Imperfect Information State Updates by Utterances

Imperfect Information State Updates by Utterances Tsutomu Fujinami Institut fur Maschinelle Sprachverarbeitung Universitat Stuttgart 23 March, 1996

1 Introduction There are two complementary views on the meaning of sentences, static and dynamic . When one pays his attention to the static aspect, he is interested in what a sentence represents and how it could be interpreted against what model. When one is concerned with the dynamic aspect, on the other hand, he becomes interested in how the representation can be changed by uttering the sentence. Models for such a state change have however not been investigated until recently. Among various theories applicable to the study of state changes, Channel Theory [Bar93, SB93] seems to be most promising because it provides us with a pairwise values of perfect and imperfect for changes, a counterpart of true and false for representations. We discuss here how the notion of imperfect information ow is useful through the investigation on the use of a Japanese phrase- nal particle and the inde nite in English.

2 Introducing a reference to discourse 2.1 A Japanese phrase- nal particle, tte The phrase- nal particle, tte , marks noun phrases when the speaker introduces something unfamiliar to their discourse, unfamiliar relative to their common ground. The below is an excerpt from the Japanese Map Task Corpus [AIK+ 94]. In the task, a pair of the route giver (G) and route follower (F) are given slightly dierent maps and asked to draw the correct route on the follower's only through verbal communication. In the example, they have the same item but named dierently; It is called roten-buro(open-air hot spring) in the giver's map and iwa-buro(rocky hot spring) in the follower's. Email: tsutomu@@ims.uni-sttutgart.de The paper was presented at the Munchen Workshop for Situation Semantics, 25th to 26th March, 1996. I am grateful to Anton Benz for organising the workshop and all the participants for the discussion and comments. 

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The strategy dialogue participants talk about an item whose reference has not been established yet between them may vary depending on agents and context. They are sometimes optimistic, and sometimes not. In the excerpt, they are alerted as they have just discovered that the follower has not a mountaion in his map. As they are aware that they may not share the hot spring, at rst (G1 ) the giver cautiously asks the follower if he has the roten-buro(open-air hot spring) by marking it with the particle, tte . His suspicion is actually supported by the follower's responce (F1 ). The follower too is aware that the giver may not have the item iwa-buro in his map and asks him if he has it also by marking it with the particle (F2 ). (G1 ) jaa roten-buro tte arimasu? then open-air hot spring unfamiliar do you have then, do you have an open-air hot spring? (F1 ) roten-buro mo nai mitai open-air hot spring neither I do not have it seems it seems that I don't have an open-air hot spring neither. (G2 ) nai no you don't have it. (F2 ) demo iwa-buro tte iu o-furo wa aru but rocky hot spring unfamiliar called hot spring topic I have But I have a hot spring called rocky hot spring. Takubo [Tak89] observes that a np is marked with the particle when its referent cannot be identi ed by one of the dialogue participants or when whose meaning is not known to one of them. The observation can be summarised that a np is marked when the reference is not established between dialogue participants. The phenomenon can basically be studied by presuppositional theory of the inde nite such as File Change Semantics [Hei83] though the notion of unfamiliarity must be de ned dierently for Japanese.1 We do not discuss how the unfamiliarity should be de ned for Japanese, but point out that the dynamic property of the inde nite can be also observed in the use of the particle. That is, the np marked with the particle may introduce a new reference to their common ground.

2.2 The inde nite in English For the sake of comparison and our argument, we investigate how an inde nite description may be used in dialogue. The below is an excerpt from the HCRC Map Task Corpus [ABB+ 91]. In the example, the item, trig point, appears in the giver's map, but not in the follower's. The main dierence is in that a np can be marked when the speaker attributes to it a new property or refers to a dierent individual that may not be evident to the hearer. 1

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At G14 , the giver tries to introduce the item to their discourse by expressing it as an indefinite. Having failing to establish a common reference between them, he tries again at G16 to introduce it with the utterance of \a trig point" . The attempt still fails at G17 , and the giver is hesitant to express it as a de nite at G18 even the follower aproves the existence at F17 . (G10 )Right, so you're gonna almost follow the course of that right ... that west lake to the east, the east side of it ... you're gonna follow the c the course of it. (F11 ) Just ... just coming in at the base of it, then? (G12 )Yeah, just at the base, and then follow the course of it round sort of a u, an s shape. (F12 ) So is it a very very big wide u so (G13 )Yeah. (F13 ) I'm gonna avoid som ... so that ... I'm avoiding something at the (G14 )Well you've got a trig point, do you have a trig point? (F14 ) No. (G15 )No. (F15 ) Nope. (G16 )Right, so in between your west lake and the tri There's a trig point, right? (F16 ) Right. (after 17 utterances) (G17 )So in between it would be ... It would be in between the farmed land and I have a trig point. (F17 ) Okay ne, right. (G18 )Right, okay. So it's just above the ... just at the ... just before the tip of that west lake, but just at the east co ... just at that east coast, right? (F18 ) Okay, ne right, yeah. Uh-huh . One of the interesting points the excerpt suggests is that the de niteness and inde niteness of a description may be determined relative to the mental states of dialogue participants, not to a discourse independent of them. The role of mental states play in dialogue is interesting topic, but goes beyond our scope. What we would like to draw the reader's attention to is the fact that the attempt to introduce a reference to discourse may fail. 3

3 Imperfect information state updates 3.1 State changes as a channel We have observed in the above that there is a particular way for dialogue participants to introduce a reference to their common ground: the particle, tte , in Japanese and the inde nite in English. We have seen also such an introduction may fail. This could happen for example when the hearer cannot identify the intended referent. Little attention has been paid to such a failure in the study of the semantics of natural language.2 It is usually assumed that a new reference is always successfully introduced to the discourse. Such an assumption may lead to a trouble, for example, when we study the meaning of the inde nite description in the above. Apart from the theoretical problem that we cannot interpret such an expression, we cannot explain why the giver repeats uttering the inde nite description, \a trig point" in the above exerpt from the HCRC Map Task Corpus. The answer is of course because his attempt has failed. But the information has been out of the scope of semantic theories. If we analysed the phenomenon in dynamic semantics [GS91], we might have been led to a cumbersome conclusion that the giver introduces to the discourse several references for the trig point. To approach the problem, Channel Theory provides us with a useful notion of imperfect information ow. Let us see rst how the state change by utterances can be seen as an information ow. Let A and B be the representations of their common ground between dialogue participants. We assume A represents the state before a sentence, u, is uttered andu B another state after the utterance. The change can then be schematically written as: A ?! B . This can be regarded as a channel as Barwise notes that the formulas of Hoare-style logics can be seen as a channel [Bar93] . By conceiving of the change as a channel, we can now apply the idea from Channel Theory to the problem. Let u_ be the particular change actually occurred to their common ground. If the change is certainly an instance of the transition from A to B , we write it as u_ :+ A ?! B to mean that u_ is positively classi ed by the formula. The notation is slightly dierent from the one adopted in the literature. It may be written as u_ :+ u, where u is a constraint from A to B . We however prefer our notation because it makes it easier to recapture the theory with Linear Logic.3 We may also call it that the information ow by the utterance is perfect . On the other hand, if the change is not an instance of it, we write it as u_ :? A ?! B to mean that u_ is negatively classi ed by the formula.

3.2 Exceptions relative to the positive information ow According to the theocy, there are two sorts of exceptions to the information ow, one of which is an exception relative to the positive information ow and the other an exception relative to the reverse information ow. The rst case is understood as an exception where the change, u_ , does not lead to B when A certainly classi es the state positively before the utterance. If A fails to classify the state, the change is outside the domain of the positive One can nd only one another attempt by Healey and Vogel [HV94] in the same framework of Channel Theory, but with dierent approach to dialogue. 3 Interested readers are invited to consult another paper by the author [Fuj95b]. 2

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information ow, thus it cannot say anything about the change. The reverse information ow checks the change in opposite direction. That is, if B classi es the state after the utterance negatively, then A too must classify the state before it as a negative instance. If A is not classi ed negatively, then the reverse information ow is exceptional. Of these two sorts of exceptions, the rst one relative to positive information ow is useful for interpreting the meaning of the sentences uttered to introduce a reference unsuccessfully. It can be captured as a change such that its precondition A holds while its postcondition B does not, the precondition that the reference is unfamiliar to their common ground. The exception relative to the reverse information ow is however not applicable to dialogue. One cannot argue that the common ground was not in the state of A by observing that it is not in the state of B ; Simply the speaker may not utter a sentence classi ed as u in A. That is, the precondition does not determine what sentence will be uttered. It can only allow for certain sentences to be uttered.

3.3 Conclusion We have observed that there is a case where an utterance fails to update the information state properly and have proposed to interpret such a change as an exception relative to the positive information ow by turning to Channel Theory. The semantics may in the long run enable us to study how dialogue participants can reach an agreement on their common ground, where both intentional and extentional models fail to interpret the expressions in ux yet contributing towards establishing a common ground. A number of issues must be discussed to develop the idea into a real semantics. Firstly, we have not discussed here what the common ground is and how it can be represented in the framework. The reader is referred to the author's another paper for the topic [Fuj95b], where a construction of common ground as a system of communicating processes is proposed on the basis of the idea due to Barwise [Bar89]. Secondly, we have not shown how an utterance can update the common ground. As for the problem, there is a preliminary work by the author, where the change of Discourse Representation Structures by utterances is encoded into a -calculus [MPW92], an algebraic model for communication and concurrency [Fuj96]. In the author's disseration [Fuj95a], it has been shown that all these ideas can be grounded to Channel Theory.

References [ABB+ 91] Anne H. Anderson, Miles Bader, Ellen G. Bard, Elizabeth H. Boyle, Gwyneth M. Doherty, Simon C. Garrod, Stephen D. Isard, Jacqueline C. Kowtko, Jan M. McAllister, Jim Miller, Catherine F. Sotillo, Henry S. Thompson, and Regina Weinert. The HCRC Map Task Corpus. Language and Speech, 34(4):351{366, 1991. [AIK+ 94] Motoko Aono, Akira Ichikawa, Hanae Koiso, Shinji Sato, Makiko Naka, Syun Tutiya, Kenji Yagi, Naoya Watanabe, Masato Ishizaki, Michio Okada, Hiroyuki Suzuki, Yukiko Nakano, and Keiko Nonaka. The Japanese Map Task Corpus: an 5

interim report. In Spoken Language Processing, volume SLP3(5), pages 25{30. Information Processing Society of Japan, 1994. in Japanese. [Bar89] Jon Barwise. On the model theory of common knowledge. In The Situation in Logic, pages 201{220. Center for the Study of Language and Informaiton, 1989. [Bar93] Jon Barwise. Constraints, channels, and the ow of information. In Peter Aczel, David Israel, Yasuhiro Katagiri, and Stanly Peters, editors, Situation Theory and its Applications, volume 3, pages 3{27. Center for the Study of Language and Informaiton, Stanford, California, 1993. [Fuj95a] Tsutomu Fujinami. A process algebraic approach to computational linguistic. PhD thesis, Centre for Cognitive Science, University of Edinburgh, Edinburgh, 1995. avaibable in /pub/papers/tsutomu through ftp.ims.uni-stuttgart.de. [Fuj95b] Tsutomu Fujinami. A process algebraic approach to situation semantics. In Proceedings of 10th Amsterdam Colloquium, Amsterdam, The Netherlands, December 1995. University of Amsterdam. in press. [Fuj96] Tsutomu Fujinami. A dynamic syntax-semantics interface. 1996. to be presented at the second conference on Information-Theoretic Approaches to Logic, Language, and Computation. [GS91] Jeroen Groenendijk and Martin Stokhof. Dynamic predicate logic. Linguistic and Philosophy, 14(1):39{100, 1991. [Hei83] Irene Heim. File change semantics and the familiarity theory of de niteness. In Bauerle, Christoph Schwarze, and Arnim von Stechow, editors, Meaning, Use, and Interpretation of Language, pages 164{189. Walter de Gruyter, Berlin, 1983. [HV94] Pat Healey and Carl Vogel. A situation theoretic model of dialogue. In Kristiina Jokinen, editor, Pragmatics in Dialogue Management. Goteborg Monographs in Linguistics, 1994. [MPW92] Robin Milner, Joachim Parrow, and David Walker. A calculus of mobile processes, parts I and II. Information and Computation, 100:1{40 and 41{77, 1992. [SB93] Jerry Seligman and Jon Barwise. Channel theory: toward a mathematics of imperfect information ow. Unpublished ms., May 1993. [Tak89] Yukinori Takubo. Meishikku-no modality (the modality of noun phrases). In Nihongo-no modality (The modality in Japanese), pages 211{233. Kurosio, Tokyo, 1989. in Japanese.

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