Semantics and Pragmatics in the ELTA Dialogue ... - Semantic Scholar

Semantics and Pragmatics in the
ELTA Dialogue Project Harry Bunt ITK, Tilburg University (NL) [email protected]

Proceedings Second Workshop of HCM Project `Spoken Dialogue and Discourse, Dublin, April 1995

Abstract

This paper describes work in progress concerning the semantic and pragmatic interpretation of utterances in human-computer natural language information dialogues, as developed in the
ELTA project at Tilburg University. This project aims at developing and applying an integrated approach to semantic and pragmatic interpretation of dialogue utterances, where the application is sought in the form of a dialogue system capable of acting as a cooperative partner in an information dialogue. The
ELTA project continues a line of work in language understanding, dialogue studies, and designing intelligent interactive systems. A salient feature of the
ELTA approach is that it considers semantic (truthconditional) and pragmatic (speech act) interpretation to be fundamentally context-based; the resolution of ambiguity and vagueness, often considered to be the main task of natural language interpretation, is not approached as a goal in itself, but as something to be done only as demanded and to the extent required by the context of the application. In this paper we will be concerned with three issues in the study of dialogues: (1) underspeci cation in the semantic content of dialogue utterances; (2) the communicative functions of dialogue utterances as context-changing functions, and (3) the formal modelling of dialogue context. 1

1 Introduction The
ELTA project at Tilburg University aims at developing and applying an integrated approach to the semantic and pragmatic interpretation of utterances in the context of a dialogue. The application of the approach is sought in the form of a computer dialogue system, capable of acting as a cooperative dialogue partner in an information dialogue. The
ELTA project continues a line of work in language understanding, dialogue studies, and designing intelligent interactive systems, starting with the PHLIQA project in the seventies (see e.g. Bronnenberg et al., 1979), continuing with the TENDUM and SPICOS projects in the eighties (see Bunt et al., 1984; Van Deemter et al., 1987; Bunt, 1989; Thurmair, 1989), and culminating in the PLUS and DenK projects in the nineties (e.g. Black et al. 1992; Beun et al., 1995; Ahn et al., 1995; Bunt et al., 1995). Common to all these projects is the view that it may be advantageous to design language understanding systems as having a `cascaded' organization, where several levels of meaning representation are distinguished, at which dierent knowledge sources are consulted and dierent 1 This paper was partly written during a stay at LIMSI resarch lab in Orsay, France. I would like to thank the direction of LIMSI for making this stay possible and fruitful.

1

degrees of speci city in meaning are targeted. What distinguishes these projects, besides technical dierences in the syntactic and semantic formalisms they employ, is that, generally speaking, the more recent projects give an increasingly prominent place to contextual information as a knowledge source in semantic interpretation, and increasingly recognize the importance of non-local and non-truthconditional aspects of meaning. The PHLIQA question-answering system, in line with the philosophy of Montague Grammar, distinguished (among others) a level of interpretation where semantic representations are constructed in a formal language with nonlogical constants corresponding to syntactically dierentiated senses of content words, and another level where representations are built in a formal language dierent from the rst one only in that its nonlogical constants denote concepts in a formal model of a certain discourse domain. The semantic analysis at the rst level thus corresponds to formal semantics, that at the second to lexical semantics (cf. Thomason's introduction to Montague, 1974). A consequence of this approach is that the referential terms at the rst level preserve most of the ambiguity and vagueness of the natural language words they correspond to; the formal representation language used at this level therefore exhibits lexical ambiguity (but not structural ambiguity). At the second level in the PHLIQA system, with constants determined by concepts in a formal `world model', ambiguity and vagueness are resolved relative to the granularity of that model. A third level of interpretation, with semantic primitives determined by the elements of a data base schema, provides further referential re nement relative to the ner but often arti cial granularity of the data base. The PHLIQA system can be said to have a level of context-independent interpretation, if we take `context' in the sense of domain of discourse, and context-dependent levels. The only form of semantic indeterminacy allowed at the context-independent level in PHLIQA is that of lexical ambiguity and vagueness. The motivation of this indeterminacy is that precise lexical interpretation is in general only possible given a domain of reference (see e.g. Bronnenberg et al., 1979). The TENDUM system (Bunt et al., 1984) went a step further in recognizing that the resolution of certain forms of structural ambiguity and vagueness in general also require domain-speci c knowledge, and should therefore also be left undetermined at a domain-independent level of interpretation. This applies for instance to deciding whether a quanti cation is to be taken collectively or distributively, and to whether a noun like `cake' is to be taken as a count noun (as in \three cakes") or as a mass noun (as in \slice of cake"), as n the PHLIQA system. Representations leaving quanti er distributivity and mass/count distinctions underspeci ed were designed, based on the PHLIQA technique of using ambiguous constants; dierent `instantiations' of these constants correspond to dierent semantic interpretations. To this end, a family of representation languages was de ned and implemented called the EL (`Ensemble Languages') family (Bunt, 1985). Innovative of the TENDUM system was thus the use of ambiguous constants not corresponding to ambigous lexical items, but to sources of structural semantic ambiguity in natural language. The SPICOS system, a joint Philips-Siemens research experiment and precursor, in seferal respects, of the current Verbmobil project (see e.g. Wahlster, 1993; Maier & McGlashan, 1994; Bos et al., 1994a; 1994b), used many of the TENDUM techniques for semantic analysis in the context of a document retrieval application with a German speech front-end (see van Deemter et al., 1985; Thurmair, 1989). The Core Language Engine (Alshawi, 1992) which, unlike the systems mentioned above, was not aimed at performing a speci c interactive task like data base question answering (PHLIQA), document retrieval through spoken interaction (SPICOS) or travel information supply through typed 2

dialogue (TENDUM), but which was intended as a general-purpose natural language front-end to be customizable to a variety of applications, provided a translation from English sentences to underspeci ed representations of their truthconditional semantic content in structures called Quasi-Logical Forms (\qlfs"). Like the rst-level EL-representations of the TENDUM system, these structures were intended to describe entirely context-independent meaning aspects; a speci c feature of qlfs is that they were designed to represent unscoped quanti ers. The TENDUM system was also innovative in another respect: it attempted to deal, albeit in a primitive fashion, with `pragmatic' meaning aspects by treating natural language utterances in a human-computer dialogue as speech acts, having a functional (`illocutionary') meaning aspect relating to the speaker's intentions and other attitudes with a certain propositional content, rather than as denoting propositions. The analysis of the meaning of the user's utterances thus goes beyond the propositional level, and includes attributing goals and beliefs of various sorts to the user; together, these constitute a user model (Bunt, 1989a). Exactly which interpretation is assigned to a user contribution now depends in general not only on the context in the sense of the discourse domain under consideration, but also on the more `local' context formed by the current user model (more `local' in the sense of changing as the discourse develops). Consider, for instance, the following dialogue fragment: 1. 2. 3. 4.

U: S: U: S:

What are the daily departure times of ights to Munich? That's 7.45, 8.30, 9.50, 14.30, 18.25, and 20.30. On Sunday too. On Sunday too.

Utterance 3 in this fragment is syntactically indistinguishable from utterance 4, and yet it is clear that it has a dierent function. How do we know that 3 functions as a veri cation, and 4 as a con rmation? We know this in view of the information each of the participants may be assumed to possess at the relevant point in the dialogue; the correct interpretation of utterance 3 thus relies on the use of the user model current at that moment (see further Beun, 1989 for the analyis of this type of so-called `declarative questions', i.e. questions asked by means of an utterance having the syntactic and prosodic form of a declarative sentence). The user model, understood here as the user's beliefs and intentions (and possibly other propositional attitudes, depending on the domain of discourse), is thus considered in TENDUM to be part of the model of the current context; in fact, the user's and the system's beliefs and intentions are considered to be the `backbone' of the dialogue context (see further below). The Esprit project PLUS (`Pragmatics-based Language Understanding System') started from the point of view that the robustness of language understanding systems could bene t greatly from taking contextual information into account in order to deal with linguistic imperfections, unanticipated constructions, unknown or misspelled words, etc., assuming that this is what humans do as well: the proverbial good understander only needs half a word in order to get the message. Technically, this view was elaborated in a design where a kind of quasi-logical form language was de ned (Geurts & Rentier, 1993) and an HPSG-grammar was developed producing such forms as intermediate semantic representations; these were subsequently translated into a restricted form of EL-representations, where a form of abduction was used to bring contextual information to bear in the interpretation in order to produce representations that are free of ambiguity or vagueness, relative to the domain of discourse. This design has been developed and implemented only partially, however, as the project was prematurely ended due to shortage of EC funds in the 1994 Esprit II 3

round. The
ELTA project at Tilburg University continued where the PLUS project ended. First, the quasi-logical form language, called more appropriately (and distinguishing it from the qlf-language of the Core Language Engine) underspeci ed logical form (ulf-) language, has been redesigned and improved (Rentier, 1993; Kievit, 1994). Second, the philosophy was adopted that, dierent from what previous projects have aimed at, the construction of precise and unambgiuous interpetations should not be an aim in itself; rather, ambiguity and vagueness should be resolved on demand, and only inasmuch as required by the circumstances. The design of the
ELTA system therefore does not have a stage of full-blown contextual desambiguation and vagueness resolution, but assumes that ambiguity and vagueness may exist and persist in the system at all levels. (See further below.) Third, a variety of sources of ambiguity and vagueness is being investigated for the possibility of de ning formal representations (in EL) with well-de ned inferential properties which leave the ambiguities and vague elements in question unresolved. Extending the previous TENDUM-work on formal representations for quanti er distributivity and mass/count ambiguities, proposals have been developed for handling unscoped quanti ers, unattached prepositional phrases, and the like. Fourth, the EL-formalism has been extended with constructions for representing propositional attitudes and anaphoric references (see Bunt, 1984b;1985), leading to representations somewhat reminiscent of Discourse Representation Structures. Combined with the possibility of scope-unresolved quanti er representation, these EL-structures bear some similarity to underspeci ed DRSs (Reyle, 1993). The ulf- formalism for underspeci ed semantic representation, as developed in the
ELTA project, is also used and further developed in the project DenK, a joint project of Tilburg University, Eindhoven University of Technology, and the Institute for Perception Research in Eindhoven (see Bunt et al., 1955). Kievit, 1994; Rentier, 1995. This project aims at the design of a `cooperative' multimodal user interface, combining natural language with direct manipulation and animation. It shares the use of HPSG and ulf with the
ELTA project; a notable dierence is that ulf representations are translated into an extension of constructive type theory, rather than into EL (see Ahn et al., 1995). The recent Verbmobil project in Germany is also developing techniques for underspeci ed semantic representations (see Bos et al., 1994a; 1994b). In this project, which is concerned with on-line translation of spoken German and Japanese to English, the motivation for entertaining underspeci ed semantic representations is primarily that ambiguities in a source language expression often do not have to be resolved (should not even be resolved, sometimes), in order to be translated adequately into the target language. Figure 1 summarizes the history of related systems and approaches as outlined here, where the arrows indicate the ow and further development of technologies for semantic interpretation.

2 Context-independent interpretation and underspeci city A context-independent stage or `level' of semantic interpretation, as entertained in the `cascaded' design, is a stage where, by the fact that no context information is employed, many aspects of the interpretation cannot be decided. How can semantic representations be built if many aspects of the semantics are undecided? Basically, there are three possible ways one can go. For a given sentence, with aspects A1 , A2 , .., Ak that are undecided and for which there are N1 , N2, .., Nk possibilites: 4

'79

'86

'93

'95

PHLIQA

SPICOS

?

TENDUM

CLE

-

?

PLUS

DenK Figure 1: From PHLIQA to
ELTA

5

?


ELTA

1 create a separate representation for every combination of possibilities. (That is, build N  N  :::  Nk representations.) 2 create a single representation containing disjunctions for the undecided aspects A , A , .., Ak , 1

2

1

2

for instance, by allowing disjunctions in feature structures. 3 create a single representation which is underspeci ed in the respects A1, A2 , .., Ak , for instance, building a representation with unscoped quanti ers, unattached PPs, etc.

In practice, it is hard to imagine that any of these alternatives is fully satisfactory and feasible; moreover, there may be theoretical reasons for treating dierent sources of ambiguity with dierent techniques. We should therefore also consider the possibility of combining these techniques:

4 Use some combination of these alternatives, that is, build less than N  N  :::  Nk representations, which are underspeci ed in some respects.

1

2

Let us therefore consider some of the main sources of ambiguity, and technical means of dealing with them.

2.1 Sources of ambiguity

By `ambiguity' one usually means: the phenomenon of allowing more than one interpretation. A rst distinction to make is between those cases where a linguistic expression allows a limited number of well-distinguished readings, versus the case where the expression allows a very large, inde nite number of interpretations on a more or less continuous scale. The rst case is illustated by homonyms, like book (form of printed text; to engage a place (in a theatre, a restaurant, an airplane,..); to register on police records); the second case by vague words with little meaning of their own, like do or have. In accordance with established terminology, we will henceforth use the term ambiguity only for the rst case, and the term vagueness for the second. Both ambiguity and vagueness occur at the level of words as well as at the level of complex expressions. The following taxonomy of kinds of ambiguity may be useful for the present discussion:2

Phrasal ambiguities 1. Syntactic ambiguity: an expression can be assigned more than one

syntactic structure, with corresponding dierent semantics, as e.g. in the case of PPattachment ambiguities (I saw the man with the telescope), or dierent assignments of grammatical functions (I don't like the killing of the sharks). 2. Structural semantic ambiguity: one and the same syntactic interpretation of an expression can have more than one interpretation, corresponding with dierent ways of structuring elements in a semantic representation. Example: relative scope orderings of quanti ers (Everyone in this room speaks two languages). 3. Referential ambiguity: a phrase, e.g. an NP, may be ambiguous as to what object(s) it refers to. De nite noun phrases, with dierent possible anaphoric and deictic interpretations, exemplify this. 4. Idiomatic ambiguity: an expression may have an idiomatic as well as a `literal', compositional meaning. For instance, the sentence John kicked the bucket may be taken to mean that John kicked some bucket, or that he died. Similarly for the standard Dutch greeting Hoe maakt u het? (\How do you make it?", meaning \How do you do"), to which people sometimes respond jokingly, saying "I'm not gonna tell you!".

2

The list is not meant to be exhaustive.

6

5. Extensional/intensional ambiguity: an expression can be taken to denote certain entities here and now, or a more general concept. For instance, the phrase The president of the USA can denote the current president, or more generally whoever happens to have the function of president, as exempli ed in the sentences: The president of the USA said, on a press conference, that he backed the new UN policy and The president of the USA lives in the White House as long as he's in oce. Lexical ambiguities 1. Intercategorial ambiguity: a word belongs to more than one syntactic category (e.g. book, plan). 2. Intracategorial homonomy: a word is homonymous in the sense of having distinct, unrelated meanings all belonging to the same syntactic category, e.g. plant (factory; vegetable); bank (for money; of river). 3. Intracategorial polysemy: a word has a variety of related meanings, not re ected in dierent syntactic behaviour, e.g. mouth (of person; river), fork (for eating; in a road). 4. Subcategorization ambiguity: a word has related meanings, with corresponding dierent subcategorization properties (e.g. transitive and intransitive variant of verbs: walk (to go for a walk; to walk the dog), open (she opened the door; the door opened). 5. Structural morphological ambiguity: a word can be split into morphemes in dierent ways, as in composites in Dutch (loodspet, decomposable as loods-pet (pilot's cap) or as lood-spet (lead spatter), or in diminutive forms like Dutch buurtje, which can be decomposed as buur-tje (little neighbour) or as buurt-je (little neighbourhood). 6. In ectional morphological ambiguity: dierent in ectional forms of a word may be morphologically indistinguishable, like the singular and plural form of sheep, or the gerund and participle forms of a verb, responsible for the famous (structural syntactic) ambiguity of Flying planes can be dangerous. 7. Count/mass ambiguity: nouns and nominal phrases can mostly be used with a mass noun as well as with a count noun interpretation, such as lamb in There's no lamb in the garden vs. There's no lamb in the stew. 8. Anaphoric (/deictic) ambiguity: especially pronouns, like it, he, or that can refer to various entities in the linguistic or physical context. In this paper we will focus on structural syntactic and semantic ambiguities on the phrasal level, and on the lexical level on those ambiguities that have no syntactic consequences: intracategorial homonomy and polysemy, structural morphological ambiguity, in ectional morphological ambiguity, count/mass ambiguity, and anaphoric (and deictic) ambiguity. Besides the various kinds of ambiguity that we nd at lexical and phrasal levels, there's also vagueness at both levels. Vagueness is most often related to lack of precision in referential meaning, as exempli ed by the verb do mentioned above: in a sentence such as I have done it the speaker can refer to any kind of action; the meaning of the verb seems to be extremely context-dependent. The same goes for many prepositions; of, for example, can be used to indicate an enormous variety of relations, which is practically impossible to delineate out of context. Vagueness at phrasal level is exempli ed in English, by noun-noun combinations where the relations between the constituent elements have a similar vagueness as the preposition of. A case of `structural semantic vagueness' is the distributivity of quanti ers: in the sentence The boys carried all the boxes upstairs it isn't clear whether the boys did the carrying collectively, individually, in pairs, or in still dierent ways. Dealing with vagueness is methodologically an even greater challenge than dealin with ambiguity: since a vague word or expression cannot be assigned a representation where its dierent 7

possible meanings are enumerated, (at least not out of context), it is impossible in principle to treat it following the methods [1] or [2], mentioned above; the only possibility is [3]: we must use representations which are underspeci ed in some respects.

2.2 Techniques for ambiguity representation

Of the methods for avoiding to build fully unambiguous representations mentioned above, method [3] has been pioneered in the PHLIQA system for dealing with intracategorial homonomy and polysemy, and referential vagueness. In this system, English content words are represented at the context-independent level (i.e., in this sytem, the domain-independent level) by constant terms of the representation language that are assumed to have the same ambiguity and vagueness as the English words. This assumption comes out when, in the context-dependent stage of interpretation, these terms are translated into expressions built up from domain-speci c constants, which are unambiguous and precise relative to the system's model of the discourse domain. For example, a sentence like A Canadian machine is landing would be represented at the context-independent level as:

9x 2 fy 2 machinesjcanadian(x)g: landing(x) which would, at the domain-speci c level of representation, be translated into its two possible disambiguations:

9x 2 fy 2 ightsjnationality(owner(x)) = canada g: arrival-time(x) = t

0

9x 2 fy 2 ightsjcountry(departure-place(x)) = canadag: arrival-time(x) = t

0

Formally, this approach is sanctioned by giving the context-independent representation language a semantic de nition that allows terms to have multiple denotations (Landsbergen & Scha 1979; Bunt, 1985). In the TENDUM system, the use of essentially the same technique was pioneerd at the lexical level for handling the count/mass ambiguity (Bunt, 1985) and at the phrasal level for representing the structural semantic vagueness of quanti er distributivity. For instance, to represent the sentence The boys carried all the boxes upstairs without detailing the distributivity of the carry action over the boxes, the object-NP is represented as follows:

P : 8x 2 (boxes): P (x) where  (the `distribution function') can be translated in various ways into a function that makes clear whether the quanti cation ranges over individual boxes, over groups of boxes, or over the group of all boxes. In the rst case, for instance,  is translated into the identity function X : X ; in the second case into X : P (X ), and in the latter case into the function X : fX g. (See further Bunt, 1984.) Similarly, the count/mass ambiguity is handled by means of an ambiguous function  such that, depending on the translation of this function, (lamb) denotes either the set of all individual lambs or the continuous object including as parts all pieces of lamb (Bunt, 1985). The method of using `metavariables', like , seems a promising approach to the formal representation of all kinds of underspeci ed meanings. We will return to this below, in section 3. 8

In the Core Language Engine project, Alshawi developed a representation for unscoped quanti ers using the notation called `Quasi Logical Form'. This notation was indeed quasi-logical in the sense that, although syntactically the representation looked like that in a logical language, this notation had no semantic de nition. Later, such a de nition has been given (as in the PHLIQA system) by de ning the semantics of a QLF expression in terms of its possible unambiguous instantiations (Alshawi & Crouch, 1992). Method [2], the use of representations containing disjunctive parts, seems attractive for dealing with in ectional morphological ambiguity and count-mass ambiguity when a feature logic is used. In that case, we can e.g. for the ambiguous noun sheep say that it is [number sing _ plur] and [ntype mass _ count]. Such a characterization would seem to be syntactic rather than semantic, however; unless feature expressions like [ntype mass _ count] have a foraml interpretation. Use of disjunctions in semantic representations in general does not seem appropriate because it doesn't give the right truth conditions; an ambiguous sentence typically is supposed to mean one of its possible readings, not their disjunction. The use of ambiguous terms, as outlined above, diers precisely from the use of disjunctions at this point: an ambiguous term should not be translated into the disjunction of its possible translations, but into one of them. Ahn et al. (1995) mention the use of typed feature structures in the DenK-proejct (Bunt et al., 1995) as an attractive alternative to the use of disjunctions in attribute-value matrices. The use of typed feature structures (see e.g. Carpenter, 1992) opens an interesting way to represent in ectional morphological ambiguity due to the fact that attributes can be given underspeci ed values which are de ned as elements in a type hierarchy. For instance, the types numb and ntype dominate the subtypes sing, plur and count, mass, respectively, so that sheep can be characterized as [number numb, ntype ntype]. Again, this is a syntactic rather than a semantic characterization of certain ambiguities. In the DenK project an attempt is made to systematically relate such attribute-value matrices to unambiguous formal representations in constructive type theory, via an intermediate stage called ulf, mentioned above. This intermediate representation is designed in such a way that ulf-expressions can be obtained relatively straightforwardly as linearized forms of the semantically relevant parts of the typed feature structures produced by an HPSG parser (notably a version of the ALE parser; Carpenter & Penn, 1994). An approach that should also be mentioned is that of searching for the least speci c interpretation. Ahn et al. (1995) argue that the use of constructive type theory is advantageous for underspeci ed semantic representation, using the case of quanti er scope ambiguity in the sentence Every button controls a lens, with the two readings: a. 8x:button(x): ! 9y:lens(x)^control(x; y) b. 9y:lens(x) ^ 8x:button(x): ! control(x; y) Their treatment boils down to assigning the sentence only one semantic representation, namely the one corresponding with reading a, since this reading is less speci c than reading b, and adding a context-speci c constraint to the eect that the lenses controlled by the various buttons are in fact all the same lense, thus arriving at reading b, if the context warrants this constraint. The same idea has been employed by Bunt (1985) for dealing with quanti er distributivity (structural semantic vagueness). He argues that a sentence like The boys carried all the boxes upstairs is not really ambiguous between a collective and a distributive reading, as the linguistic literature claims, but is just unspeci c as to how the boxes were carried upstairs by the boys. He thus constructs a representation for this reading, with so-called `unspeci c distributivity', and 9

adds contextual constraints making the interpretation collective, distributive, or still dierent (e.g., pairwise), as indicated by the context. The idea of dealing with ambiguity and vagueness by representing only one least speci c reading from which other readings can be derived by adding constraints, can of course only work for cases of ambiguity where one of the readings is less speci c than all the others. For dealing with vagueness, such a `minimal' interpretations seems attractive: assuming that the various readings of a vague expression have something in common, it would seem ideal to just represent this common part of their meanings, and use contextual constraints to arrive at some more speci c, contextually appropriate meaning.

2.3 Ambiguity and vagueness in the
ELTA system

2.3.1 Design of the interpretation process

In the
ELTA system, we follow the strategy of dealing with vagueness and ambiguity in terms of `metavariables': we extend the approach of using ambiguous constants like the - and -functions to other cases of ambiguity, and we treat predicates corresponding with natural language content words all as variables, to be instantiated by means of context-speci c knowledge. Before going into this, let us outline the design of the interpretation process in the
ELTA system, already hinted at above. First, natural language inputs are analyzed by a constraint-based parser, for which an adapted version of Carpenter's ALE parser (Carpenter & Penn, 1994) is used, and an HPSG grammar which is shared with the DenK-project. From the resulting HPSG sign the semantically and pragmatically relevant parts are extracted. The semantic parts are linearized into `underspeci ed logical forms' (ulf expressions); the pragmatic parts, which only contain attributes with atomic values, are stored in a list. Ideally, an input sentence corresponds to a single pair consisting of an ulf expression and a list of pragmatic features; in practice, some structural syntactic ambiguities give rise to alternative HPSG signs and thus to dierent ulf expression (and, exceptionally, to dierent pragmatic feature lists). In a subsequent step, ulf expressions are transformed into underspeci ed expressions of the language EL/F, which is that instance of the EL-language, mentioned above, whose terms correspond to natural language content words.3 We then have arrived at a fully respectable logical formula, which is syntactically no longer dependent on its history as part of an HPSG sign; this is the end of the context-independent part of the interpretation process. Contextual information is subsequently brought to bear for interpreting both the ulf expressions and the pragmatic feature lists. On the semantic side, this means that ambiguous EL/F terms are replaced by constructions built up from domain-dependent EL/R-terms.4 This takes care of the resolution of lexical ambiguity and vagueness. For dealing with structural ambiguity and vagueness we will explore, in the rest of this section, the possible bene ts of adding terms to EL/F that stand for ambiguous functions that operate on EL-expressions; in this sense, these terms may be called metavariables. These terms do not correspond to natural language content words, but to ambiguous or vague semantic relations between concepts as expressed in natural language. Meanings of struccturally vague or ambiguous natural language expressions are narrowed down to More precisely, the terms of EL/F correspond to syntactically indistinguishable word senses. For instance, the verb form saw and the noun saw correspond to dierent EL/F-terms, since they are syntactically distinguished. A homonym like bank, by contrast, will correspond to a single EL/F-term. This instance of the EL-language family is called EL/Formal, since it is intended to be used when dealing with formal semantic analysis only, not with lexical semantic analysis. 4 EL/R is another member of the EL-family, having the same syntactic constructions as all EL-languages, but distinguished in having terms that correspond to the concepts of a model of a certain discourse domain. 3

10

natural language | | constraint-based parsing | HPSG sign | |extraction & linearization | +--------------------+ ULF pragmatic features | | transformation | | | | underspecified EL/F +---------+--->| interpretatie | | context | | interpretation | = < x : y :with(x; y); < the0 ; telescope0 >> = < x : y :with(x; y); < S : P : t 2 S : P (t); telescopes>> Similarly for the verb:

V 0 = < V10; V20 > = ; V20 >= =; see> For the sentence build we build a representation where the -function acts on the NP- and Vrepresentations, and we do this before scope assignment. For the present sentence this gives us: ((< NPj0 >  2 (< NPm0 ; (V 0 )1 >; PPt0 )) ((V 0 )2 ) The asterisk denotes concatenation; 3 is the ambiguous three-place scoping function; 2 is the two-place ambiguous attachment function. The instantiations of the -function not only select the element to which the PP is attached, but also do the necessary work for the attachment. Attachment of the PP to the rst argument, for instance, is realized by the instantiation:

2 ; T :< T111 ; (fx 2 T112 jz : ( (T221 (T222 ))(T21 (z)) ) (x)g; T12 > Substitution and -conversion gives the desired result.6 We only considered a very simple case of ambiguous PP-attachment here, but the approach generalizes in a straightforward way. In a forthcoming paper, Rentier studies the possibility to tune the HPSG grammar and parser in such a way that the parser will deliver only one HPSG sign, from which the corresponding ulf is obtained. This looks very promising, as the ambiguity caused by possible PP-attachments is an important eciency problem for practical parsers.

2.3.6 Summary

Taking the inheritance from predecessor projects (PHLIQA, TENDUM, PLUS) into account we have in the
ELTA project so far developed methods for underspeci ed semantic representation of: 6 This approach to PP-attachment requires a slight adaptation of the -function, since the representation of NPs changes. Instead of the usual NP representations, formed by combining a determiner QUANT with a nominal expression NOM to obtain P : QUANTx 2 NOM : P (x), we now have representations of the form < det ; nom >. 0

15

0

     

lexical and phrasal referential ambiguity and vagueness; quanti er distributivity (collective/distributive/..); quanti er scoping; count/mass ambiguities; some other scope-bearing elements (negation; adjectives); PP-attachment.

The treatment of anaphoric expressions as a kind of referential ambiguity may also be promising. Other ambiguities are currently being explored. We now turn to the integrated pragmatic-semantic theory underlying the
ELTA system, which has been developed over time starting in the TENDUM project.

3 Dynamic Interpretation Theory

3.1 Meaning and function in dialogue

Dynamic Interpretation Theory7 views dialogues in an action perspective, the participants using communicative actions to cause changes in each others information states, in particular in what each participant knows about the other. Dynamic Interpretation Theory owes its name to the idea that the meaning of an utterance in a dialogue should be de ned dynamically, in terms of the changes that the agent intends to bring about. This idea is similar to that in Dynamic Semantics (see Groenendijk & Stokhof, 1991), except that Dynamic Semantics aims at capturing sentence meaning where Dynamic Interpretation Theory is concerned with utterance meaning, relative to speakers and addressees and their beliefs, and intentions, and other aspects of dialogue context.8 Dynamic Interpretation Theory (DIT) is concerned both with the analysis of utterance meaning and with modelling the pragmatics of dialogue, the two being considered as intimately related because the meanings of dialogue utterances can only be understood fully when taking their functions in the dialogue into account. DIT assumes, like other action-based analyses of communication (e.g. Allwood, 1976; Searle, 1969) that the participants in a dialogue perform communicative actions of dierent types, where each type of action has certain characteristic eects. In particular, we consider the eects of a communicative action on the state of information of the addressee. Let a communicative action A , upon correct understanding by the addressee, have the characteristic direct eects9 E1 ; E2 ; ::; En . We assume that these eects are caused by the fact that associated with every type of communicative action is a set of characteristic conditions that must be satis ed for the action to be appropriate (`appropriateness' or `felicity' conditions), such as to ask a question presupposes that the speaker wants to know the answer to his question. Let C1 ; C2 ; ::; Cn be the appropriateness conditions for action A . Then the addressee H of A believes (unless there is evidence to the contrary) that these conditions are satis ed:

H believes that Ci , for i = 1; ::; n The reader is referred to Bunt (1989; 1991; 1993; 1994; 1995) for expositions of aspects of Dynamic Interpretation Theory. Parts of the present section have also been published, in a slightly dierent form, in Bunt, 1994. 8 See Bunt 1989b and Groenendijk & Stokhof 1989 for a discussion on this issue. 9 By the stipulation upon correct understanding by the addressee we are restricting the eects of the action to what in speech act theory would be called `illocutionary eects'. 7

16

This is what the speaker S expects to happen. Moreover, it is commonly believed that speakers have such expectations; in particular, this is a mutual belief of H and S . Using an attitude `weakly believes' for this `expectation' on the part of the speaker, we thus get the further direct eects:

H and S mutually believe that S weakly believes that H believes that Ci , for i = 1; ::; n The eects of understanding the act A on the addressee are thus:

H believes that Ci ^ H believes that H and S mutually believe that S weakly believes that H believes that Ci , for i = 1; ::; n Taking both speaker and addressee into account, we get, altogether, that the communicative act A has the direct eects E1 ; E2 ; ::; En , where

Ei = H believes that Ci ^ H and S mutually believe that S weakly believes that H believes that Ci Note that these are only the the `direct' eects of A , i.e. purely the eects of succesful communication. There are, of course, usually many indirect eects as well, as the result of further cognitive processing by the participants. DIT takes these direct eects as a description of the meaning of an utterance whose function in the dialogue is exhausted by expressing the communicative act Ci. (We will see below that utterances are in general multifunctional, and thus have more complex meanings.)

3.2 Context and local context change

The state of information of the dialogue partners constitutes a very important part of the dialogue context. The term `context' is used in many dierent ways in relation to discourse, referring for example to the preceding discourse, to the physical environment, or to the domain of discourse. What is common to the various uses of `context' is that they all refer to factors, relevant to the understanding of communicative behaviour. We suggest that these factors can be grouped into ve categories: linguistic, semantic, physical, social, and cognitive. Moreover, for each of these `dimensions' of context we may fruitfully distinguish between global aspects, determined at the beginning of the dialogue and remaining constant throughout, and local aspects, whose values develop and change as the dialogue proceeds, and which have a momentary signi cance in determining the continuation of the dialogue. Some of the most important local aspects of these context dimensions are the following.

 Linguistic context:

the surrounding linguistic (textual or spoken) material (including prosody, interpunction, etc.); raw material as well as relevant properties, detected by analysis.  Semantic context: facts in the domain of discourse; the current state of the underlying task, motivating the dialogue. 17

 Physical context:

current availability of communicative and perceptual channels and, in the case of communication at a distance or through electronic devices, the partners' presence at the device.  Social context: the communicative rights, obligations and constraints of each participant at a given point in the dialogue.  Cognitive context: current participants' beliefs, intentions, and other attitudes; plans for performing the underlying task and for continuing the communicative task; participants' states of processing; current attentional states. The rst and most obvious contextual changes that communicative actions may bring about concern new information becoming available to the hearer, i.e., they change the local cognitive context.10 The beliefs that a hearer builds up on the basis of his interpretation of the speaker's communicative actions are, initially, always beliefs about the speaker; indirectly, they can relate to any of the context factors listed above. For factual questions and answers, the beliefs generated indirectly in the interpreter concern the underlying task and its domain of discourse, and are thus part of the local semantic context. For feedback utterances, the beliefs generated concern only the local cognitive context, viz. beliefs about the speaker's processing of the other's previous utterances. A communicative act may also create `social obligations' for the hearer. For instance, when the speaker greets the hearer, he thereby puts a certain pressure on the hearer to respond with a return greeting. Similarly for introducing oneself, for apologizing, and for thanking, where utterances like \Thank you" create a pressure to say something like \You're welcome"; we refer to such pressures as `reactive pressures' (Bunt, 1991b).11 Resolving reactive pressures is one of the basic mechanisms in dialogue, besides acting on the basis of intentions. Creating and resolving reactive pressures are ways of changing the local social context of the dialogue. Taking turns in a dialogue is also a case of creating and resolving a kind of reactive pressure; when a speaker indicates that he considers his turn to be nished, for example, he puts pressure on his partner to take over. Obviously, a communicative action always changes the local linguistic context. This aspect of utterances is only rarely addressed explicitly in dialogue; it comes to the fore most clearly when there is uncertainty or disagreement about what one of the partners has contributed to the dialogue (\Did you say `Thursday'?"; \But you said...").

3.3 Dialogue acts

Communicative behaviour, according to Dynamic Interpretation Theory, is the expression of communicative actions, aimed at changing the context in speci c ways. We introduce the concept termed `dialogue act' as the functional units used by the speaker to change the context. These functional units do not correspond to natural language utterances or other instances of communicative behaviour in a simple way, because utterances in general are multifunctional, as we will see We will often speak of hearer beliefs rather than information, to avoid the connotation with factual truth. We think this term is more appropriate than other terms found in the literature, such as communicative `obligations'(Allwood, 1994); `adjacency pairs' (Scheglo & Sachs, 1973), and `preferred organization' (Levinson, 1983). `Obligation' is slightly too strong, as the `obligating' utterance does not really oblige the addressee to respond in the `obligated' way. `Adjacency pair' is also too strong, since the two elements of the pair do not really have to be adjacent, and in fact the second element does not necessarily have to appear at all. `Preference organization' would seem to have the right kind of strength, but this term belongs to a structural framework of dialogue analysis, where the term `preference' is not meant to have a cognitive interpretation (Levinson, 1983, p. 332-333). Our approach, by constrast, does have a strong cognitive orientation and considers reactive pressures to be an aspect of the local cognitive context. 10

11

18

below. The important point of the stipulation ... used by speakers is that we are not considering update functions that are elementary in a mathematical or computational sense, but elementary update functions that speakers try to perform with their utterances. We therefore require every communicative function to correspond to utterance features. The most important aspects of a dialogue act are its communicative function, and its semantic content. In addition, a dialogue act is expressed through its utterance form, which determines the changes to the linguistic context that a dialogue act causes. The idea of the communicative function and semantic content is that the semantic content will have a particular signi cance in the new context, resulting from the performance of the dialogue act; the communicative function de nes precisely what this signi cance is. In other words, the semantic content forms a piece of information with which the context has to be updated; the communicative function speci es in what way the update should be done. Using the term `utterance' to refer to everything contributed by a speaker in one turn, an utterance may correspond to more than one dialogue act, and thus be multifunctional, for several reasons. First, an utterance may consist of several sentences or phrases that each express dialogue acts. So dialogue acts often relate to parts of utterances. Moreover, these utterance parts often carry more than one functional meaning, for the following reasons. 1. Indirectness. A question like \Do you know where John's oce is?" may function indirectly as a request to tell where John's oce is. 2. Functional subsumption. Some dialogue act types are more speci c than others. The promise \I will come tonight" is, besides a promise, also an informative statement. 3. Functional multidimensionality. Aspects of performing the underlying task are very often combined in one utterance with aspects of dialogue control. As an example of functional multidimensionality, consider the utterance \Thank you". Used in reaction to an answer, the utterance not only expresses gratitude but also oers feedback information, since it implicitly indicates that the answer was understood and accepted; depending on intonation, it may in addition have a turn management function.12 Goal-driven dialogues, like instruction dialogues and information-seeking dialogues, by their very nature nd their motivation in an underlying task that the participants want to carry out and for which the dialogue is instrumental. Since cooperative communication is an activity with its own rules, rights and obligations, two kinds of elements are commonly found in cooperative goal-driven dialogues: communicative actions motivated by the underlying task, such as instructions, questions, and answers, and actions motivated by the communicative task, such as acknowledgements, attention signals, self-corrections, and turn taking signals. We call these actions task-oriented dialogue acts and dialogue control acts, respectively. Dialogue control acts have a variety of functions in making communication smooth and succesful, and are largely responsible for the naturalness of a dialogue. The idea to view communicative acts as context-changing operations has occasionally been suggested in the speech act literature (e.g., Gazdar, 1979; Isard, 1975), but has not been worked out to the point of formalization. In Bunt (1989; 1990) a proposal has been formulated for formalizing task-oriented dialogue acts in information dialogues in terms of context changes, context construed as the pair of the cognitive states (consisting of intentions and strong and weak beliefs) of the two participants. Dialogue control acts, which have received much less attention in the speech act literature, are discussed in Bunt (1994). In terms of context change, we can make the distinction between taskoriented and dialogue control acts precise as follows. Every dialogue act, when interpreted by the 12

On multifunctionality see also Allwood et al. (1990).

19

addressee, changes the cognitive context; the dierence between a task-oriented (`TO-') dialogue act and a dialogue control (`DC-') act is that the former only causes further changes in the semantic context, whereas a dialogue control act may cause changes in the social or physical context, but does not aect the semantic context. Note that the TO/DC-distinction is primarily one between classes of dialogue acts, not between communicative functions. Although there are indeed communicative functions speci c for dialogue control purposes, a dialogue control act can also be formed by combining a communicative function, seemingly typical for a task-oriented dialogue act, such as inform, with a semantic content relating to some aspect of context other than the semantic dimension, as in \I didn't hear you". For identifying a communicative function we have two criteria, that follow immediately from the de nition of dialogue act:

 the function de nes a speci c way of changing the context, which is elementary in the sense that this context change cannot be obtained through a combination of dialogue acts with other communicative functions;13  speci c features of communicative behaviour (notably linguistic or paralinguistic features of utterance forms) are used to refer to the context change de ned by this communicative function;

Applying these criteria to task-oriented dialogue acts, a classi cation of TO-communicative functions was obtained in Bunt (1989), which is reproduced here in Fig. 3. Small letters indicate classes of communicative functions; capitals indicate communicative functions. A communicative function F that is dominated by another function G in the hierarchical structure of Fig. 3 has the property that, when both functions are combined with a semantic content s, the resulting dialogue act F (s) is more speci c than the dialogue act G(s), in the sense that F (s) conveys more information about the agent A who performs the act than G(s). This notion of `more information' can be formalized in terms of logical relations between the properties of the cognitive state of A as expressed by the dialogue act. Let C1F;s(A); C2F;s (A); ::; CkF;s (A) be the conditions on the state of A which an addressee of the act assumes to hold, if he understands the act correctly.14 Similarly, let C1G;s(A); C2G;s (A); ::; CmG;s (A) be the conditions corresponding to the information about A conveyed by G(s). Then the conjunction of C1F;s(A); C2F;s (A); ::; CkF;s (A) is logically stronger than that of C1G;s(A); C2G;s (A); ::; CmG;s (A):

C1F;s(A) ^ C2F;s(A) ^ :: ^ CkF;s(A) j= C1G;s(A) ^ C2G;s(A) ^ :: ^ CmG;s(A): For example, a CHECK is more speci c than a YN-QUESTION with the same semantic content, having the additional condition that the speaker has a weak belief about the answer. Among the dialogue control acts, of particular interest are those that have communicative functions speci c for dialogue control purposes. We call such functions `dialogue control (DC) functions'. The above criteria lead to a classi cation of DC functions, de ned on the basis of similarity w.r.t. associated utterance features and update operations, depicted in Figure 4. This aspect of the de nition of a communicative function can be expressed in terms of the preconditions for appropriate use of a dialogue act with that function; see further Bunt (1989) and Beun (1989). 14 One may think of C1F;s(A); C2F;s(A); ::; CkF;s(A) as the felicity conditions of the corresponding speech act. 13

20

+--CONTRA-CHECK | +--YN-QUESTION--| +--POSI-CHECK | | | infor| +--CHECK--| +--mation ---|--WH-QUESTION | | seeking | +--NEGA-CHECK | +--ALTS-QUESTION | infor | +--weak +--CONFIRM mative--| | CONFIRM | | weak | | | +--YN-ANSWER----|--YN-ANSWER----| | | | | | | +--weak +--DISCONFIRM | | DISCONFIRM | infor| +--mation ---+--weak WH-ANSWER--+--WH-ANSWER providing | | +--weak +--AGREEMENT | | AGREEMENT | | weak | | +--INFORM--|--INFORM-----| | | +--weak DIS- +--DISAGREEMENT AGREEMENT-+-CORRECTION

Figure 3: Task-oriented communicative functions Four major clusters of dialogue control functions are those concerned with feedback, discourse structuring, interaction management, and social obligations management. The interested reader is referred to Bunt (1984) for a discussion of these dialogue control functions. We now turn the question of context modelling, focusing on the modelling of the information state of a participant in an information dialogue.

4 Modelling cognitive context

4.1 Information conveyed in dialogue

Dynamic Interpretation Theory assumes that factual information is never communicated directly; a speaker in rst instance can only convey his beliefs about certain facts. For example, suppose I inform you what time it is, saying \It's twelve o'clock". If you can see at your watch that it is 12.30, then my statement will probably not change your state of factual information. It may change your information about my state of information: if you take my statement seriously, you believe that I believe it's twelve o'clock. The adoption of factual beliefs about the domain of discourse is thus always an indirect eect of communciation. Let us brie y look at some properties of the information conveyed in communication, and what these properties imply for their formalization and representation in a computational system. 21

+--perception +--positive------| | |--interpretation +--feedback-----+ | | | |--evaluation | +--negative------| | +--dispatch | | +--topic management | discourse | |--structuring--| +--opening | +--dialogue------| | delimitation +--closing | dialogue | +--turn management control ---| | | |--time management | interaction | +--management---|--own communication management | | | +--contact management | | +--self-introduction | | | social | +--welcome---+--initiating +--obligations-----|--greeting--| | management | +--farewell--+--reacting | |--apology | +--thanking

Figure 4: Dialogue control functions 1. First, participants have various kinds of information at their disposal. We will informally also describe this by saying that A believes that p or, equivalently, that A knows that p. Clearly, an epistemic (or doxastic) attitude is required to deal with this in a formal model of the states of the participants in a dialogue. 2. Second, we have to take more than one epistemic attitude into account. In information dialogues, one nds a substantial amount of veri cation; this means that a participant often has certain information p available which isn't fully trusted. Having such weak beliefs is thus a situation that has to be taken into account. There can be nestings of strong beliefs about weak beliefs as well as the other way round. 3. An information dialogue, like most communication, is goal-driven. In information dialogues the overall goal is always an epistemic goal: to want to know something, or to want something to be known to the dialogue partner. Of course, these epistemic goals can be the object of strong as well as uncertain beliefs, and can be nested in complex ways. 22

4. Information about the partner is typically highly incomplete: one usually has incomplete information about what the dialogue partner intends, knows and does not know. So a requirement for any representation formalism is that it should deal adequately with incomplete information. 5. Closely related to the previous point, incomplete information should not only be represented in a formally correct way, but also in a computationally eective way. Typically, the information about the user's knowledge and intentions is very limited at the beginning of a dialogue; as the dialogue proceeds, more and more information becomes available. To handle this in a computationally eective way, these models should not have an eliminatory character, as standard logical models do, but should be incremental in character. 6. Sixth, the models representing the information in dynamic dialogue contexts should be suited to updating. The interpretation of a dialogue utterance typically aects only some of the many dimensions of the dynamic context. Therefore, the context representation should be organized in a modular fashion. This should also facilitate the incremental construction of a model, hand in hand with the development of a dialogue. In the following, we very brie y outline a representational formalism that satis es these requirements (see further Bunt, 1995).

4.2 Modelling multiple agents' states

4.2.1 Possible worlds and partial models

The standard approach to modeling knowledge and belief in logic is the possible-worlds approach, where an agent's knowledge (or belief), is expressed in terms of the alternative worlds that the agent considers possible. For an agent S , those worlds are distinguished among the set of all logically possible worlds by taking part in the relation `accessible for S '. When S knows that p, this is represented by p being true in all worlds accessible for S ; when S knows that not p, this is represented by p being false in all S -accessible worlds. When S does not know whether p, there is at least one S -accessible world where p is true and one where it is false. As it stands, this approach is unattractive from a computational point of view, since S not knowing the truth of a fact q which has not been considered before, is modelled by adding to each S -accessible world one where q is true and one where q is false. Therefore, the less an agent knows, the more worlds have to be represented. Moreover, the facts whose truth an agent does know have to be represented as such in every one of these worlds. All in all, this has the eect that for a realistic domain of discourse, with a large number of potential facts, the representation of an agent's incomplete knowledge involves an astronomic number of sets of facts; moreover, each of these sets is huge, since possible worlds are complete: every atomic proposition must have a truth value in every world. Ideally, one would prefer to model an agent's knowledge by representing only the facts he knows, and to represent these only once. This leads to preferring partial models, where truth values are assigned to only those propositions whose truth is known. Partial models can in fact be use to `implement' the possble-worlds approach in a computationally acceptaptable way. We have developed an approach which constructs `modular' partial models using structured sets of valuation functions, somewhat similar to Fagin, Halpern and Vardi's `knowledge structures' (Fagin, Halpern & Vardi, 1984; Fagin & Vardi, 1985).

23

+--->[q] | Fs' --s-->[p]--->+ Fs | +--->[-r] Fs"

Figure 5: S knows that p and that q _ :r

4.2.2 Partial valuations and incomplete information

A consequence of considering the beliefs of two dierent agents is that the valuation of propositions must be agent-dependent. To introduce the idea of modelling beliefs states with `modular partial models', we begin by considering some of the properties of the valuation F for a xed value of the agent index , and we consider only beliefs with the complexity of propositional logic. We will later turn to more complex beliefs, with rst-order complexity. If agent  does not know whether the atomic proposition p is true or false, F should be unde ned for p. Absence of information can, however, not in general be modelled by making valuation functions partial. If  knows that p or q, but not which of the two, we need to do more than making F unde ned for p. What we do in this case is introduce two partial valuations F0 and F00 , one that makes p true and one that makes q true, and relate these two functions in a particular way to F . Agent 's knowledge then consists of those atomic propositions to which F assigns true or false (or 1 and 0), plus the complex propositions which are true according to both F0 and F00 (plus all complex propositions that logically follow from this knowledge). In the present example, S knows that p _ q, as this proposition is true according to F0 as well as according to F00 , since they each validate one of the disjuncts. The diagram in gure 5 gives a pictorial representation of a model which represents such a situation, where  is the agent S , and where S knows that p and that q _ :r. In this diagram [p] represents the partial function Fs with domain p and Fs (p) = 1; similarly for [q]; [-r] represents the function with domain r which assigns the value 0 (or false) to r. To represent knowledge of one agent about the other's knowledge, say knowledge that S possess about U 's knowledge, we introduce a partial valuation Fs u , so that Fs u (p) = 1 represents that S knows that U knows that the atomic proposition p is true; Fs u (p) = 0 represents that S knows that U knows that the atomic proposition p is false, and Fs u (p) is unde ned means that S has no knowledge of U 's knowledge of p. Can we also represent that S knows that U does NOT know whether p? To this end we introduce the additional valuation Fs u , which expresses S 's negative information about U 's information. In general, in partial models it is necessary to represent explicitly not only what is known to be true, but also what is known to be false. For atomic propositions, this is simply achieved by evaluating them to false. Knowledge of the falsehood of complex propositional knowledge does not need any further measures, since e.g. knowledge that :(p _ q) can be represented as the knowledge that (:p ^ :q), pushing the negation to atomic level. However, `negative knowledge' concerning another agent's knowledge requires an additional device: a partial function which assigns truth values to those atomic propositions which S knows that U doesn't know to be true; we designate this function by Fs u . We now turn to the formal de nition of the structured sets of partial valuation functions for propositional logic; we later generalize this to rst-order logic. 24

4.3 Modular partial models for propositional knowledge

In this section we present in brief the formal de nition of modular partial models, or mpms. We rst describe mpms for the simple case where two agents are considered and one propositional attitude, viz. to have the information available that, for the sake of brevity also referred to as to know or to believe, and where the embedded logic is propositional logic. The corresponding logical language we call 2a-DpL: Two-agent Doxastic propositional Language. Note that, while we want to deal with situations with two agents, our primary aim is to de ne mpms representing the cognitive state of a single agent, who takes the state of another agent into account. Such an mpm can be used for context modelling in a computer dialogue system, the agent whose information state is modelled being the machine.

4.3.1 Formal de nition of mpms

A modular partial model is essentially a highly structured set FI of partial valuations. To de ne the structure of this set, we use indices taken from a set I which is de ned as follows. Definition. The index set I of a modular partial model is de ned using the symbols `s0 , `u0 , `  s0, `  u0 , and the natural numbers, as follows.

1. < s > 2 I . 2. if i 2 I then i < s > 2 I and i < u > 2 I , where  denotes concatenation; 3. if i 2 I then i 2 I and i 2 I . 4. if i 2 I and m is a natural number, then im 2 I . We will use indices as subscript of valuation functions, omitting the sharp brackets < and > when no confusion is likely to arise. Instead of imn we sill write imn . Not all the objects of I , as de ned above, will actually be used as indices of valuation functions. One of the valuations in FI plays a particular role, as its extension represents the elementary facts known to the agent whose belief state we want to model (our (F ) above). Some of the valuations have a special signi cance in representing disjunctive knowledge, like the F0 and F00 in the informal introduction above. Such functions bear a special relationship to a valuation whose representation of atomic facts they extend with disjunctive knowledge; we therefore refer to this relationship is as alternative extension. Formally, a modular partial model is thus a triple consisting of (1) an indexed set of agent-dependent partial valuations; (2) the particular valuation describing a particular agent's knowledge of atomic facts; (3) the speci cation of the alternative extensions. Definition. A modular

partial model for 2a-DpL is a triple (3) M = < F ; FI ; A >, where: - FI is an indexed set of partial functions from the propositional

letters of 2a-DpL to truth values, such that: 1. F 2 FI ; 2. if Fi 2 FI then for all pairs < m; n > 2 A(i), Fimn 2 FI ; 3. if Fi 2 FI then Fi s 2 FI , Fi s 2 FI , Fi u 2 FI , and and Fi u 2 FI ; - A is a partial function from indices to sets of index sets (from I into P (P (I ))), specifying the nonempty alternative extensions present in M 25

+--1--> [q] --s-->O--| +--2-->O--~u--> [p]

Figure 6: S knows that q or U does not know that p For instance, the mpm graphically represented in Figure 5 is the triple: (2) < Fs ; fFs ; Fs1 ; Fs2 g; f< Fs ; ffFs1 ; Fs2 gg >g > where Fs = ;, Fs1 = fpg, and Fs2 = fqg In what follows we will mostly use `S ' to name the agent (`System') whose information state is modelled, and U as that of the other dialogue participant (`User'). Corresponding small letters `s' and `u' will be used in the indices of valuation functions. Note that, according to the constraints on FI , every valuation Fi is assumed to have `links' to both agents (Fi s and Fi u ). Many of these links will connect up to empty valuations, which contain no information. When specifying a certain mpm, we will just leave out all empty valuations (as we already did in the example of gure 5). We will use a simple graphical notation for mpms, where we replace empty boxes `[]' with outgoing connections to nonempty structures by small circles, and leave out empty boxes without (`nonempty') outgoing connections, The following mpm illustrates this.15

4.3.2 Normalization in modular partial models

The above de nition of modular partial models must be supplemented with certain normalization constraints, because otherwise it would allow unintended and undesirable ways of using alternative extensions, which would have the eect that dierent mpms can represent the same information; in other words, the mpm formalism would not associate a unique, canonical representation with every information state.16 Constraints on the proper use of alternative extensions should for instance rule out the structure 7a, where one of the extensions contains information, viz. p being true, which is already present in the `base' function, which con icts with the idea of an extension. The corresponding normalized model is that of gure 7b. Also, the structure of gure 7c is undesirable, since the alternative extensions all contain the same piece of information; according to the idea of alternative extensions, this information should instead by expressed by the `base' valuation function, as in gure 7d.

4.3.3 Truth in a modular partial model A modular partial model Ms = < Fs ; FI ; A > is intended to represent the beliefs of an agent S . We will write S k?  to denote that S believes that . We thus want 2a-DpL expressions S k?  and S k? : , the latter corresponding to `S disbelieves that ', to come out true, false, or 15 We draw connections horizontally or vertically as is convenient, mostly following the convention of drawing negative connections vertically, without attaching any formal signi cance to the layout. Also, we usually attach numerical labels to alternative extensions, the particular choice of numbers of course being insigni cant. 16 With appropriate normalization, there is for every set ? of 2a-DpL formulae a unique canonical model M which represents only the knowledge ?, i.e. it only represents ? and what is logically entailed by it. There are, of course, in nitely many models representing knowledge stronger than ?; for instance, any model representing that S knows that p also represents that S knows that p _ q.

26

+--1--> [p] | --s-->[p]--|--2--> [q] | +--3--> [r] Figure 7a

Figure 7b

+--1-->O--u--> [p] | --s-->O--| | +--2-->O--u--> [p] Figure 7c

+--1--> [q] | --s-->[p]--| | +--2--> [r]

--s-->O--u--> [p]

Figure 7d

Figure 7: Normalization in modular partial models unde ned when evaluated against the model M . We will de ne this with the help of the relations of veri cation, denoted by j, and falsi cation, denoted by j. A formula  is veri ed by an mpm or a sub-mpm Mi , i.e. the relation Mi j  holds, if evaluation of  against the model Mi yiels true. Similarly,  is falsi ed by Mi , i.e. the relation Mi j  holds, if evaluation of  against the model Mi yields false. The relations j and j are de ned below by simultaneous recursion. Definition. The veri cation and falsi cation of a 2a-DpL formula w.r.t. a normal (sub-) mpm Mi = < Fi ; FI ; A > are de ned as follows.17 17 The disjunctive clauses in this de nition all correspond to cases where a formula is veri ed (falsi ed) as the result of a stronger formula being veri ed (falsi ed); see below about `honest' models, i.e. models which, for a given set of formulas ?, only represent ?.

27

(10) 1 If p is a propositional constant: a. Mi j p b. Mi j p

() Fi (p) = 1 () Fi (p) = 0

The remaining clauses apply to any 2a-DpL expressions ; . 2 a. Mi j :  b. Mi j : 

() Mi j  () Mi j 

3 a. Mi j  & b. Mi j  &

() Mi j  and Mi j () Mi j  or Mi j or for every index j 2 Ai ; Mj j  or Mj j

4 a. Mi j  _

() Mi j  or Mi j , or for every index j 2 Ai ; Mj j  or Mj j ,

b. Mi j  _

or the index i is of the form ; where  stands for s or u (the agent indices), and M j (S k?  _ S k? ) () Mi j  and Mi j

5 a. Mi j U k?  () Miu j  b. Mi j U k?  () Miu j  or Mi u j  6 a. Mi j S k?  () Mis j  b. Mi j S k?  () Mis j  or Mi s j 

4.4 Modular partial models for rst-order knowledge

4.4.1 Partiality in rst-order models

For knowledge and belief with respect to information with predicate-logical rather than propositionallogical complexity, we have to take other, more complex forms of partiality into account. For propositional knowledge the only forms of partiality are disjunctive knowlegde and absence of knowledge. For predicate-logical knowledge we have, in addition, the generalization from disjunctive to existentially quanti ed knowledge, and the possibility of partial knowledge of the extension of a predicate. To deal with the two new forms of partiality, we need three provisions in mpms: 1. the introduction of a kind of `pseudo-objects' (borrowing Scott's terminology), for representing individuals that `exist' only within existentially quantifying beliefs, but not necessarily in the actual world (see below); 2. the representation of negative, existentially quantifying beliefs (which indirectly allow the representation of universally quantifying beliefs); 3. the representation of an agent's belief whether his knowledge of the extension of a predicate is complete or partial. Concerning the latter point, it may be worth noting that human agents typically have incomplete knowledge of the extensions of many predicates. Take a predicate like `Restaurant', whose extension is the set of all restaurants in the domain of discourse. In many natural situations, human agents 28

do not know such extensions fully (but a computerized agent, like a local information service, may very well know such an extension completely). On the other hand, a more restrictive predicate like `Thai restaurant downtown' may well have an extension which is fully known to a lover of Thai food. In the latter case, the agent may also very well believe that he has complete knowledge of this extension, whereas in the former case he may believe that his knowledge is incomplete. In in between cases, an agent may have no belief about the completeness of his knowledge. Our strategy in representing an agent's knowledge and beliefs is all the time that we deal with lack of knowledge by having nothing corresponding to that lack in our representation structures. The case where an agent does have a belief about the completeness of his knowledge is, however, a case where our representation structures should represent this belief. We will do this by introducing a `second-order' valuation function T that indicates the believed completeness of the valuations Fi for predicate- and function terms (for functions such as `address-of', `employer-of', etc.). Compared to models of propositional logic, models of rst-order logic have an additional component consisting of a domain of individuals. This is also the case in modular partial models for 2-agent Doxastic First-Order Logic (`2a-DFOL'). Moreover, mpms for 2a-DFOL also include sets of `pseudo-individuals', available only to one of the agents and within the scope of certain propositional attitudes (`believed individuals', for instance). We call these special kinds of individuals, anonymous objects, since they are not named by 2a-DFOL constants. In order to represent beliefs and other attitudes involving anonymous objects we of course need symbols to designate them; we will use a1 , a2 , a3 .. for this purpose. These symbols are a kind of variables, in that they do not have xed denotations in a model and in that the anonymous objects designated by two distinct anonymous terms may be identical (i.e., they may in fact be one and the same object). Anonymous objects are clearly reminiscent of the discourse markers of DRT; they have a similar purpose in that they are meant to allow the expression of identity of objects accross traditional boundaries such as quanti er scopes. Their purpose is dierent in that, where the identity expressed in a DRS is that of coreferentiality in textual linguistic material, in DIT models we express the identity believed by a speaker to hold between two objects whose existence he believes and that play a role in dierent elements of his cognitive state - cognitive states being what we are dealing with in Dynamic Interpetation Theory. Where in DRT the boundaries, crossed by discourse markers, originate in syntactic structure of natural language, in DIT the boundaries crossed by anonymous terms originate in `cognitive modularity': dierent propositional attitudes and dierent agents having these attitudes. Definition. An mpm for 2a-DFOL is a sixtuple

(4) M = < D; N ; F ; FI ; A >; J , where: - D is a domain of individual objects; - N is an indexed set of sets Nj of individuals called `anonymous objects'; - F , FI , A and J are as before, except that additional indices of the form i nex will be used for the representation of negative existential knowledge; formally, if Fi 2 FI then Fi nex 2 FI . The partial valuation functions in FI assign values to the individual constants, the individual variables, and the predicate constants of 2a-DFOL. An important dierence between the values assigned to individual constants and variables is that individual constants have values belonging to the domain D, while variables may be assigned domain objects or anonymous objects as values. More precisely, F( xj ) 2 D [ Avi , i.e. the value assigned to a variable xj at index i is either a domain object or an anonymous object available at that index (see below for the notion of availability). 29

+--s-->[a1: ]--u-->[a2: P(a1), Q(a1,a2)]

In an alternative, DRT-like box notation, we would have: +-----------+ +-----------+ | a1 | | a2 | +-s-->|-----------|--u-->|-----------| | R(a1) | | P(a1) | | Q(eve,ann)| | Q(a1,a2) | +-----------+ +-----------+

Figure 8: Linear and box notation for simple modular partial model The indexed set of sets N introduces certain anonymous objects for those indices j where Nj is not empty. An anonymous object ak is thus introduced at some point in an mpm, namely at the index i where ak 2 Ni . This gives an anonymous object something like a scope: it may be used at every index of the form i , which `extends' i, but it may not be used at indices `smaller' than i. We deal with this idea of scope by introducing the notion of availability. This is de ned recursively as follows. Definition. An anonymous object ak is available at index i if either ak is introduced at that

index, i.e. ak 2 Ni , or ak is available at some index j of which index i is an extension, i.e., i is either js, or ju, or j nex, or jk for some k 2 Aj . We write Avi(ak ) to indicate that ak is among the anonymous objects available at index i. By way of illustration, consider the following model, where we write [a1 : introduction of an anonymous object.

]

to indicate the

Formally, the mpm depicted here is the following model: (5) < fann; eveg; fNs ; Nsu g; F; fF; Gg; ;; f< s; F >; < su; G >g > where Ns = fa1 g, Nsu = fa2 g, F = f< R; fa1 g >; < Q; f< eve; ann >g >g, G = f< P; fa1 g >; < Q; f< a1 ; a2 >g >g

4.4.2 Truth in a 2a-DFOL modular partial model

The truth de nition in 2a-DFOL models diers form that of 2a-DpL models at two points: for elementary propositions, which are no longer atoms but predicate-argument combinations, and for 30

quanti ed expressions, which do not exist in 2a-DpL. We formulate the two new clauses of the truth de nition here, as (6a) and (6b), respectively. In addition, the interpretation of quantifying expressions calls for the assignment of values to individual variables, as in standard predicate logic; to take care of this, we will simply assume that the partial valuations Fi of a model assign values not only to constants of the language, but also to variables. (6a) For any (sub-)mpm M = < D; N ; Fi ; FI ; A >: 1. If P is a k-ary predicate constant and (t1 ,..,tk ) a sequence of k individual constants or variables:

Mi j P (t1 ; ::; tk ) () Fi (t1; ::; tk ) 2 Fi(P ) Mi j P (t1 ; ::; tk ) () Fi (t1; ::; tk ) 2 Fi neg (p). We further use the notation Mi [x=a] to designate the submodel that diers from Mi at most in that Fi (xj ) = a. To formulate the truth condition for existentially quanti ed knowledge, we should take into account that knowledge of the form 9x :  can be represented as such, i.e. the agent in question has no more knowledge than that  is true of at least one individual (this is the case of `honestly' knowing only that 9x : ), or he may have stronger knowledge, for example knowing that  is true of some particular individual. This is the rst-order generalization of the phenomenon that an agent may know that a disjunction is true because he knows of one of the disjuncts that it is true. (6b) Mi j 9x :  () there is an a 2 D [ Avi such that Mi [x=a] j ) Mi j 9x :  () there is an a 2 Ni nex such that Mi[x=a] j )

4.5 Modular Partial Models as Representations of Belief States

The importance of the above formal de nitions of modular partial models is that they allow us to prove that every honest set D of 2a-DFOL formulas, that is every set of formulas that characterizes a state of knowledge, has a unique mpm (up to alphabetic variation) which veri es exactly the formulas of D plus their logical consequences.18 The notion of `honesty' of knowledge has been introduced by Halpern and Moses (1984) (see also Thijsse, 1992, and Thijsse & Van den Hoek (1995) in relation to knowledge bases. They note that not all formulas of an epistemic logical language characterize a state of knowledge. For example, it cannot be the case that all a knowledge base `knows' is that it either knows P or it knows Q. (Which is of course very dierent from knowing that P or Q.) For if the only knowledge a knowledge base has is that it knows P or it knows Q, then it does not know P and it does not know Q, and this is an inconsistent state of aairs. The notion of honesty is also relevant when it comes to modelling states of human knowledge, although the situation is more complex here since it is less clear to what extent such states must be required to be logically consistent. Still, it seems obvious, for instance, that a human agent cannot honestly claim to only know whether P , without knowing that P or that :P . (This is a special case of the above example, with :P for Q.) 18 The alphabetic variation is in the choice of names for anonymous objects. This variation can be eliminated by stipulating that these names are always of the form ak , with some natural number k, and by stipulating that the numbers k are always chosen in some particular order depending on the index where they are introduced, e.g. start numbering the anonymoys objects introduced at index s, next those at index su, next those at index s u, and so on, in some well-de ned order depending on the length of the index.

31

We have formulated the truth de nition of our logical language 2a-DFOL for modular partial models in such a way that an mpm M supports or rejects the truth of a 2a-DFOL formula only if that formula is of the form S k? , i.e. S believes that . Such formulas are honest by de nition, as they express a belief. Notice that the embedded formula  may be a `dishonest' one, like `U knows that P or U knows that Q; the complete expression S k? (U k? P _ U k? Q) is a perfectly honest formula, characterizing a belief state of S . Our mpms are thus only concerned with the representation of the information corresponding to honest formulas; still, a set D of such formulas may be dishonest, as it may be inconsistent. A central theorem of the mpm-formalism will be that for any consistent set D of honest 2a-DFOL formulas there is exactly one modular partial model supporting only the formulas of D and anything which logically follows from the premises in D. Theorem. For any denumerable honest set D of 2a-DFOL formulas there is exactly one mod-

ular partial model supporting only the formulas of D and any formula that logically follows from D, leaving the truth of any other formula unde ned.

Proof (sketch only). The proof goes by double induction: (1) on the cardinality of D; (2) on the complexity of the formulas in D.19 For singleton sets, the proof is trivial. For instance, if D = fP (b)g, with predicate constant P and individual constant b, then the mpm is < fbg; ;; F; fF g; ;; f< s; F >g >, where F = f< P; fbg >g: If D consists for instance of a conjunction, D = f ^ g, then the mpm is the merge of the mpms corresponding to the two conjuncts: M = M M , where the merge of two mpms is de ned in the intuitively obvious way, which also takes care not to duplicate information present in both of the mpms being merged. The existence of the constituting mpms M and M is guaranteed by the induction hypothesis on the complexity of the formulas in D. If D contains more than one formula, the induction step from k to k + 1 simply consists in picking some arbitrary member  from D, such that D = D0 S fg, and taking the merge MD = MD0 M .

4.6 Modular Partial Models and Context Modelling

The formalism of modular partial models as outlined so far, needs further extensions in order to be of real use in modelling that part of the dynamic dialogue context that consists of the information states of the participants. In section 4.1 above, we have listed 6 properties of the information conveyed in a dialogue, corresponding with the following requirements on a context modelling formalism: 1. 2. 3. 4. 5. 6. 7. 19

the formalism should allow the modelling of belief states; besides strong beliefs, weak beliefs should also be taken into account; beliefs about mutual beliefs should also be taken into account; epistemic goals (`intentions') should also be modelled; the formalism should deal adequately with incomplete information; the formalism should be incremental (as opposed to eliminative) in character; the representation structures should be modular.

See also the previous footnote, on avoiding alphabetical variants of mpms.

32

+--s!-->+ | | v +--s--->[a1: ]--u-->[L(b, a1)]

Figure 9: S wants there to be an a1 such that S knows that Bill lives in a1 , and S believes that there is an a1 such that U knows that Bill lives in a1 The mpm formalism, outlined so far, is clearly designed to meet the rst, fth, sixth and seventh requirement. Requirements 2-4 all mean that we should take additional attitudes into account: weak beliefs, mutual beliefs and (epistemic) intentions. In Bunt (1995), we have sketched how mpms can be extended to represent epistemic intentions. The extension of mpms to model the additional doxastic attitudes is technically rather straightforward, but it does complicate the truth de nitions enormously, because of the interactions between the various attitudes. Leaving the formalization of these extensions, which goes far beyond the scope of the present paper, aside we may just indicate for a concrete example of a dialogue act what the mpm might look like when it comes to modelling its preconditions. Consider the example of a WH-question such as Where does Bill live? Let us symoblize the proposition that Bill lives in Manchester as: L(b; m). We consider the two most important preconditions, when S asks this question to U :

 S wants to know where Bill lives;  S strongly believes that U knows where Bill lives. Using the index s! for S has the goal, we may represent this using the following mpm: Returning to the interactions between the various attitudes mentioned, the most obvious ones to take into accoutn are the following.

 weak and strong beliefs should be mutually compatible, in the sense that one cannot weakly believe that p and at the same time strongly believe that :p; also having a weak belief about p creates some `awareness' of p, and, thus, the strong belief that p _ :p. Introspective

capabilities may further link weak and strong beliefs: it may be stipulated that, if S weakly believes that p, then S strongly believes that he weakly believes that p. It may also be convenient, though not logically necessary, to require strong belief to entail weak belief;  epistemic intentions should also be compatible with strong beliefs. One cannot want to know whether p while at the same time knowing that :p, for instance. Also, intentions create awareness, so one cannot honestly claim to only want to know whether p without at the same time strongly believing that p _ :p.  mutual belief entails strong belief of the part of both dialogue partners, as well as nested strong beliefs with arbitrary level of nesting. For instance, if S weakly believes p to be mutually believed, than S weakly believes that U strongly believes that S strongly believes that p. 33

Such dependencies among the various doxastic and epistemic attitudes should be re ected in the truth de nitions of doxastic and boulomaic formulas for modular partial models. Another desirable extension of the context modelling formalism, that we argued for in section 2 above, is that context models should be allowed to be underspeci ed in certain respects, notably as the result of extracting information from dialogue utterances. We are currently investigating possible ways of realizing that; representing knowledge with unscoped quanti ers and negations have for instance been de ned (Bunt, 1994b), which lead to structures that have some super cial similarity to Underspeci ed DRSs, as proposed by Reyle (1993). To this end, we introduce building blocks of mpms as formal objects, and de ne a uni cation operation on these structures, which allow us to build mpms incrementally from their components. A kind of `switches' then correspond to ambiguous functions like the  function, building up mpms with a structural ambiguity in how the components are combined to form an `unambiguous mpm'. Whether it is worth pursuing this in detail depends on what would be the advantages of such ambiguous or `underspeci ed' representations over models with explicit disjunctions for the alternative possibilities. It would seem that underspeci ed models have computational advantages if:

 they `pack' a large number of alternatives, that dier only in the way the components are

connected by instances of the ambiguous element, and  it is possible to reason directly with the `packed', underspeci ed models, without unpacking them rst or on the y.

As it does indeed seem possible to reason with underspeci ed mpms, we believe it to be worth pursuing this line of research further.

5 Conclusions and Future Work In this paper we have described work in progress in the
ELTA project. We have addressed three aspects of the design of a natural language dialogue system which takes the context of the dialogue seriously into account: 1. The use of context-independent versus context-dependent aspects of semantic interpretation. A `cascaded' design of the interpretation process calls for underspeci ed semantic representations, that can be further speci ed as contextual constraints become available. We have seen several instances of how such representations are developed in the
ELTA project for a variety of cases of ambiguity and vagueness. The limits of how far the
ELTA approach may be pushed are not yet clear. 2. The interpretation of the communicative functional meanings of utterances in a dialogue, in terms of context-changing actions. This calls for an analysis of the relevant aspects of context and communicative activity. Much work remains to be done here, but we are con dent that all the relevant types of communicative action, including the various subclasses of dialogue control acts, can be de ned in terms of context changes. 3. The formal and computational modelling of dialogue context. We have focussed on the cognitive part of the context, consisting of the participants' beliefs and intentions. Here, too, a lot of work remains to be done. We believe that partial models are very interesting to consider here, especially if we give them a certain amount of `modular' structure to support their eective use from a computational point of view. The structure of these models may 34

also prove fruitful for interpreting the `information packaging' of utterances in a dialogue (Ravnholt, 1995). Using underspeci ed semantic representations, which are not necessarily ever resolved completely, seems to call for allowing underspeci city in context models as well, as these are built up for an important part through communication. Structured partial models promise to be a powerful instrument for developing such context models.

Acknowledgement

I would like to thank the members of the
ELTA team for many stimulating discussions on the issues discussed here; these thanks go to Gerrit Rentier, Harry Bego, Ko van der Sloot, Ole Ravnholt, Wessel Kraaij and Wim van Loo. I would also like to thank the members of the informal dialogue working group at LIMSI in Orsay (France), where I spent a short sabbatical leave and partly wrote this paper. The discussions in this group have in uenced my thinking on matters related to dialogue modelling, even though this may not be immediately apparent form the paper. These thanks go to Gerard Sabah, Francoise Neel, Anne Vilnat, Brigitte Grau, Violaine Prince, and Samir Bennacef.

References Ahn, R., Kievit, L., Rentier, M. Verlinden, M. (1995) Two levels of semantic representation in DenK. DenK Research Report 95/12, ITK, Tilburg University. To appear in Proc. CLIN'94. Allwood, J. (1976) Linguistic communication as action and cooperation. Gothenburg Monographs in Linguistics 2. Allwood, J. (1984) Obligations and options in dialogue. THINK Quarterly, vol. 3 no. 1, 9-18. Allwood, J., Nivre, J., & Ahlsen, E. (1990) Speech Management - On the Non-written Life of Speech. Nordic Journal of Linguistics 13, 1-48. Alshawi, H. (1992) The Core Language Engine, Cambridge: Cambridge University press. Alshawi, H. & Crouch, R. (1992) Monotonic Semantic Interpretation. Proc. 30th Ann. Meeting of the ACL, Newark (Delaware), 32-39. Bego, H. (1993) A context change view of feedback acts. In: Proc. LACUS'93 Beun, R.J. (1989) Declarative or interrogative, that is the question. PhD Dissertation, Tilburg University. Beun, R.J., Ahn, R., Bunt, H.C. & van Overveld, C. (1995) An Overview of the DenK Multimodal Dialogue System. AI Review. Black, W.J. et al. (1991) A Pragmatics-based Language Understanding System. In: Information Processing Systems and Software: Results of Selected Projects. EC Esprit, Brussels, 454-463. Bos, J., Mastenbroek, E., McGlashan, S., Millies, S. & Pinkal, M. (1994a) The Verbmobil semantic formalism. Technical Report, Dept. of Computational Linguistics, University of Saarbrucken, 35

February 1994. Bos, J., Mastenbroek, E., McGlashan, S., Millies, S. & Pinkal, M. (1994b) A Compositional DRSbsed Formalism for NLP Applications. In H.C. Bunt, R.A. Muskens & G. Rentier (eds.) Proceedings of the International Workshop on Computational Semantics, Tilburg, December 1995. Bronnenberg, W.J., Bunt, H.C., Landsbergen, J., Scha, R., et al. (1979) The PHLIQA1 Question Answering System. In L.Bolc (ed.) Natural Communication with Computers, Munchen: Hauser Verlag. Bunt, H.C. (1984) The treatment of quanti cational ambiguity in the TENDUM system. COLING'84 Proceedings, Stanford University, Ca. Bunt, H.C. (1985) Mass terms and model-theoretic semantics. Cambridge: Cambridge University Press. Bunt, H.C. (1989a) Information Dialogues as Communicative Actions in Relation to User Modelling and Information Processing. In M.M. Taylor, F. Neel & D.G. Bouwhuis (eds.) The Structure of Multimodal Dialogue. Amsterdam: North-Holland Elsevier. Bunt, H.C. (1989b) Towards a dynamic interpretation of utterances in dialogue. In H. Bouma & B. Elsendoorn (eds.) Working models of human perception. Academic Press, New York. Bunt, H.C. (1989c) Recent Advances in Natural Language Dialogue Systems. In H. Niemann, F. Guntherer & G. Sagerer (eds.) Recent Advances in Natural Language and Speech Dialogue Systems, Berlin: Springer. Bunt, H.C. (1991a) DIT - Dynamic Interpretation in Text and Dialogue. In L. Kalman & L. Polos (eds.) Papers from the Second Symposium on Logic and Language, Budapest: Akademiai Kiado. Bunt, H.C. (1991b) Dynamic interpretation and dialogue theory. In: M.M. Taylor, F. Neel, & D.G. Bouwhuis, (eds.) (forthc.) Proceedings of the Second Venaco Workshop on Multimodal Dialogue, Acquafredda di Maratea 1991. Bunt, H.C. (1993) Dialogue managment through context dynamics. In: W.J. Black & H.C. Bunt (eds.) Computational Pragmatics. London City University Press (forthc.). Bunt, H.C. (1994) Context and Dialogue Control. THINK Quarterly 3(1), 19-31 . Bunt, H.C. (1995) Representing information extracted from natural language dialogue.
ELTA Working Paper, February 1995, ITK, Tilburg University. Revised and extended version of a paper with the same title, published in H.C.Bunt & Z. Shi (eds.) Proc. PRICAI'94 International Workshop on Knowledge Engineering and Applications, Beijing, August 1994. Bunt, H.C., Beun, R.J., Dols, F., v.d. Linden, J. & Schwartzenberg, G. (1984) The theoretical foundations of the TENDUM system. In IPO Annual Progress Report 19, Institute for Perception Research IPO, Eindhoven 1984. Bunt, H.C., Ahn, R., Beun, R.J., Borghuis, T. & van Overveld, C. (1995) Cooperative Multimodal 36

Communication in the DenK Project. In: H.C. Bunt, R.J. Beun & T. Borghuis (eds.) Proc. of the Int. Conference on Cooperative Multimodal Communication CMC/95, Eindhoven, May 24-26. Carpenter, B. (1992) The Logic of Typed Feature Structures. Tracts in Theoretical Computer Science, Cambridge University Press, Cambridge, UK. Carpenter, B. & Penn, G. (1994) The Attribute Logic Engine User's Guide. Technical Report, Carnegie-Mellon University, Pittsburgh. Deemter, C. van, Brockho, G., Bunt, H.C., Meya, M., & J. de Vet (1985) From TENDUM to SPICOS - or how exible is the TENDUM approach to question answering? In IPO Annual Progress Report 20, Institute for Perception Research IPO, Eindhoven 1985. Fagin, R., Halpern, J.Y. and Vardi, M.Y. (1984) A model-theoretic analysis of knowledge; preliminary report. In: Proceedings of the 25th IEEE Symposium Foundations of Computer Science. Fagin, R. and Vardi, M.Y. (1985) An internal semantics for modal logic. In: Proceedings of the 17th ACM Symposium on Theory of Computing, Providence. Gazdar, G.R. (1979) Speech act assignment. In: A.K. Joshi, I.A. Sag & B.L. Webber (eds.) Elements of discourse understanding. Cambridge University Press. Groenendijk, J. & Stokhof, M. (1989) Context and information in dynamic semantics. In: H. Bouma & B. Elsendoorn (eds.) Working models of human perception. Academic Press, New York. Groenendijk, J. & Stokhof, M. (1991) Dynamic Predicate Logic. Linguistics and Philosophy 14: 39-100. Geurts, B. & Rentier, G. (1993) Quasi Logical Form in PLUS, ESPRIT Project P5254 (PLUS) Internal Report, ITK, Tilburg University. Isard, S. (1975) Changing the context. In: E.L. Keenan (ed.) Formal semantics of natural language. Cambridge University Press, Cambridge, UK. Kievit, L.A. (1994) Proto-ULF. DenK Research Report 94/02, ITK, Tilburg University. Landsbergen, J. & Scha, R. (1979) Formal languages for semantic representation. In S. Allen & J. Peto (eds.) Aspects of automatized text processing. Buske, Hamburg. Levinson, S. (1983) Pragmatics. Cambridge University Press, Cambridge, UK. Maier, E. & McGlashan, S. (1994) Semantic and Dialogue Processing in the Verbmobil Spoken Dialogue Translation System. In: Progress and Prospects of Speech Research and Technology, 270-273. Montague, R.A. (1974) Formal Philosophy. Papers by Richard Montague edited and introduced by R.H. Thomason. New Haven: Yale University Press. 37

Nivre, J. (1993) Communicative action and feedback. In: M. Baker, R.J. Beun & M. Reiner (eds.) (forthc.) Ravnholt, O. (1995) Information structuring in
ELTA. Paper presented to the HCM Workshop `Dialogue and Discourse', Dublin, April 1995. Rentier, G. (1993) ULF.
ELTA Working Paper, May 1994, ITK, Tilburg University. Rentier, G. (1995) Head-driven Phrase Structure Grammar and Underspeci ed Logical Form. DenK Research Report (forthc.), ITK, Tilburg University. Reyle, U. (1993) Dealing with ambiguities by underspeci cation: construction, representation and deduction. Journal of Semantics 10:123-179. Scheglo, E.A. & Sachs, H. (1973) Opening up closings. Semiotica 7 (4), 289-327. Searle, J.R. (1969) Speech Act Theory. Cambridge University Press. Thurmair, G. (1989) Semantic interpretation in the SPICOS system. In H. Niemann, F. Guntherer & G. Sagerer (eds.) Recent Advances in Natural Language and Speech Dialogue Systems, Berlin: Springer. Wahlster, W. (1993) Verbmobil: U bersetzung von Verhandlungsdialogen. Verbmobil Report 1, Saarbrucken: Deutsches Forschungszentrum fur Kunstliche Intelligenz.

38