a. Surii ti:cl) khm s5:JI) bOt k wn ti:c jal) maj sed Surii compose poem two CL ascend but still not finish 'Surii composed two poems, but has not finished it yet.' b. Surii ti:cl) kb:Jn bot nii khwn ti:c jal) maj sed Surii compose poem CL this ascend but still not finish 'Surii composed this toem, but has not finished it yet.' c. Surii ti:cl) man k wn ti:c jaD maj sed Surii compose it ascend but still not finish 'Surii composed it, but has not finished it yet.'

Since all forms of direct object NPs in Thai lead to a non-necessarily completive interpretation of the event description, assigning the locus of this semantic effect to the direct object would be tantamount to claiming that NPs like kb:m s5:JIJ bot 'two poems', kb:Jn bot nii 'this poem', or man 'it' mean something like some part of two poems, some part of this poem, or some part of it, respectively. But, NPs cannot always be ascribed such a 9 By contrast to Hindi non-completive perfective markers discussed in Singh ( 1 991), whether the measures of food are described by natural or rational number names does not affect the non­ completive nature of the overall sentence, as a comparison of sentences (i) and ( 1 s ) demonstrates. h (i) dek phw-chaaj kin keek ntit.J c in knUu lou t:Cc kin niaj moo eat cake one piece half descend but eat NOT finish.up the boy 'The boy ate one and half pieces of cake, but did not finish it.'

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Surii compose poem ascend but still not finish 'Surii composed a/the poem, but has not finished it yet.' ti:c kin maj mod (I s) Surii kin khaaw siam chaam lol) Surii eat rice three bowl descend but eat not finish.up 'Surii managed to eat three bowls of rice, but did not finish them.'

1 5 8 How to End Without Ever Finishing: Thai Semi-perfectivity

partitive interpretation. In particular, when the verb describes a punctual event, this interpretation is not available, as illustrated in (I7). . ( I 7) n:>I)nan phaiJ 1OIJ school collapse descend 'The school collapsed.'

{I 8) a. ?Surii ti:ciJ khm siam bOt lc? kamlaiJ ti:ciJ JUU Surii compose poem three CLASS and PROG compose CONT 'Surii is composing/composed three poems and is still composing them' b. # Surii ti:ciJ kb:m siam bot khwn lc? kamlalJ ti:clJ J UU Surii write poem three CLASS ascend and PROG compose CONT 'Surii composed three poems and is still composing them' Sentence (I Sa) is slightly odd pragmatically, but is grammatical. By contrast, {I 8b) is ungrammatical: the activity of composing must have been terminated prior to speech time. K!' c.im thus indicates that the described event of composing ended. This conclusion is confirmed by the behavior of duration and interval adverbials. A5 sentence (I 9) shows, durationfor-phrases are not compatible with kh c.im. Conversely, sentences containing k\im are compatible with an interval in-phrase, as (2o) shows. (Similar contrasts exist for the other two perfective markers, loa 'descend' and ??:>:>k 'exit'.) {I9) *Surii ti:clJ khm siam bot khwn pen wee-laa nwlJ chua-m:>:>IJ Surii compose poem three CLASS ascend be time one hour 'Surii composed three poems for an hour' (2o) Surii ti:ciJ kb:>n siam bot khwn n�j nwlJ chua-m:>:>IJ Surii write poem three CLASS ascend in one hour 'Surii wrote three poems in an hour' The ungrammaticality of { I 9) is easily accounted for if a sentence containing khmn describes an event rather than a state or activity, and we assume, as argued in for example de Swart (I998), that for-phrases are functions from states or activities onto (bounded) events. Sentences

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(I 7) can only mean that the whole school collapsed. Ifonly part ofthe school collapsed, it must be explicitly mentioned. We conclude that the absence of necessary completion in (I 4) or ( I 5) cannot be ascribed to the vagueness of the interpretation of Thai NPs. Rather, it arises from the combination of accomplishment stems and the semi-perfective markers k\.im or lov. Despite the absence of any indication that the telic act was completed in either ( I 4) or (I 5 ), there is clear evidence that the inclusion of kh c.im, lov, or ?:,:Jk means that the described eventuality must include a boundary, i.e. that it ended. Compare the sentence in { I 8a) to the sentence in {I 8b).

Jean-Pierre Koenig and Nuttanart Muansuwan

1 59

containing k\ im describe individuals of the wrong sort for the domain of the function denoted by the for-phrase. Sentence (2o) is more interesting from a theoretical perspective since, despite what the English translation suggests, it does not entail that all three poems were finished (although it seems to imply that all three were begun). We discuss this issue at length in section 3· Sentence (I Sa) demonstrates that Thai sentences do not need to include any aspect or tense marking and that one possible translation of bare verbal stems is an English present progressive form. But this is not the only possible aspectual or temporal interpretation of such sentences. Thus, sentence (2 I) is four-ways ambiguous or vague, as its translation indicates.

In fact, a fifth interpretation of (2 I) is possible, provided a past reference point is provided, as shown in sentence (22). h (22) Surii tecl) kb;)n milia c an paj haa go vtstt Surii compose poem when I 'Surii was composing a/the poem when I went to visit her.'

The same temporal ambiguity or vagueness applies to sentences describing states, as shown in (23). (23) Surii mii khwam suk Surii have NOM happy 'Surii is/was/will be happy.' Thai sentences containing bare stems and no aspect or tense marking (hereafter bare sentences) are therefore ambiguous or vague both aspec­ tually and temporally. They can describe bounded or unbounded eventua­ lities, and they can describe eventualities that hold at time intervals that overlap, precede, or follow the time of utterance, as sentences (2 I) and (24) establish. (24) pruQ-nii Surii khian codmiaj tomorrow Surii write letter 'Surii will write a letter tomorrow.' Sentence (25) shows that the addition of the perfect marker maa to a bare sentence preserves its aspectual, but not temporal, vagueness: the described eventuality that led to a state that currently holds is either imperfective or perfective, but must have occurred in the past. In other words, it marks

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kb:m (2 I) Surii ti:crJ Surii compose poem 'Surii is composing/ composes (habitually)/will compose/composed a/ the poem.'

r6o How to End Without Ever Finishing: Thai Semi-perfectivity

either that a past event resulted in a state that presently holds or that a state or activity that started in the past still presently holds. kh:m maa (25) Surii ti:ciJ Surii compose poem come 'Surii has composed/has been composing a/the poem.'

Because of the aspectual vagueness of the Thai perfect marker maa, its occurrence with accomplishment verbs does not entail the completion of the eventuality, as sentence (26) illustrates. (The aforementioned disclaimers regarding the appropriateness of English translations apply to (26).)

Interestingly enough, the combination of khr.im 'ascend' and maa 'come' seems to entail the completion of the act of writing, as (27) illustrates. This emergent semantics appears to defy compositionality, since neither the sentence's component parts nor the syntactic construction via which they combine carries the additional information that the event was completed. The perfective marker khr.im says that the event stopped, it does not require it to be finished. The perfect marker maa, on the other hand, does not even require the event to be bounded in the past. The activity might still be going on. The next section discusses this apparent emergent semantics in more detail. h kb:m k llin maa ti:c jaiJ maj sed (27) # Surii tCCIJ Surii compose poem ascend come but still not finish 'Surii composed a/the poem but did not finish it yet.'

We have now presented the most important data for our model of non­ completive perfective or semi-perfective marking in Thai and turn to a formal model of semi-perfective aspect in Thai.

3

AN ANALYSIS O F THAI ASPECT W I T H I N D i S C O URSE REPRE SENTAT i O N THE O RY 3.1

Are Thai accomplishment verb stems ambiguous?

Sentences (21), (22), and (24) demonstrate that Thai bare sentences can receive either a past, present, or future temporal interpretation, and an imperfective or perfective aspectual interpretation. At least two ways of

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(26) Surii ti:ciJ kb:m maa ti:c jaiJ maj sed Surii compose poem come but still not finish 'Surii has composed a/the poem, but did not finish it yet.'

Jean-Pierre Koenig and Nuttanart Muansuwan 1 6 1

modeling this interpretive vagueness of Thai bare sentences suggest themselves. One assumes that the semantics of bare sentences is appro­ priately vague. The other assumes that some of the interpretations are derived through covert aspectual (or temporal) operators, which have been independently argued for in the description of aspectual shifts. Consider sentence (28a) from de Swart (1998) (her (22)), and its proposed informal semantic representation in (28b). The operator Che is an unexpressed coercion operator that semantically converts homogeneous eventualities (i.e. states or activities) into eventualities that are bounded (events), thus creating an eventuality description of the right semantic type for the aspectual constraint on the use of in-phrases. e

Similarly, we could describe the interpretations ofThai bare sentences as aspectually ambiguous because of the presence, for some of their interpreta­ tions, of a covert coercion operation that maps homogeneous eventualities (states or activities) onto events or, conversely, events onto homogeneous eventualities. Since Thai bare sentences can involve verbs that describe events or homogeneous eventualities (compare (22) to (23)), we can, for example, posit that the primary aspectual interpretation of bare sentences is the one that is consistent with the type of eventuality being described: the bounded event interpretation, if the verb constellation describes a class of events, and a homogeneous eventuality if the verb constellation describes a class of homogeneous eventualities. A covert coercion operator would, then, be needed to derive other possible aspectual interpretations from this primary interpretation. Because the proposed primary and coerced aspec­ tual interpretations cover the two possible aspectual interpretations of bare sentences, it is hard to find empirical evidence against this analysis. Our reasons for rejecting this approach are therefore only metatheoretical. By contrast to English or other languages for which covert coercion operators have been invoked, the covert coercion operator needed to derive the non­ primary aspectual interpretation of Thai bare sentences must be used irrespective of any aspectual constraints imposed by adverbial phrases or other overt morphosyntactic material. Whereas the use of a covert coercion operator for (28a) is motivated by the semantic requirements of the interval phrase in Jour minutes, the use of a covert coercion operator for (21) is not required by independently motivated semantic constraints associated with a word or phrase. Such 'uninvited' uses of a coercion operator contrast with other cases in which coercion is typically invoked, which all involve a sortal mismatch between the semantic types of two morphosyntactically expressed elements (see Moens & Steedman 1988; Pustejovsky 199 1 ; Sag & Pollard

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(28) a. The program ran in four minutes. b. [PAST [IN four minutes [Ch [the program run)]])

162 How to End Without Ever Finishing: Thai Semi-perfectivity ev x y Surii (x) poem (y) lmpfv (ev, f..e '

Figure

3

I x compose y I

An example of a DRS for a sentence containing a bare verb stem

3 .2

The semantics of Thai accomplishment stems

We use Discourse Representation Theory to formalize our description of the aspect system of Thai. Since we follow traditional representations of Discourse Representation Structures, we do not introduce DRT in the text. (See Kamp & Reyle (I993) or de Swart (I998) for details on the representations of tense and aspect in DRT.) The appendix presents a compositional, linear DRT fragment of Thai that covers the data we discuss in this paper. Accounting for Thai semi-perfective markers requires the introduction of two new event description operators. Other changes in our DRT representation of aspect are purely technical. I . An Impfv operator that all accomplishment verbal stems carry; 2. A Max operator that encodes the notion of semi-perfectivity.

Our account of the Thai aspect system relies on the hypothesis that Thai accomplishment stems are fundamentally 'imperfective' in that they do not refer to complete eventualities, but to (non-necessarily proper) subparts of inherently bounded eventualities. This fundamental imperfectivity of Thai accomplishment stems is indicated informally in the paraphrase of our hypothesized semantics for (2I) (repeated in (29a) below) in (29b). By 'inertia' worlds, we mean Portner's (I 998) definition of this notion, first introduced in Dowty (I979). Simplifying somewhat, 'inertia worlds' in this Kratzer's ( I 98 I )-style rewording of Dowty's account of the progressive are

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I 99I ; de Swart I 998). The appeal to covert coercion in the absence of sortal mismatches between expressed constituents weakens theories of the inter­ face between syntax and semantics: the ability to postulate covert operators that are not independently motivated increases the space of possible analyses. We therefore do not pursue the covert coercion approach, but assume instead that Thai bare sentences are vague in their interpretations. It should be noted, though, that our analysis of the Thai aspect system can be recast with minimal changes within an analysis that assumes the presence of covert coercion operators.

Jean-Pierre Koenig and Nuttanart Muansuwan 1 6 3

worlds that are compatible with what is relevant to Surii's completion of the poem and in which Surii is not subsequently interrupted. In all those worlds, she Hnishes the poem. (29) a. Surii tcciJ khm Surii compose poem 'Surii is composing/was composing/composes (habitually)/will compose/composed a/the poem.' b. There is an eventuality ev which is a subpart of an eventuality e' such that in 'inertia' worlds, e' is an event ofSurii composing a poem.

(3o) a. o: = lmpfv(ev, ¢) b. An eventuality ev and an event description ¢ satisfy condition o: if and only if there is an e' which (non-necessarily properly) includes ev and satisfies ¢ in all 'inertia' worlds-i.e. in all worlds compatible with what it would mean to complete ev without being interrupted. The embedding of the event description that characterizes ev within the Impfv operator is needed since, by hypothesis, Thai accomplishment bare stems do not encode completion: only in 'inertia' worlds did an event of Surii writing a poem occur. The inclusion of condition o: renders Thai accomplishment bare sentences similar to sentences marked with imper­ fective markers or the English progressive. Intuitively, Thai accomplish­ ment bare sterns are like imperfectively marked accomplishment verbs in French illustrated in (3 r ).1 1 Like the corresponding French verbs in the imparfait, Thai accomplishment bare stems either carry a non-completive semantics (compare (29a) to (J ia)) or an habitual interpretation (compare (29a) to ( 3 r b)). 10

The inclusion in the main

DRS

of the predicative condition

poem(y) on the discourse marker y

erroneously suggests that a poem was created. The same issue arises for progressive forms of English verbs of creation, as Kamp & Reyle

(1993: 577)

note. Since this issue is orthogonal to the main point

of our paper, we do not discuss it further. 11

We assume here the traditional analysis of French 'imparfait' as an imperfective past tense

rather than as an aspectually sensitive past tense as de Swart on this choice.

( 1 998) does. Nothing substantial hinges

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The Discourse Representation Structure which this paraphrase explicates is given in Figure 3· Figure 3 reads as follows. There is an eventuality ev which is a part of an eventuality of Surii composing a poem. We call ev the described situation and Surii's composition of a poem the characterizing situation. The use of the predicate Impfv encodes our hypothesis that Thai accomplishment stems are fundamentally biased toward imperfectivity. The meaning of the condition that includes this predicate (hereafter, condition o:, see (3oa)) is given in (3ob).10

r64 How to End Without Ever Finishing: Thai Semi-perfectivity

(3 I )

Martha composait un rondo (quand on sonna Martha compose.IMPF.PST a �:ondo (when INDEF ring.PFVE.PST a la porte) at the door) 'Martha was composing a rondo (when someone rang the bell).' b. Martha composait un rondo tous les jours Martha compose.rMPF.PST a rondo every the days (quand elle etait jeune) (when she be.IMPF.PST young) 'Martha used to compose a rondo a day (when she was young).' a.

12

Many analyses of the progressive assume that the progressive shifts the aspectual class of the verb constellation from a non-stative evenruality to a state (see Herweg 1 99 1 a; Kamp & Reyle 1993: S76 and de Swart 1998, among others). Since condition o is included in the semantic translation of stems (see the appendix), it is impossible to determine whether or not the operator lmpfv shifts the aspectual class of the verb constellation to which it is added. 1l Portner's ( 1998) definition of the progressive operator is in term of time intervals i and ; ' rather than eventualities ev and e'. His proper inclusion requirement therefore applies to time intervals: i must be a non-ftnal subinterval of i'. Nothing substantial hinges on this difference.

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Our characterization of the semantics of Impfv focuses on the non­ habitual, progressive translation of Thai bare stems illustrated in (2 r ) and (22) . It embodies the hypothesis that the simple past translation we give for sentence (2 r ) corresponds to pragmatically induced interpreta­ tions that bare stems can receive in context, not to additional meanings they might have; only the progressive and habitual translations corre­ spond to meanings. Furthermore, we do not explicitly discuss how the habitual reading of Impfv arises. We assume the same mechanism which leads to the availability of habitual readings of imperfective operators in other languages is also at play in Thai (see Smith 1 997 for some details). Our analysis of the semantics of Impfv closely parallels modal theories of the progressive. In both cases, sentences describe subparts of eventua­ lities. But, despite this parallel, the predicate Impfv differs from ordinary progressive operators in one important respect.12 Ev is not required to be a proper subpart of e' . 1 3 This relaxation of the constraint on the relation in which ev and e' must stand is critical to the analysis of Thai semi-perfective markers, as we will shortly see. This difference between the predicate Impfv and traditional analyses of the progressive operator PROG is motivated by the different functions of the two operators. The English progressive marker modifies a stem whose tense form would otherwise transparently describe eventualities of the type denoted by the verb constellation, as we discussed in section r . It is thus fitting to treat the progressive as an aspectual shift operator. The function of the predicate Impfv, on the other hand, is merely to characterize the

Jean-Pierre Koenig and Nuttanart Muansuwan 165

14 The addition of na- results in a complete event description, according to Zucchi. The Russian sufftx na- thus contrasts with Thai k\im. It is a {completive) perfective marker, not a semi-perfective marker.

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described eventuality ev, with the help of a description of the type of eventuality e' which would ensue, if ev were completed. The inclusion of an additional Impfv operator might seem unsatisfactory to some readers since it adds some complexity to the lexical meanings of Thai accomplishment stems. They always include two pieces of meaning, a basic relation among participants in the described eventualities and an aspectual operator mapping this class of situations onto their subparts. Furthermore, the inclusion of two meaning components in the semantics of Thai accomplishment stems blurs Verkuyl (1993) distinction between inner and outer aspect. The basic relation between participants in the described eventualities belongs to the accomplishment Aktionsart and is a component of the sentence's inner aspect. The Impfv operator pertains to what Verkuyl calls outer aspect in that its semantic import, once the relation is saturated, is to map an event description onto another event description. Thus, Thai accomplishment stems comprise both a component that is traditionally viewed as part of inner aspect and a component that is traditionally viewed as part of outer or grammatical aspect. Can such a complexity be avoided? We do not think so, as suggested by the fact that others who have discussed similar phenomena include, explicitly or implicitly, the same kind ofcomplexity in the lexical meaning of stems. Talmy (1991) and Talmy (2ooo), for instance, discuss a similar phenomenon in Chinese in terms of the concept of implicated fulfilment verbs. Such a notion clearly requires Chinese accomplishment stems to include information relative to the sought-after telic result (the fulfilment) and an indication that it need not be reached (that it is only implicated). Zucchi's (1 999) use of Parsons' notion of incomplete events to model the seemingly similar behavior of certain Russian verb stems might suggest we could avoid our two meaning components analysis. A Zucchi-style analysis would, for instance, say that the Thai accomplishment stem ti:cl) 'to compose' simply denotes incomplete (or non-necessarily complete) events of composition. But, in fact, such an analysis would not lead to a reduction in the complexity of the semantics of Thai bare stems since the concept of incomplete event is itself complex. It must include both information relative to what the completed event would be and an indication of the relation between the incomplete event and its completion. Zucchi's use of the predicate Cui to model the effect of adding the perfective prefix na- to Russian incomplete event denoting stems demonstrates this.14 The predicate Cui is meant to account for the following observation. Whereas occurrences of inflected forms of the root pisat' 'to write' denote

r66

How to End Without Ever Finishing: Thai Semi-perfectivity e ev x y Surii (x)

Max (e,

poem (y) lmpfv (ev, 'M'

Figure

4

An example of a

DRS

Ix

compose y I

for a sentence containing a bare verb stem and kh im

x

(32) a. ,\Q,\z,\e [writing(e) 1\ Agent(e, ) 1\ Theme(e, Q)] b. :Je [writing(e) 1\ Agent(e, John) 1\ Theme'(e, a letter)] c. :Je :lt [writing(e) 1\ Agent(e, John) 1\ Theme'(e, a letter) 1\ Cul(e, t)] By including the operator Cui, (32c) insures that the event corresponding to e culminated. But what event? The same event e of writing a letter, which is described by the formula in (32b) as incomplete. The stem pisat' must therefore include enough information relative to what kind of eventuality writing ( e) can describe that we know whether or not Cul(e, t ) is satisfied. This is tantamount to saying that the stem must include information about what a culminated instance of writing ( e) is as well as information to the effect that the event e did not necessarily culminate. As was the case for Talmy's concept of implicated fulfilment, the notion of incomplete event informally includes the two components of meaning our representation of the meaning of Thai bare accomplishment stems explicitly includes.

3·3

The semantics of semi-peifectivity

Equipped with our characterization of the aspectual interpretation of bare sentences, we can easily represent the semantic contribution of non-

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incomplete events, inflected forms of the stem napisat' 'write out' describe complete events. Thus, if napisat' is used in a sentence which describes John's activity of writing a letter, the sentence entails that the letter was completed. The Parsons-style formulas in (32) illustrate this observed shift in meaning which the prefix na- carries. (32a) is Zucchi's semantic translation for pisat', (32b) is the formula which results from combining pisat' with the relevant arguments, and (32c) is the formula which results from prefixing na- to pisat' before combining its with its arguments.

Jean-Pierre Koenig and Nuttanart Muansuwan 167

completive perfective or semi-perfective markers, like Thai k1'rim. Sentence (9) which contains this semi-perfective marker (repeated below as (3 3a)), can be paraphrased informally as in (3 3b). kb:m khum (33) a. Surii ti:co Surii compose poem ascend 'Surii composed/will compose a/the poem.' b. There is an eventuality ev which is a subpart of an eventuality e' such that in 'inertia' worlds, e1 is an eventuality of Surii composing a poem; AND, in the 'real' world, there is no e" of which ev is a proper subpart and which is a subpart of e1•

(34) The referent of a discourse marker e satisfies the predicative condition Max (e, ¢) if and only if e is the largest eventuality which satisfies ¢, that is, if there is no eventuality e" such that e C e" which satisfies the eventuality description ¢. The condition Max (e, ¢) encodes the fact that kh rim indicates that e is bounded with respect to the eventuality description encoded by the VP over which it has scope. Formally, it is interpreted as an operator that maps an eventuality description onto another eventuality description. The fact that the eventuality description ¢ that Max takes as argument includes a predicate whose semantics includes a modal component (the predicate Impfv) ensures that the boundedness of e does not entail completion of the eventuality description by which e is characterized. Note that if the composition of the poem was completed, Max (e, ¢) requires e-not a larger event of which e is a part-to be that event of Surii composing a poem, a consequence which accords with our empirical data. Sentence (3 3a) can describe a situation in which Surii completed the poem. In Smith's (1997) terms, the 'natural' boundary of the situation in which Surii wrote a poem and the 'arbitrary' boundary of the situation which the sentence describes coincide in this use of (3 p) and the inclusion of the described situation in the characterizing situation is not proper. Hence our relaxation of the inclusion requirement in the semantics of Impfv in (3ob). Now that we have formally defined the semantic contribution of kh rim, let

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The relevant DRS for this sentence is diagrammed in Figure 4· The additional condition which semi-perfective markers such as k\im introduce follows AND in the informal paraphrase in (3 3b), namely that ev is a maximal subpart of the continuations e' that would fit the eventuality description of Surii writing a poem. This condition corresponds to the notion of the terminal point of an event relative to an event-description ¢ in Krifka (1989). The definition of the condition is shown in (34) below (c stands for a (strict) part-whole relation on eventualities).

168 How to End Without Ever Finishing: Thai Semi-perfectivity

us return to the interaction of the semi-perfective with duration and interval adverbial phrases. Our observation was that sentences that include k\ im can felicitously combine with interval adverbial phrases, but not duration ones. This suggests that Thai semi-perfective sentences are telic, an expected property for an aspectual marker traditionally classified as perfective.15 But matters are more complex. Another diagnostic of telicity-one that is often part of the definition of telicity-is the anti -subinterval property stated below in (3 5) (to be compared to the subinterval property given in (36)).

Whereas atelic sentences obey the subinterval property stated in (36), telic sentences obey the anti-subinterval property. Informants report that the truth of sentences such as (3 3a) at time interval t is compatible with its truth at interval t' properly included in t, suggesting that sentences that include kh wn are not telic after all. Thus, sentences that include the perfective marker k\ im pass one test of telicity (the ability to co-occur with interval in-phrases), but fail another (the anti-subinterval property). The cause of this split behavior is easy to explain when the 'intensionality' of the notion of telicity is taken into account. As convincingly argued in Krifka ( 1989, 1998), telicity is a property of eventuality descriptions rather than of eventualities themselves. One and the same eventuality can be telic or atelic depending on how it is described. Krifka (1998) defines telicity as follows (p. 206): 'we can characterize telicity as the property of an event predicate X that applies to events e such that all parts of e that fall under X are initial and final parts of e.' The fact that teliciry applies to eventuality descriptions explains why sentences containing k\u n do not conform to Krifka's definition of telicity. k\ im is added to sentences containing bare sterns which are atelic. It adds the information that the eventuality stopped. Speakers do not interpret this assertion of the presence of a boundary as adding to the eventuality description associated with bare sentences. In other words, speakers take the whole DRS in Figure 4 to be a description of the eventuality denoted by 1 5 As we mentioned earlier, (a )telit, in this paper, is taken to be a property of event descriptions and as such can apply either to verb constellations that are not modified by outer or grammatical aspect operators or to the output of the application of such operators (assuming they are modeled as functions from event descriptions to event descriptions).

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(35) ANTI-SUBINTERVAL PROPERTY: If an eventuality description ¢ applies to a situation s whose temporal trace is t, it does not applies to any situation s' properly included in s whose temporal trace t' is properly included in t. (36) SUBINTERVAL PROPERTY: If an eventuality description ¢ applies to a situation s whose temporal trace is t, it applies to (all) situations s' included in s whose temporal traces are included in t.

Jean-Pierre Koenig and Nuttanart Muansuwan 169

(3 7) Max( e , ¢)

+-->

( ¢ (e)

1\

( • 3e" E UE[e C e" 1\ ¢( e") J ) )

(37) says that an event e is maximal with respect to a description ¢ if and only if there is no larger event e" which satisfies ¢. It is clear that if a description ¢ is telic in Krifka's sense, then every event which satisfies it is maximal with respect to ¢. Otherwise, two events e and e" such that e is properly included in e" would satisfy ¢; e would then be an event which both satisfies ¢ and is not a final part of e", contra Krifka's definition of telicity. Of course, maximality is weaker than telicity since it does not preclude the existence of an event e" smaller than e which satisfies ¢. The contrast between maximality and telicity provides a formal definition of the informal distinctions between natural and arbitrary boundaries or between boundedness and telicity found in Smith ( 1997) and Depraetere (1995), respectively. The operator Max also ressembles de Swart (1998) function BOUND which maps a state onto a quantized portion of the state. It differs from it in two points. First, its input is not a state, but an eventuality. That the input to the operator denoted by kh rim can be a dynamic eventuality is best demonstrated by its effect on achieve­ ment verbs. If the input to Max was required to be a state, its application to an achievement verb constellation would require the eventuality description encoded in (I Ia), repeated below in (3 8a) to be first coerced into a stative eventuality description. The ensuing effect of this coercion would parallel the often discussed effect induced by the application of the English progressive to achievement verbs illustrated in sentence (39) and we would expect (38b) to carry a similar interpretive trace of this coerc10n.

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the discourse marker ev included in the second argument of the operator Max and still conceive of the description of ev as that of an eventuality that is a part of a larger, maybe non-completed, eventuality e' in which Surii wrote a poem. The description of ev is therefore still not telic: a proper subpart of ev is also a subpart of e' and therefore satisfies the characterization of ev encoded by the verb constellation. The failure of sentences that contain kh rim to obey the anti-subinterval property still raises the question of how we shall semantically characterize the boundedness of events described by sentences containing k\ un. It turns out that characterizing this non-telic notion of boundedness is a simple generalization of Krifka's notion of telicity, which we call maximality and is encoded in our Max operator. We define the notion of an event's maximality with respect to a description ¢ in (37) (UE stands for the set of eventualities).

1 70

How to End Without Ever Finishing: Thai Semi-perfectivity ev n s x y

Surii (x) ev -v-. s poem (y)

r (ev) s n

Imp.fv (ev, A.e' 1 x compose y j)

Figure

5

An example of a

DRS

for a sentence containing a bare verb stem and

maa

But neither sentence in (38) conveys the reading that the (coerced) stativization of an achievement predicate typically conveys. The absence of any such interpretive aftermath suggests that the semantic contribution of kh cim (namely the operator Max) does not require states as input. Second, it is not clear that the semantics of de Swart's BOUND operator is appropriately sensitive to the eventuality description it takes as input. By contrast, the semantics of the operator Max as we stated it in (37) crucially depends on the nature of the description ¢. To understand the need for this relativization of Max to eventuality descriptions, consider the following, felicitous context of use of sentence (33a). Surii did finish composing a poem. In fact, she composed two other poems afterwards. Thus, the eventuality described by (3 p) is included in a larger eventuality of Surii writing three poems. A strictly 'extensional' definition of Max such as the one in (4o) is therefore inadequate: a larger eventuality of which the eventuality of Surii writing one poem is part does exist. • 3e11 E UE[e C e"] (4o) Max(e) +---1

By including the additional constraint ¢(e") in (37) VvTc capture the fact that what k\ un indicates in sentence (33a) is that there is no strictly larger eventuality that can be characterized as a subpart of Surii writing a poem. Our analysis of semi-perfectivity ressembles Talmy's (1991, 2ooo) analysis of Chinese sentences containing -le; like his, our analysis of Thai aspect hypothesizes a lexical basis of semi-perfectivity. We claim that the Impfv operator is lexically associated with accomplishment stems (either

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(38) a. k�;Jd ri?-b�;Jd happen explosion 'There was an explosion/There used to be explosions.' b. B;)d ra? -b�;)d khilln happen explosion ascend 'There was an explosion.' (39) The bomb was exploding.

Jean-Pierre Koenig and Nuttanart Muansuwan

171

I.

2.

an Impfv operator associated with accomplishment stems; a Max operator associated with the semi-perfective marker kh r.im or -le.

Furthermore, by contrast to Smith, we provide a formal account of the interaction of Impfv, Max, and the non-aspectual predicates contributed by verbal stems.16 3 ·4

The semantics of the Thai peifect marker

Finally, we propose the following analysis of the perfect marker maa. The meaning of sentence f25) (repeated below as {41a)) is paraphrased in {41b). As was the case for k rim, the contribution of maa follows AND. (41) a. Surii tccu kb:m maa Surii compose poem come 'Surii has composed/is composing a/the poem.' b. There is an eventuality ev which is a subpart of an eventuality e' such that in 'inertia' worlds, e' is an event of Surii composing a poem; AND ev occurred in the past; AND ev can be associated with a final boundary which entails the presence at the time of utterance of a state s. The 16

DRS

that corresponds to this paraphrase is represented in Figure

S·

Our analysis ressembles somewhat more Park's (1993 ) suggestion that a modal operator be used

to represent seemingly corresponding data in Korean. We would like to thank Roberr Van Valin for pointing out this parallel to us.

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directly or through redundancy rules or templates). Similarly, while Smith {1997) attributes the absence of an entailment of completion in (s) to the perfective marker -le, Talmy attributes it to the lexical semantics of Chinese accomplishment verbs, which, as we mentioned earlier, he dubs implicated fulfilment verbs. But Talmy does not precisely describe what makes Chinese accomplishment verbs implicated fulfilment verbs. Nor does his analysis explicitly relate the semantics of Chinese implicated fulfil­ ment verbs to corresponding English attained-fulfilment verbs. By contrast, our analysis of Thai semi-perfectivity explicitly models the relation between English-style and Thai -style accomplishment verbs. Thai verbs embed English -style accomplishment semantics inside of an aspectual Impfv operator. Because both Impfv and Max are aspectual operators, our account is also similar to Smith 1997 analysis of Chinese -le discussed in section I . But whereas Smith entirely attributes the semi-perfectivity of sentence (s) to -le, we claim semi-perfectivity arises from the combination of two factors:

1 72

How to End Without Ever Finishing: Thai Semi-perfectivity

The DRS in Figure 5 follows the representation of the perfect presented in K.amp & Reyle (1993) but for the substitution of the notion of resulting state to that of abuting state in conformity with van Eijck & Kamp ( 1 997). It says not only that the temporal trace of ev (or r(ev)) precedes or overlaps with speech time (represented by n) and that ev is characterized by condition a, but also that ev resulted in a state s that holds at speech time. This representation covers both usages of maa in which ev has ended before speech time, but ev's resulting state still presently holds and usages of maa in which ev is still currently holding. Thus, we use the word resulting (represented in the figure by ) as a cover term for a loosely defmed notion of consequence which subsumes both so-called existential and resultative readings of perfect markers. We cannot attempt to solve the complex issue of the semantics of the notion of result in this paper (see Michaelis 1998 for a comprehensive survey). But we need to describe in more detail the possible contextual interpretations of sentences that contain maa in order to account for the unfelicity of sentence (27), repeated below for convenience. �

#

h Surii ti:ciJ kb:m k wn maa ti:c jao maj sed Surii compose poem ascend come but still not finish 'Surii composed a/the poem but did not finish it yet.'

We first note that maa can receive both existential and resultative readings (McCawley 197 1). Sentence (43) illustrates the existential reading (using the before test discussed in Michaelis 1998). Sentence (41a) (under the non-progressive reading) illustrates the resultative reading. (43) chin kin h3::lj -tiak maa b:m I eat snail come before 'I have eaten snails before.' Second, even when maa combines with verbs that belong to the class of accomplishments and receives a resultative reading, it does not require the event to be completed, as (44) shows and is marked in Figure 5 by the predicative condition r (ev ) ::; n. Determining what resulting state of current relevance is involved in such cases requires the contextualization of sentences like (44). Sentence (45) illustrates th1s. (44) th::�;} teco naosiinu maa tee ka;}d puaJ cwo maJ teco she write book come buthappen sick therefore NOT write tJ::l continue 'She has written a book, but she got sick, so she did not continue.'

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(42)

Jean-Pierre Koenig and Nuttanart Muansuwan

173

en ev "'-"+ s T (e) s n ev x y

Surii (x)

Max (e,

poem (y) lmpfv (ev,

Figure 6 An example of a

DRS

)

f..e' I x compose y I )

for a sentence containing both k\m and

maa

The following situation is one possible context of interpretation for (45). The addressee is a native speaker of Thai and knows French much better than English. She is afraid of writing an article in French. She has written part of a book in English (say, r so pages), but never finished it (she realized its content was not stellar, although the English was quite good). Under those circumstances, the utterance of (45) is felicitous and the second clause expresses the state of current relevance that maa requires. Crucially, this resulting state does not depend on the completion of the book. Third, we follow Depraetere (1998) and assume that the notion of current relevance often used to characterize the resultative interpretation of the present perfect covers two classes of relations between the past event and the state that holds at speech time (between the referents of ev and s in Figure s). Both are illustrated in (46) (adapted from Depraetere's example ( r o)). (46) a. Susan has watered the plants. b. The plants have been watered. c. Susan must be recovering as she has managed to water the plants. (46b) describes one possible currently relevant state for the interpretation of (46a). This state is entailed by sentence (46a). (46c) describes another possible currently relevant state for the interpretation of (46a). But the relation between (46a) and (46c) is this time one of conversational implicature (more precisely, particularized conversational implicature) in

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(45) khun tCCIJ nai)SWw phaa5aa ?al)-krid maa, bot-kwam phaa5aa language you write book language English come article fariiJseed k5? IJiaj French then easy 'You have written a book in English, so (writing) an article in French is easy.'

174 How to End Without Ever Finishing: Thai Semi-perfectivity

the sense of Grice (1975). More generally, currently relevant states can be related to the past event described by sentences containing a perfect marker either via implicatures or lexical entailments.17 The discussed contextual interpretation of sentence (45) shows that even in the case of verb constellations that belong to the class of accomplishments, the resulting state which maa requires to presently hold need not be related to the described event through lexical entailment. Thus, sentence (45) does not require the book to be finished; that is, the lexically entailed state need not hold at speech time. The state of current relevance whose presence maa demands is in this case the one described by the second clause: writing an article in French is now easy for the addressee.

The pragmatics of combining the semi-perfective and the perfect markers

Having formally described the aspectual interpretations of bare sentences and sentences that contain a single aspect marker (the semi-perfective kh cim or the perfect maa), we can discuss the aspectual interpretation of their combination. As mentioned previously, when both markers co-occur, the completion of the event which the sentence describes (the event whose corresponding discourse marker in the previous figure was ev) seems entailed. The relevant sentence is (42), the first clause of which is repeated below in (47a). Adding kh cim excludes interpretations of the sentence in which the characteristic eventuality ev is still going on at speech time. Ev must have ended prior to speech time, although, the presence of maa requires a resulting state of ev to currently hold. A paraphrase of the contextual semantic value of sentence (47a) is given in (47b). The DRS derived by merging the DRS in Figures 4 and 5 is diagrammed in Figure 6. h (47) a. Surii tcclJ kb:m k illn maa Surii compose poem ascend come 'Surii has composed a/the poem. b. There is an eventuality ev which is a subpart of an eventuality e' such that in 'inertia' worlds, e' is an event of Surii composing a poem; AND, in the 'real' world, there is no e" of which ev is a proper subpart and which is a subpart of e' ; AND ev occurred in the past; AND ev can be associated with a final boundary which entails the presence at the time of utterance of a state s.

Since neither of the 17 As mentioned in fn.

r,

DRS

from the merger of which the

DRS

in Figure

6

we must here relativize the notion of lexical entailment to ftllers of

argument positions which are specified quantities.

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3.s

Jean-Pierre Koenig and Nuttanart Muansuwan

175

derives requires the poem to have been completed, the resulting DRS does not either. How can we, then, account for the infelicity of (42)? We claim that sentence (47a) does not in fact entail that Surii finished the poem, although it strongly implicates it. It merely requires that the composition event be finished, which the sentence without k\ un does not, as Figure s shows. To understand why sentence (4 7a) strongly implicates the comple­ tion of the poem, we must first consider an interesting additional restriction on the use of the perfective marker kh rim, which we have not heretofore discussed and which sentences (48a) and (49a) illustrate. (48 ) a. Surn tham khwaam sa' ')I aa ' d bAaan kh wn Surii do NOM clean house ascend 'Surii cleaned the house.' ' ') aa b. Surn tham khwaam sa' d bAaan maa Surii do NOM clean house come 'Surii has cleaned the house.' S ' ')' I aad bA c. urn tham khwaam saaan khwn maa clean house ascend come Surii do NOM 'Surii has cleaned the house.' . kh tan kl:>:>n phaasaa . f:araiJSee ' d bon kr'adaan kh wn (49) a. chan I write poem language French on blackboard ascend 'I wrote a poem in French on the blackboard.' . . kh .tan kl :>:>n phaasaa f:aral)see ' ' d bon kr'adaan maa b . chan I write poem language French on blackboard come 'I have written a poem in French on the blackboard.' Consistent with our analysis of semi-perfective kh wn, (48a) does not entail that the house was entirely cleaned. But its interpretation requires that the subportion of the house that was cleaned remains clean at speech time. Similarly, (49a) does not entail that the poem was entirely written on the board, but its interpretation requires that the portion of the poem that was written remains on the blackboard at speech time. This additional interpretive constraint does not hold when maa replaces kh wn. Thus, (48b) can felicitously be uttered if the portion of the house which was cleaned got dirty before speech time and (49b) is felicitous if the portion of the poem that was written on the board has been erased before speech time. The additional condition on the interpretation of kh wn that we illustrated with sentences (48a) and (49a) provides the key, we believe, to the strength of the implicature of completion, which sentences that combine kh wn and maa typically induce. The constraint that the partial result of the subpart of the accomplish­ ment that was carried out lasts until speech time renders kh wn similar to a present perfect. But, by contrast to true present perfect markers, the A

o o

o o

A

y

y

A

'

•

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1

0 0

1 76 How to End Without Ever Finishing: Thai Semi-perfectivity

reference time of kh rim sentences is not the time of utterance, but the past interval at which the event occurred. The fact that sentences containing kh t.im can combine with temporal adverbials such as mwa-waan-nii 'yester­ day', but not t:xm nii 'now' supports our claim that kh wn is not a perfect marker. The fact that the reverse is true of maa confirms that it is indeed a perfect marker. Sentences (so) and (s 1 ) illustrate. h (so) a. Surii tham k waam sa-?iad baan khwn mwa-waan-nii

Surii think word answer exit then write report ascend dak nan th;};} tham ?aa-haan khwn leave that she do food ascend 'Surii found the solution, then she wrote the report. Mter that, she cooked.'

Sentence (45) shows that, in general, the state of current relevance whose existence is guaranteed by maa may be derived via particularized conversa­ tional implicatures. Why, then, does the derivation of the resulting state via lexical entailment appear to be the only available option when maa combines \.vith kh Wn, as in sentence (42)? We say appear, because despite what sentence (42) suggests, lexical entailment is not the only possible source of the resulting state for sentences which contain both kh wn and maa. Consider the sentences in (s 3). (s 3a) can receive a resultative reading either via lexical entailment or implicature. (5 3b) requires that a partial, lexically entailed, result hold at speech time (the portion of the book which was written must still exist). Finally, the resultative reading of (s3c), like that of

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Surii do NOM clean house ascend yesterday 'Surii cleaned the house yesterday.' b. *t;:,:m nii Surii tham khwaam sa-?iad baan khwn moment this Surii do NOM clean house ascend 'Surii cleaned the house now.' (5 1) a. *Surii tham khwaam sa-?aad baan maa mwa-waan-nii Surii do NOM clean house maa yesterday 'Surii has cleaned the house yesterday.' b. t;:,;:,n nii Surii tham khwaam sa-?iad baan maa clean house maa moment this Surii do NOM 'Surii cleaned the house now.' Furthermore, the fact that kh wn-but not maa-can be used in story telling-a genre that favors perfective markers and tends to exclude perfect markers-confirms the results of the frame adverbials test. The discourse in (52) illustrates this. (The same discourse with maa substituted for kh wn is ungrammatical.) (52) Surii khid kham t;:,;:,b ??l;:,k cwu khian raaj -IJaan khwn

Jean-Pierre Koenig and Nuttanart Muansuwan

1 77

(5 3a), can stem from a lexical entailment or a conversational implicature, but it additionally requires that the portion of the book that was written still be available at speech time. (5 3) a. Surii tcru nauslirw kh5:>IJ th�� maa come khurn ascend khurn maa ascend come

The implicature-driven resultative reading of (53c) is certainly not its favored reading, but it is possible. One possible such contextual interpreta­ tion of (53c) is paraphrased in (54). The sentence in bold represents the additional constraint on the interpretation of k\ im we discussed in the context of sentences (48a) and (49a). The sentence in italics represents the particularized implicature-based resultative reading induced by maa. (54) Surii partially wrote a book in the past (but did not complete it). The p art that was written is still available. (Since it's difficult to write) she's exhausted. Situations that fit the interpretation paraphrased in (54) are rare and this explains why, outside of particular contexts, (42) is unfelicitous. But the cause of this unfelicity is pragmatic and not semantic, as shown by the fact that (5 3c) can receive an implicature-driven resultative reading. Further­ more, we can easily account for the decreased salience of the implicature­ based resultative reading when k\ im precedes maa. Michaelis (1998) notes that the lexical entailment reading of resultative perfects is the favored reading for verb constellations that belong to the accomplishment class. The presence of k\ un, which requires that a lexically entailed partial result of carrying out the accomplishment still holds at speech time, only reinforces this interpretive bias toward a lexically based resultative reading. Hence the strength of the implicature of completion reflected in the judgment in (42).

4 CONCLUS I O N Although perfectivity is often assumed to entail completion of events that belong to the accomplishment class, several languages possess perfective

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Surii compose book of she 'Surii has composed her book.' nauslirw kh5:>IJ th�� b. Surii tCCIJ Surii compose book of she 'Surii composed her book.' c. Surii tCCIJ nal)SWw kh5:>IJ th�� Surii compose book of she 'Surii has composed her book.'

178

How to End Without Ever Finishing: Thai Semi-perfectivity

18

APPEN D I X : C O M P O S I T I O NAL C O N STRUCTION RULE S F O R S IMPLE THAI SENTENCES This appendix contains sample lexical semantic translations necessary to the constructions of the

DRS

for the simple sentence types we discuss in this paper. We adopt the

compositional and linear version of

DRT

advocated in Zeevat

1989

and van Eijck

&

1 8 Ikegami (1985) discusses a seemingly similar phenomenon in Japanese, but our consultants did not confirm his analysis. Whether Slavic non-completive perfective markers also belong in this group is unclear to us, because of the high degree of lexicalization displayed by Slavic imperfectives and perfectives.

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markers that contravene this assumption (those we call semi-perfectives). Scholars who have discussed semi-perfective markers either remain informal in the description of their semantics or provide an inadequate model of it. This paper tries to remedy this gap and presents a formal account of the semantics of semi-perfective markers based on a description of a portion of the Thai aspect system. Our model of Thai semi-perfectivity relies on the inclusion of an imperfective operator in the lexical meaning of Thai accomplishment verbs and the notion of maximal event relative to an event description. This latter notion, inspired by Krifka's 1 99 8 definition of telicity, is strictly weaker than telicity: any event which satisfies a telic event description ¢ is maximal relative to ¢, but the converse is not true. Our paper thus demonstrates that (a)telicity is not the sole property of event descriptions relevant to the semantics of grammatical aspect; mere maximality sometimes matters too. Furthermore, by providing a model of semi-perfectivity which extends existing theories of telicity, the notion of event maximality grounds the informal notions of arbitrary boundary and atelic boundedness discussed in Smith ( 1 997) and Depraetere ( 1 995 ). We also argue in this paper that Thai accomplishment sentences never mark completive perfectivity; they always describe subparts of telic eventualities and leave it to processes of pragmatic enrichment to determine whether an event description that belongs to the class of accomplishments was completed. We demonstrate that even in circumstances where completion seems to be marked-that is, when the perfective and perfect markers combine-completion is merely a strong implicature. Although our analysis of semi-perfectivity was based exclusively on Thai, we believe it extends to other South Asian and East Asian languages for which a similar phenom­ enon has been reported. These include Chinese (see e.g. Talmy 1 99 1 ; Smith 1 997) , Hindi (see e.g. Singh 1 99 1 ) , Korean (see e.g. Park 1 993 ), and Tamil (see e.g. Paramasivam r 977). Whether an analysis along the lines of the one we proposed for Thai fits all these languages is left for future work.

Jean-Pierre Koenig and Nuttanart Muansuwan

Table

179

2 Some words of Thai

Word

Translation

Type

kb:m

>.P(a & poem(a) & P(a)) >.P(b & Surii(b) & P(b)) >.P>.c>. e 2 (P>.d(!mpfv(e , >.e , compose(e , , c, d ) ) ) ) >.P>.c>.e3 ( Max(e3 , P(c) ) ) >.P>.c>.e, (s & P(e, ) (c) & e4 ....... s) >.P(e5 & P(es ) )

( (e, T), T) ) ( (e, T) , T)) ( ((e, T), T), (e, (e, T) ) ) ( (e, ( e , T))(e, (e, T) ) ) ( (e , (e, T)) , (e, (e,T))) ((e, T) , T)

'poem' Surii 'Surii' tll: l) 'compose' khum 'ascend' maa, 'come'

Kamp

(1997). Table 2

lists the semantic translations and types of a few Thai words which

illustrate the semantic issues on which this paper concentrates. The relative complexity of the translations is the result of two factors:

2.

parameters introduced by the VPs over which they have scope. Our assumption that semantic composition proceeds as dictated by surface constitu­ ency. Clauses in the translations that consist of single letters from the upper half of the

alphabet, such as

a,

introduce discourse markers and correspond to variables at the top of

boxes in the box representation we have used until now. All other clauses correspond to predicative conditions.

&

is a merge operator which can be thought of as a dynamic form

of conjunction. (See van Eijck

& Kamp (1997) for details on various possible interpretations (55 b) in box representation.

of merge operators.) ( s 5 a) thus corresponds to

(55) a. a

&

poem (a)

a b.

poem (a)

The lexical meanings summarized in Table

2

give rise, after ,8-reduction, to the

semantic translations of the numbered nodes of Figures

(58),

7,

8, and

respectively.

( 56) EJ ,\c,\e2 (a & poem( a) & Impfv(e2 , >.e , compose(e. , c , a)))

[±] [l] [±] (57) EJ [±] ( 58) EJ [±]

9 shown in ( 56), (57), and

,\c,\e3 (Max(e3 , Ae2 (a & poem(a) & Impfv(e2 , >.e , compose(e. , c, a) ) ) ) ) ,\e3 (b & Surii(b) & Max(e3 , Ae2 (a & poem(a) & Impfv(e2 , >.e, compose(e. , b, a ) ) ) ) ) (e5 & b & Surii(b) & Max(e5 , >.e, (a & poem(a) & Impfv(e, , >.e , compose(e. , b , a ) ) ) ) ) ,\c,\e4 (s & a & poem(a) & Impfv(e4 , >.e , compose(e, , c , a)) & e4 .,... s) (e5 & b & Surii(b) & s & a & poem(a) & Impfv(e5 , >.e, compose(e. , a, b) ) & e5 .,... s) >.c>.e4 (s & Max(e4 , >.e, (a & poem(a) & Impfv(e, , >.e , compose(e, , c, a) ) ) ) & e4 .,... s) (e5 & b & Surii(b) & s & Max(e5 , >.e, (a & poem(a) & Impfv(e2 1 >.e,compose(e. , c, a ) ) ) ) & e5 .,... s)

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I. The need to make available to the perfective and perfect markers the eventuality

1 80 How to End Without Ever Finishing: Thai Semi-perfectivity

V PIII

NP

I

�

VPUJ

Surii

�

V

NP

tEEI)

kb:m

I

I

A Thai sentence which contains kh rim

7

SIII

�

s

�

V PITJ

NP

�

I

ymax

VP

Surii

�

V

NP

tEEI)

kb:m

I

I

I

maa

Figure 8 A Thai sentence which contains

maa

SIII

� � s

V PITl

NP

I

�

ymax

VP

S urii

�-�

ymax

VP

�

v

NP

tE£1)

kb:Jn

I

Figure

9

I

maa

I

k h wn

A Thai sentence which contains khrim and maa

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Figure

Jean-Pierre Koenig and Nuttanart Muansuwan 1 8 1

khrim.

The DRS embeddings that result from the semantic representations of aspectual operators have an unintended adverse consequence that we cannot fully address in this paper. Discourse markers corresponding to a subset of NPs-all posrverbal NPs in our paper and van Eijck & Kamp's (1997), all NPs in de Swart (1998)-may be introduced in embedded DRSs when aspectual operators which have VP or sentential syntactic scope modify main verbs. These discourse markers are nonetheless accessible to cross-sentential anaphoric pronouns, as the English discourses in (59) demonstrate: (59)

a. John was talking to a woman,. She; looked unhappy. b. John has written a book1 on this issue. I!j is quite good.

Established definitions of accessibility within DRT render the discourse markers introduced by the NPs a woman and a book impossible antecedents of the pronouns she and he in de Swart's (1998) analysis of the English progressive or in van Eijck & Kamp's (1997) analysis of the English perfect. 1 9 This prediction is clearly not borne out. Amending the definition of accessability to accommodate such discourses is not difficult, but it comes at a cost: a purely structural definition of accessability is not longer feasible. We conclude this appendix by providing the model-theoretic interpretation of the two aspectual operators on which our analysis of semi-perfectivity relies, lmpfv and Max. For 1 9 Determining whether sentences which include Max are similarly problematic is difficult in view of the prevalence of null anaphors in Thai

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A few more comments on our semantic translations are in order. First, we included the Impfv operator directly in the semantic translation of the word tU:v 'compose'. A linguistically more appropriate representation would let a lexical redundancy rule or template introduce this operator, which the semantic translation of all Thai accomplish­ ment verbs must contain. We leave the formulation of such a rule or template to another occasion. Second, since maa can adjoin to a VP which may or may not contain khiun and neither khiun nor maa need occur, the final reduction of the A-abstracted eventuality variable that the semantic translations ofVPs include must be left to a constituent that has scope over the largest VP. We decided to ascribe this fmal ,8-reduction to the end of sentence marker ' . ' which already carries a semantic function in linear compositional DRT. (For ease of exposition, we left out of the translations the other semantic contribution of end of sentence markers.) The semantic translation of any verb or operator that takes a propositional argument would also need to effect the ,8-reduction of this eventuality variable. Third, the desire to provide a compositional treatment of aspect sometimes leads to a nesting of DRS. van Eijck & Kamp's ( I 997) analysis of the English perfect already requires one level of embedding. So does de Swart's (1998) analysis of the progressive as a sentential operator or our analysis of the Max operator. These embeddings are mere technical artefacts of the fact that, within a compositional approach to DRT, operators cannot just grab eventuality descriptions such as Impfv(e, .Xe' compose(e' , c, a)) to serve as an argument of an aspectual operator such as Max. The entire semantic representation of the constituent over which Max has syntactic scope must serve as one of its arguments. To get around this purely technical need for DRS embeddings, we could adopt a metalanguage that provides us with the ability to 'grab' arbitrary sub-representations, such as a Feature Logic of some kind (see Carpenter 1 992). But such a move would require a complete restatement of DRS construction rules. We opt for a more conservative approach and simply accept an additional level of DRS embedding in our representation of sentences which contain

r82 How to End Without Ever Finishing: Thai Semi-perfectivity convenience, we state the interpretive rules in terms of the notion of an embedding function from discourse markers to individuals of the domain as presented in Kamp & Reyle (1993). (6o) a.

An embedding function J verifies the condition Impfv(e, ¢1) at world w iff J maps e onto an eventuality E such that in all 'inertia' worlds w' there is an eventuality E' of which E is a part such thatf verifies if:i(e') (f(e') E ').20 An embedding functionf verifies the condition Max(e, ¢1) iffj maps e onto an eventuality E such that there is no E' of which E is a proper subpart which verifies if:i (e') ( J(e') E ' ). =

b.

=

Acknowledgements

JEAN-PIERRE KOENIG Linguistisc Department 6og Baldy Hall University at Buffalo, the State University of New York Buffalo, NY 14260- 1 030 USA [email protected] http://wings.buffalo.edu/linguistics/koenig/index.html

Received: r 9.0 r .oo Final version received: or.o8.oo

REFERE NCES Binnick, Robert (1991), Time and the Verb: A Guide to Tense and Aspect, Oxford Uni­ versity Press, Oxford. Carpenter, Bob (1992), The Logic of Typed Feature Structures, Cambridge University Press, Cambridge. Depraetere, lise (1995), 'On the necessity of distinguishing between (un)boundedness and (a)telicity', Linguistics and Philosophy, r 8 , r - 1 9.

Depraetere, lise (1998), 'On the resultative character of present perfect sentences', journai of Pragmatics, 29, 597-61 3. Dowty, David (1979), Word Meaning and Montague Grammar, Reidel, Dordrecht. Eijck, J. van, & Hans Kamp (1997), 'Representing discourse in context', in 20

As

(1998).

J. van Benthem & A. ter Meulen (eds), Handbook of Logic and Language, MA, MIT Press, Cambridge, 1 79-23 7. Galton, Antony (r984), The Logic of Aspect, Clarendon Press, Oxford. Grice, Paul (1975), 'Logic and conversation', in Peter Cole & Jerry Morgan (eds), Syntax and Semantics ;: Speech Acts, Aca­ demic Press, New York, 4 1 -58. Herweg, Michael (r991a), 'A critical exam­ ination of two classical approaches to aspect', journal of Semantics, 8, 363-402. Herweg, MichaeL (r99Ib), 'Perfective and imperfective aspect and the theory of events and states', Linguistics, 29, 969-1010. Hornstein, Norbert (1990), As Time Goes

mentioned earlier, the definition of 'inertia' worlds we adopt is that proposed in Portner

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We would like to thank Laura Michaelis, Karin Michelson, and Luis Paris as well as two anonymous reviewers for their helpful comments on previous versions of this paper. They all made this paper much better than it would otherwise have been.

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