Semantics and Interaction in Dialogue

Semantics, Interaction, and NSUs: some data and issues Theoretical antecedents for a semantic theory of moves The simplest theory of questions in dialogue: outline Semantic Ontology in Type Theory with Records References

Semantics and Interaction in Dialogue Jonathan Ginzburg Dept of Computer Science King’s College London The Strand, London WC2R 2LS UK

June 6, 2006

Jonathan Ginzburg, King’s College London

Sem & Int in Dialogue: lec. 1


Today’s Talk 1

Semantics, Interaction, and NSUs: some data and issues Betrayal 999 World Domination NSUs and Turn Taking Puzzles Turn taking puzzles Course overview

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Theoretical antecedents for a semantic theory of moves The Frege-Searle propositional content hypothesis Intens(t)ionalism

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The simplest theory of questions in dialogue: outline Short Answers Semantic Notions of Answerhood: aboutness Semantic notions of answerhood: resolvedness

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Semantic Ontology in Type Theory with Records Why use TTR? Basics of TTR Ontological summary




Betrayal 999 World Domination NSUs and Turn Taking Puzzles Turn taking puzzles Course overview

Where we are now 1


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An example from Pinter (1)

(a) Emma: We have a flat. (b) Robert: Ah, I see. (Pause) Nice? (Pause) A flat. It’s quite well established then, your . . . uh . . . affair? (c) Emma: Yes. (d) Robert: How long? (e) Emma: Some time. (f) Robert: But how long exactly? (g) Emma: Five years. (h) Robert: Five years? [p. 85, H. Pinter Betrayal, Faber, London 1991.]





Dialogue v. Text Conciseness: conversation is, by comparison with text, a highly efficient medium: Robert’s noting that Emma and her cohort have a flat, Emma’s affirmation of the well-established nature of the affair, Robert’s wondering how long the affair has been going on, Emma’s informing Robert that it has gone on for five years and Robert’s astonishment at Emma’s informing him this:

50 words dialogue version: 15 words Radical Context Dependence: Isolated from their occurrence in a dialogue many utterances lose most of their import and are ambiguous. Jonathan Ginzburg, King’s College London




A 999 call Wragg I’ve just murdered my son. Operator And your name is? Wragg (spelling) W-R-A-G-G. Operator When you say murdered, what do you mean? Wragg I’ve killed him. Operator How? Wragg With a pillow over the face. Operator How old was he? Wragg He is 10. Operator Why have you done this? Wragg I don’t want to comment any more. That’s all you need to know. Operator Is there anyone else there with you? Wragg My wife is there, yeah. Operator Are there any children in the house? Wragg No. Operator Where is your wife? Wragg She’s in the house. She’s safe. She’s all right. Operator If you’d like to wait there I’ll get someone to come round Wragg Super. Thank you.





Some interactional phenomena Wragg: I’ve just murdered my son. Operator: And your name is? gap utterance, metacommunicative utterance Wragg: (spelling) W-R-A-G-G NSU, multimodal utterance Operator: When you say murdered, what do you mean? metacommunicative utterance Wragg: I’ve killed him. Operator: How? NSU Wragg: With a pillow over the face. NSU Jonathan Ginzburg, King’s College London




















Some interactional phenomena

Operator: How old was he? Wragg: He is 10. false answer? Operator: Why have you done this? long distance, highly ambiguous event anaphor Wragg: I don’t want to comment any more. That’s all you need to know. metacommunicative utterance

















Some interactional phenomena Operator: Is there anyone else there with you? Wragg: My wife is there, yeah. Operator: Are there any children in the house? Wragg: No. NSU Operator: Where is your wife? Wragg: She’s in the house. She’s safe. She’s all right. ‘Superfluous’ answer Operator: If you’d like to wait there I’ll get someone to come round Wragg: Super. Thank you. NSUs Jonathan Ginzburg, King’s College London












A simple example (2)

1 L(ieutenant): What happened here? 2 S(ergeant): An accident. 3 L: Who’s hurt? 4 S: The boy and one of our drivers. 5 L: How bad is he hurt? 6 S: The driver or the boy? 7 L: The boy. 8 S: Tucci? 9 M(edic): The boy has critical injuries. 10 S: OK.





Paraphrase generation as basic semantics

1 L(ieutenant): What happened here? L is asking what (situation/incident) happened in location l0 . 2 S(ergeant): There was an accident. S is saying that (the situation that happened in location l0 ) was an accident . 3 L: Who’s hurt? L is asking who’s hurt in this accident 4 S: The boy and our driver. S is saying that a boy b0 and a driver associated with S, d0 , were hurt in this accident.























Paraphrase generation as basic semantics 5 L: How bad is he hurt? L is asking how bad is he hurt 6 S: The driver or the boy? S is asking if L’s ‘he’ refers to b0 or does it refer to d0 ? 7 L: The boy. L is saying that ‘he’ refers to b0 . 8 S: Tucci? S is asking Tucci to answer the question about how bad b0 is hurt 9 Tucci: The boy has critical injuries. (Tucci is saying that) b0 has critical injuries. 10 S: Understood. S is saying that he understands what Tucci has just said. Jonathan Ginzburg, King’s College London
























Basic tasks An account of the verb ‘happen’—presumably this is to be analyzed somehow as involving a relation between situations/events and spatio-temporal locations that extend into them; for some discussion see ?. The accident situation involved here serves as the ‘domain’ for utterances 3, 4 Indexicality—resolution of meaning relative to the current utterance situation —is implicated in utterances (1, 3, 4, 5), e.g. in the resolution of ‘here’, ‘he’, ‘the boy’, and of course tense.





Basic tasks An account of the verb ‘happen’—presumably this is to be analyzed somehow as involving a relation between situations/events and spatio-temporal locations that extend into them; for some discussion see ?. The accident situation involved here serves as the ‘domain’ for utterances 3, 4 Indexicality—resolution of meaning relative to the current utterance situation —is implicated in utterances (1, 3, 4, 5), e.g. in the resolution of ‘here’, ‘he’, ‘the boy’, and of course tense.





Basic tasks Metacommunicative meaning: (6) is a request for the clarification of (5). complex process combining ellipsis resolution with a grammatical device relating to disjunction and alternative questions; the interpretation of (10) involves the previous utterance as the argument of the predicate ‘understand’. Dialogue moves: none of the utterances involves an explicit performative (‘I’d like to ask the following:’, ‘I claim that . . . ’) and yet, minimally, the force of any given utterance is as indicated (‘L asks . . . ’, ‘S says that . . . ’ etc)





Basic tasks

Question/Answer dynamics is involved in the interpretation of utterances (2, 4, 7, 9). This includes the resolution of the short answers in (4,7) and the availability of the question raised in (5) to Tucci in utterance (9).





Theoretical requirements

A theory of external reality on the basis of which scenes like that depicted in this conversation can be described. A theory of how utterance meanings get anchored in speech events. A theory of metacommunicative interaction. A theory of dialogue moves. A theory of dialogue context.





























Sententialism

Sententialism on a number of levels is a fundamental issue in work on non sentential utterances (NSUs)—complete utterances that lack a verbal (more generally predicative) constituent. Semantic sententialism: do NSUs involve fully articulated propositional (question, fact denoting) contents? Syntactic sententialism: do NSUs involve fully articulated sentential structure?





Sententialism






Sententialism






Basic perspective Perspective on NSUs here: data–driven, computational perspective which takes language use in dialogue as primary. In conversation NSUs are very prevalent. Frequency estimates vary, depending on the taxonomic criteria one chooses, ranging from between 30-40% of all utterances (de Waijer 2001) to 11% (Fernández and Ginzburg 2002, based on random sampling of adult conversations from the British National Corpus (BNC).). On the whole NSUs are resolved effortlessly—(see below for corpus evidence, that they do not usually involve complex pragmatic reasoning typical of particularized implicatures. Jonathan Ginzburg, King’s College London




Basic perspective Perspective on NSUs here: data–driven, computational perspective which takes language use in dialogue as primary. In conversation NSUs are very prevalent. Frequency estimates vary, depending on the taxonomic criteria one chooses, ranging from between 30-40% of all utterances (de Waijer 2001) to 11% (Fernández and Ginzburg 2002, based on random sampling of adult conversations from the British National Corpus (BNC).). On the whole NSUs are resolved effortlessly—(see below for corpus evidence, that they do not usually involve complex pragmatic reasoning typical of particularized implicatures. Jonathan Ginzburg, King’s College London




NSUs and Context

NSUs as akin to indexicals. So: systematic study of NSUs presupposes (and informs) a theory of dialogue context. Basic claim: given a detailed and precise theory of dialogue context, the theory of NSUs is relatively simple. Main task—articulating a sufficiently detailed theory of context.





Equal Access A commonly exploited but rarely enunciated piece of common sense concerning the sharing of context: (3)

Equal Access to Context: As a conversation proceeds a shared context (the common ground) emerges: A has her turn, reaches a transition relevance point(TRP); Then either A proceeds or B takes over from the common ground point at which A spoke.

(4)

A: Who should we invite to the conference? A/B: Noam, perhaps?





Turn taking puzzle 1 There is reason to doubt a simplistic version of Equal Access. (5) a. A: Who does Bo admire? B: Bo? Reading 1 ( short answer): Does Bo admire Bo? Reading 2 (clausal C(larification) E(llipsis)): Are you asking who BO (of all people) admires?; Reading 2 (constituent C(larification) E(llipsis)): Who do you mean ‘Bo’?) b. A: Who does Bo admire? Bo? unambiguously: ( short answer): Does Bo admire Bo? Jonathan Ginzburg, King’s College London




Turn taking puzzle 2 (6) is an even more striking illustration of this phenomenon: the resolution that can be associated with ‘Why?’ if A keeps the turn is unavailable to B if s/he had taken over and vice versa. (6c) shows that these facts cannot be reduced to coherence or plausibility—the resolution unavailable to A in (6a) yields a coherent follow up to A’s initial query if it is expressed by means of a non-elliptical form: (6)

a. A: Which members of this audience own a parakeet? Why? (= Why own a parakeet?) b. A: Which members of this audience own a parakeet? B: Why? (= Why are you asking which members of this audience own a parakeet?) c. A: Which members of this audience own a parakeet? Why am I asking this question?





TTPs: consequences The TTP highlights the existence of NSUs used to request clarification of a previous utterance. Such NSUs constitute, on one estimate, (Fernández 2006, data from the BNC), upwards of 90% of all NSUs used interrogatively. Provide data that inter alia refutes long held assumption, probably predating Hankamer and Sag 1976, that parallelism effects implies syntactic sententialism. Consequence re context: it is not useful to speak about context per se but rather one needs to look at individualized versions (or branches) of context.















TTPs: consequences

(5) illustrates that, due to the intrinsic processing asymmetry between speaker and addressee the latter has options concerning clarification that the speaker lacks (6) indicates that the contextual asymmetries also go in the other direction.





TTPs: consequences

(5) illustrates that, due to the intrinsic processing asymmetry between speaker and addressee the latter has options concerning clarification that the speaker lacks (6) indicates that the contextual asymmetries also go in the other direction.





Solving TTP1: basic ingredients Solving TTP1 involves a number of significant modifications to commonly accepted theories of linguistic meaning and context. a theory of context which uniformly integrates illocutionary and metacommunicative information, guided in part by data about the resolution of MCI-oriented NSUs. a theory of meaning in which Lewisian regularities—even in highly contextualized form suggested by situation semanticists (e.g. Perry and Israel 1990)—are modified to accommodate imperfect communication and underpin clarification interaction. an NL metaphysics with reference to utterance events and utterance event types. (cf. pace the I-language/E-language dichotomy originally set up by Chomsky and recently revived under the guise of FLB /FLN in Hauser et al. 2002.) Jonathan Ginzburg, King’s College London
















Basic plan

Lecture 1 (Rest of today) Developing a semantic ontology for dialogue in TTR; introduction to Type Theory with Records (TTR).

Lecture 2 Type theoretic constraint-based grammar: motivations from dialogue; grammatical analysis with TTR: a simple fragment. Basic Interaction in dialogue: Public v. private context in Interaction; the structure of public context in Interaction; describing simple interactions (greetings, partings); Basic Interaction in dialogue: asking, asserting, answering, and accepting; Private context in interaction. Jonathan Ginzburg, King’s College London




Basic plan

Lecture 1 (Rest of today) Developing a semantic ontology for dialogue in TTR; introduction to Type Theory with Records (TTR).

Lecture 2 Type theoretic constraint-based grammar: motivations from dialogue; grammatical analysis with TTR: a simple fragment. Basic Interaction in dialogue: Public v. private context in Interaction; the structure of public context in Interaction; describing simple interactions (greetings, partings); Basic Interaction in dialogue: asking, asserting, answering, and accepting; Private context in interaction. Jonathan Ginzburg, King’s College London




Basic plan

Lecture 3 Grounding and clarification: the data—grounding, corpus studies of clarification requests, turn taking puzzles; Interacting over grammatically governed content: informal picture; A protocol combining grounding and crification; experimenting with the dialogue experimental tool.

Lecture 4 Non sentential utterances: corpus studies, developmental data, taxonomies; describing propositional lexemes; parallelism effects: NSU resolution—syntactic or semantic?; describing short answers, clarification ellipsis. Sluicing—a corpus study; building a classifier for sluicing; building a classifier for NSUs in general. NSUs in Multi-party dialogue. Jonathan Ginzburg, King’s College London




Basic plan

Lecture 3 Grounding and clarification: the data—grounding, corpus studies of clarification requests, turn taking puzzles; Interacting over grammatically governed content: informal picture; A protocol combining grounding and crification; experimenting with the dialogue experimental tool.

Lecture 4 Non sentential utterances: corpus studies, developmental data, taxonomies; describing propositional lexemes; parallelism effects: NSU resolution—syntactic or semantic?; describing short answers, clarification ellipsis. Sluicing—a corpus study; building a classifier for sluicing; building a classifier for NSUs in general. NSUs in Multi-party dialogue. Jonathan Ginzburg, King’s College London



The Frege-Searle propositional content hypothesis Intens(t)ionalism

Where we are now 1


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The Frege-Searle propositional content hypothesis Speech Act Theory (see e.g. Searle 1969, Searle 1985), is the framework of choice for much influential work on dialogue (see e.g. Cohen-Perrault 1980,Allen-Perrault 1980 et seq). Speech Act Theory embodies an important insight: need to assign utterances an illocutionary content. illocutionary content: a content which embeds a semantic entity such as a proposition or question under a predicate that represents the current conversational move (assert, ask etc). (7) Assertions, polar queries, and commands differ on the level of illocutionary force, but share the same descriptive/propositional content (THE F REGE -S EARLE PROPOSITIONAL CONTENTSem HYPOTHESIS (FSPCH)). Jonathan Ginzburg, King’s College London & Int in Dialogue: lec. 1



The Frege-Searle propositional content hypothesis

Uttered in the same context, declarative, interrogative, and imperative variants as in (8) have the same content, namely some proposition p; (8) a. Bo will go away. (Content: Assert(A,B,p)) b. Will Bo go away? (Content: Ask(A,B,p)) c. Go away Bo! (Content: Order(A,B,p))

The difference: (8a) will be used to assert p, whereas (8b) will be used to ask p, and (8c) to command p:





The Frege-Searle propositional content hypothesis

Uttered in the same context, declarative, interrogative, and imperative variants as in (8) have the same content, namely some proposition p; (9) a. Bo will go away. (Content: Assert(A,B,p)) b. Will Bo go away? (Content: Ask(A,B,p)) c. Go away Bo! (Content: Order(A,B,p))

The difference: (9a) will be used to assert p, whereas (9b) will be used to ask p, and (9c) to command p:





The Frege-Searle propositional content hypothesis The FSPCH encodes a plausible intuition. If correct, it could underpin an explanation of the fact that quantified NPs and certain adverbs are possible in all three semantic environments: (10) a. Everyone vacated the building. b. Did everyone vacate the building? c. Everyone vacate the building! (11) a. Kim always wins. b. Does Kim always win? c. Always wear white!





The Frege-Searle propositional content hypothesis: problems Various problems with FSPCH. Here: a subcase of the FSPCH, namely the identification of propositions and (polar) questions. If a polar interrogative denotes a proposition it should be assertible and bear a truth value, neither of which is the case: (12) a. I’m going to make one claim: #Did Bo leave? b. #It is true/false whether Bo left.





The Frege-Searle propositional content hypothesis: problems Moreover, a polar interrogative utterance should be disquotable using a ‘that clause’. In fact, such a disquotation is not possible, but requires instead the complementizer ‘whether’: (13) a. A: Did Bo leave? b. A asked whether/that Bo left.

That this is not merely a syntactic idiosyncrasy is illustrated in (14). (14a) differs from (14b) in allowing for the possibility that Jo didn’t leave: (14) a. Bo knows whether Jo left. b. Bo knows that Jo left. Jonathan Ginzburg, King’s College London




The Frege-Searle propositional content hypothesis: problems Common in AI work that wh-interrogatives are also interpreted as propositions, with the wh-phrases functioning as definite descriptions. Thus, (15a) is interpreted as (15) a. Who left? b. the x: left(x)

Classic argument against, due to Karttunen 1977, derives from the existence of a class of predicates which embed interrogative but not declarative complements: (16) a. Brooke asked/wondered/investigated who left. b. #Brooke asked/wondered/investigated that Drew left. (17) a. Who wins the race depends upon/is influenced by who enters. b. Ginzburg, #That Jo wins theLondon race depends influenced by that Mary Jonathan King’s College Sem & Int on/is in Dialogue: lec. 1











Initial Spec for an Ontology (24) a. The ontology must include a class PROP of truth bearing individual entities, dubbed propositions. b. The ontology must include a class QUEST of individual entities which are not truth bearing, but to which notions such as being asked or being resolved are applicable, dubbed questions. c. The ontology must include a class OUTCOME of individual entities which are not truth bearing, but to which notions such as being fulfilled are applicable. Following Ginzburg and Sag 2000, call these outcomes. d. The ontology must provide a semantic unit which constitutes input/output of (certain) adverbial modifiers and NP quantification and which are constituents of propositions, questions, and outcomes. Jonathan Ginzburg, King’s College London




Montague’s strategy A useful starting point is Montague’s seminal work in PTQ. In that work the ontology can be identified with a relational structure R(W ) ( for a presentation of Montague Semantics in these terms, see Turner 1997, section 3.) This carries a distinguished subset W of the domain D such that W is construed as a set of possible worlds. The class of propositions is identified with the power set of W , i.e. the set of all subsets of W . Boolean operations (negation, conjunction, disjunction) are modelled simply via set theoretic operations of complementation, intersection, and union, respectively. Jonathan Ginzburg, King’s College London
















Montague’s strategy

Most important insight (?) of this intensional approach is in its intenTionality—offers picture of how assertoric utterances relate to the external world, by quasi-referential deixis to sets of alternative worlds; must include the actual world for truth. This also provides a straightforward account of how contents can be shared across speakers and across languages.





Montague’s strategy Montague himself was aware of the fact that this approach is quite coarse grained, a problem often dubbed logical omniscience. Logical omniscience constitutes a serious obstacle towards construing the Montogovian ontology in cognitive terms. There are various fairly easy fixes to that specific problem, (See e.g. Hilpinen, Muskens.). But given use of worlds still involve ontologies that are difficult to construe directly in cognitive and computational terms.





Montague’s strategy: ontological poverty Classical intensional strategy fails to make certain key distinctions among the ‘external entities’, distinctions whose importance for lexical semantics in particular have been known since the time of Vendler (1968, 1972) and earlier. The crucial distinction is between ‘semi-concrete’ objects such as events and situations and abstract objects such as facts, possibilities, and propositions. Event-like entities are spatio-temporally located and can be modified by concrete adjectives, but truth is not predicable of them: (25) a. The wedding lasted a long time/was lavish/took place in Sheikh Jarah/ #was true/false b. Tony’s savaging of the party has lasted for years/is bloody/is not limited to London/ #was true/false. Jonathan Ginzburg, King’s College London




Montague’s strategy: ontological poverty Classical intensional strategy fails to make certain key distinctions among the ‘external entities’, distinctions whose importance for lexical semantics in particular have been known since the time of Vendler (1968, 1972) and earlier. The crucial distinction is between ‘semi-concrete’ objects such as events and situations and abstract objects such as facts, possibilities, and propositions. Event-like entities are spatio-temporally located and can be modified by concrete adjectives, but truth is not predicable of them: (26) a. The wedding lasted a long time/was lavish/took place in Sheikh Jarah/ #was true/false b. Tony’s savaging of the party has lasted for years/is bloody/is not limited to London/ #was true/false. Jonathan Ginzburg, King’s College London




Montague’s strategy: ontological poverty facts/possibilities and propositions are not spatio-temporally located and resist modification by concrete adjectives. Truth is predicable of propositional entities, though not of facts/possibilities: (27) a. #The fact that Tony savaged the party has lasted for years/is bloody/is not limited to London. b. #That Tony savaged the party lasted a long time/was lavish/took place in Sheikh Jarah. c. The hypothesis was that Glyn is dangerous. #That hypothesis has lasted for years/is bloody/is not limited to London. d. #The fact that Tony was ruthless is true. e. #Tony’s being ruthless is true. f. #The possibility that Glyn might get elected is true. g. The claim/hypothesis/proposition that Tony was ruthless is true/false. Jonathan Ginzburg, King’s College London




Montague’s strategy: ontological poverty event anaphora: an assertoric utterance enables subsequent anaphoric reference to an event, even if the assertion is not accepted, as in (28c). This is of course another facet of the intentionality of propositions mentioned above: (28) a. A: My back tyre exploded. Two minutes later it started to rain. b. A: Jo and Mo got married yesterday. It was a wonderful occasion. c. A: Jo’s arriving next week. B: No, that’s happening in about a month. Jonathan Ginzburg, King’s College London




Montague’s strategy: ontological poverty event anaphora: an assertoric utterance enables subsequent anaphoric reference to an event, even if the assertion is not accepted, as in (29c). This is of course another facet of the intentionality of propositions mentioned above: (29) a. A: My back tyre exploded. Two minutes later it started to rain. b. A: Jo and Mo got married yesterday. It was a wonderful occasion. c. A: Jo’s arriving next week. B: No, that’s happening in about a month. Jonathan Ginzburg, King’s College London



Short Answers Semantic Notions of Answerhood: aboutness Semantic notions of answerhood: resolvedness

Where we are now 1


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The simplest theory of questions in dialogue What is a question? Simple answer: a propositional abstract. Simplicity: any theory of questions needs to associate an abstract-like object with interrogatives to explicate the resolution of short answers. Answerhood: Explicating answerhood involves a characterization that utilizes in some form an abstract-like object (abstract, open sentence etc). If questions are abstracts, this follows automatically (but see below for some caveats.). Tractability: Questions as propositional Abstracts (QPA) yields a transparently implementable theory. In contrast, EAC theories that identify questions with partitions of propositions (e.g. Groenendijk and Stokhof 1984 et seq.) are intractable on their most transparent implementation (see e.g. Bos and Gabsdil 1999). Jonathan Ginzburg, King’s College London




QPA: a syntactic argument Wait. But is there positive evidence that questions are propositional abstracts, as opposed to any other type of abstract? Ginzburg and Sag 2000 provide a concrete argument for the view, based on the distribution of wh-in situ phrases in English. In declarative clause-types the occurrence of such phrases leads to an ambiguity between two readings: a ‘canonical’ use which expresses a direct query and a use as a reprise query to request clarification of a preceding utterance. In all other clause types, ones which denote outcomes (30d), questions (30e), or facts (30f) the ambiguity does not arise, only a reprise reading is available. Jonathan Ginzburg, King’s College London
















QPA: a syntactic argument (30) a. The bagels, you gave to who? (can be used to make a non-reprise query.) b. You gave the bagels to who? (can be used to make a non-reprise query.) c. Who talked to who? (can be used to make a non-reprise query.) d. Give who the book? (can be used ONLY to make a reprise query.) e. Do I like who? (can be used ONLY to make a reprise query.) f. What a winner who is? (can be used ONLY to make a reprise query.) (Ginzburg and Sag 2000, example (72), p. 282) Jonathan Ginzburg, King’s College London




Requirements for QPA

A theory of (λ-)abstraction that allows for null as well as multiple abstraction A means of maintaining an ontological distinction between propositional abstracts and properties, for instance by means of the situation theoretic distinction between a proposition and a situation type A logic which does not enforce the excluded middle, i.e. in which p ∨ ¬p is not a vacuous truth.





Alternative to QPA We have no argument save Occam’s razor against a theory of questions, where questions are not reductively construed, but are constructed in terms of propositional abstracts. The proponent of such a theory would need to show either that propositional abstracts have other semantic business to do, which does not relate to questions. Alternatively, they might dispute our ontological set up, which allows us to distinguish propositional abstracts from situation type abstracts.















Short Answers An interrogative use enables non-sentential propositional responses (short answers): the nature of the question asked strongly influences the semantic type, and to some extent, the form of the short answer: (31) a. A: Who attended the meeting? B: Mo/No students./A friend of Jo’s. b. A: When did Bo leave? B: Yesterday./At two. c. A: Why did Maire cross the road? B: Because she thought no cars were passing. d. A: Who relies on whom in this department? B: Bo on Mo./Some of my friends on each of her friends. Jonathan Ginzburg, King’s College London




QPA (Montogovian Formulation)

On a questions as abstracts view, we get the following basic denotations: (32) a. Who left 7→ λx.leave(x) b. When did Bo leave 7→ λt.At(t, leave(b)) c. Why did Maire cross the road 7→ λc.Cause(c, cross(m, r )) d. Who relies on whom 7→ λx, y .rely (x, y ).





QPA (Montogovian Formulation) QPA in its original Intensional Logic formulation faces a number of severe problems: Type multiplicity: the type of any two interrogatives differing in arity (e.g. unary/binary/ternary wh-interrogative-sentences) or in the type of argument (e.g. adverbial vs. argumental wh-phrase) is distinct. Type multiplicity (in the IL setting) yields difficulties in defining Boolean operations uniformly on interrogatives. Ontological collapse: whereas type multiplicity is a theory internal problem, a more general problem is ontological. Within an IL setting (but more generally), propositional abstracts are akin to properties, the denotata of (intransitive) verbs, adjectives, and common nouns. Jonathan Ginzburg, King’s College London




QPA (Montogovian Formulation) Implication: required to identify questions with the denotata of verbs, common nouns, and adjectives. (33) a. left 7→ λx.left(x). b. rely 7→ λx, y .rely (x, y ). c. The question is who is happy—This question is unresolved. #The property of being happy is unresolved. #To be happy is unresolved. d. Can you tell me something about who is happy? 6⇒ Can you tell me something about being happy. e. Some man is happy. So we know that happiness and manfulness are not incompatible. #So we that theSemquestion of lec. who is happy Jonathan Ginzburg, King’sknow College London & Int in Dialogue: 1



QPA (Montogovian Formulation) Polar interrogatives: the distribution of polar interrogatives is essentially the same as that of wh-interrogatives, which suggests we would like to subsume them under a single semantic class. Moreover polar interrogatives, also exhibit a phenomenon akin to short answers: (34) A: Did Bo attend the meeting? B: Yes./Maybe./Probably/No. The most obvious proposal: polar interrogatives constitute the limiting case where the number of uninstantiated variables is 0. Involves identifying polar questions with the queried proposition. The literature on interrogative semantics Jonathan Ginzburg, King’s College London Sem & Int in Dialogue: lec.move. 1 provides various arguments against such a



Resuscitating QPA: basic ingredients

Austiniety: ST ontology where situation types are intrinsically distinct from propositions. λ-closure: ST ontology that is closed under simultaneous abstraction: for every element a ∈ |S| and every set B ⊂ |S|, the simultaneous abstraction λB.a exists and is distinct from a.





Resuscitating QPA: simple results Uniform type for questions (via simultaneous abstraction) Avoiding ontological collapse (via Austiniety) Simple treatment of polar questions, that avoids identifying p? and ?¬p (as EAC approaches do) (via setting up the abstraction operation to be such that (a) abstraction over empty sets is permitted. (b) (An analogue of) η-reduction fails). Simple treatment of Boolean operations (via simultaneous abstraction). Answerhood (using structure of SU+AE). Jonathan Ginzburg, King’s College London




QPA: a more recent formulation Ginzburg and Sag, 2001 showed how in a situation theoretic ontology, modelled using tools from non-well-founded set theory Seligman and Moss, 1997, the problems for an abstract-based view could be overcome. Nonetheless, a key element of Ginzburg and Sag’s account is the use of simultaneous abstraction, an operation first introduced by Aczel and Lunnon, 1991. The uniform treatment of different kinds of interrogatives—including the definition of a semantic type question and answerhood—use this ad hoc notion of λ-abstraction. The question arises (see e.g. Koenig 2004,Nelken 2005)—can the benefits of this account be preserved using standard notions of abstraction? Jonathan Ginzburg, King’s College London




Answerhood What response is appropriate to a given query depends on a variety of factors, including domain knowledge, the interlocuters’ goals, politeness etc. There is also a not inconsiderable role for semantics. Questions single out various classes of propositions as being their potential answers. There are a number of notions of answerhood that are of importance to dialogue. One relates to coherence: any speaker of a given language can recognize, independently of domain knowledge and of the goals underlying an interaction, that certain propositions are about or directly concern a given question. Jonathan Ginzburg, King’s College London




Answerhood What response is appropriate to a given query depends on a variety of factors, including domain knowledge, the interlocuters’ goals, politeness etc. There is also a not inconsiderable role for semantics. Questions single out various classes of propositions as being their potential answers. There are a number of notions of answerhood that are of importance to dialogue. One relates to coherence: any speaker of a given language can recognize, independently of domain knowledge and of the goals underlying an interaction, that certain propositions are about or directly concern a given question. Jonathan Ginzburg, King’s College London




Answerhood The simplest notion of answerhood we can define on the basis of an abstract is one I’ll call, following Ginzburg and Sag 2000, simple answerhood: (35) a. p is a simple answer to q iff p is an instantiation of q or a negation of such an instantiation. b. For a polar question: {r | SimpleAns(r , λ{ }p)} = {p, ¬p} c. For a unary wh-question: {r | SimpleAns(r , λ{b}p(b))} = {p(a1 ), . . . , p(an ), ¬p(a1 ), . . . , ¬p(an )} Simple answerhood covers a fair amount of ground. But it clearly underdetermines aboutness. Jonathan Ginzburg, King’s College London




Answerhood The simplest notion of answerhood we can define on the basis of an abstract is one I’ll call, following Ginzburg and Sag 2000, simple answerhood: (36) a. p is a simple answer to q iff p is an instantiation of q or a negation of such an instantiation. b. For a polar question: {r | SimpleAns(r , λ{ }p)} = {p, ¬p} c. For a unary wh-question: {r | SimpleAns(r , λ{b}p(b))} = {p(a1 ), . . . , p(an ), ¬p(a1 ), . . . , ¬p(an )} Simple answerhood covers a fair amount of ground. But it clearly underdetermines aboutness. Jonathan Ginzburg, King’s College London




Answerhood On the polar front, it leaves out the whole gamut of answers to polar questions that are weaker than p or ¬p such as conditional answers ‘If r, then p’ (e.g. 37a) or weakly modalized answers ‘probably/possibly/maybe/possibly not p’(e.g. 37b). As far as wh-questions go, it leaves out quantificational answers (37c-g), as well as disjunctive answers. These missing class of propositions, are pervasive in actual linguistic use.





Answerhood On the polar front, it leaves out the whole gamut of answers to polar questions that are weaker than p or ¬p such as conditional answers ‘If r, then p’ (e.g. 37a) or weakly modalized answers ‘probably/possibly/maybe/possibly not p’(e.g. 37b). As far as wh-questions go, it leaves out quantificational answers (37c-g), as well as disjunctive answers. These missing class of propositions, are pervasive in actual linguistic use.





Answerhood (37) a. Christopher: Can I have some ice-cream then? Dorothy: you can do if there is any. (BNC, KBW) b. Anon: Are you voting for Tory? Denise: I might. (BNC, KB?, slightly modified) c. Dorothy: What did grandma have to catch? Christopher: A bus. (BNC, KBW, slightly modified) d. Rhiannon: How much tape have you used up? Chris: About half of one side. (BNC, KB?) e. Dorothy: What do you want on this? Andrew: I would like some yogurt please. (BNC, KBW, slightly modified) f. Elinor: Where are you going to hide it? Tim: Somewhere you can’t have it.(BNC, KBW) Jonathan Ginzburg, King’s College London




Answerhood The simplest way to enrich simple answerhood is by closing simple answerhood under disjunction. (Proposals along these lines can be traced to Groenendijk and Stokhof, and to Stanley Peters.). (38)

p is about q iff p entails a (finite) disjunction of simple answers.

Given that for a given question, the class of simple answers always contains at least one proposition p and its negation ¬p, the definition is (79) is restrictive only within a logical framework in which the law of the excluded middle fails. That is, a setting in which (39) is the case: (39)

p ∨ ¬p is not vacuously true.

This is one motivation to use as logical underpinning for this work constructive frameworks where (39) is maintained.





Answerhood The simplest way to enrich simple answerhood is by closing simple answerhood under disjunction. (Proposals along these lines can be traced to Groenendijk and Stokhof, and to Stanley Peters.). (40)


Given that for a given question, the class of simple answers always contains at least one proposition p and its negation ¬p, the definition is (79) is restrictive only within a logical framework in which the law of the excluded middle fails. That is, a setting in which (41) is the case: (41)


This is one motivation to use as logical underpinning for this work constructive frameworks where (41) is maintained.





Answerhood Within one such framework, situation theory, ?; Ginzburg and Sag 2000 show that aboutness as defined in (79) seems to encompass the various classes of propositions exemplified in (37). Thus: By defining possibly (p) as involving (a) the truth of p ∨ r , where p, r are incompatible and (b) ¬p not being proven, one can show possibly (p) is about p?. By monotonicity, all modalities stronger than ‘possibly’ are also about p?. Existence-entailing generalized quantifiers such as existentials satisfy aboutness by virtue of their entailing the truth of a positive instantiation of a given wh-question. Generalized quantifiers such as ‘At most one N’ or ‘Few N’ satisfy aboutness by virtue of their entailing the truth of a positive or negative instantiation of a given wh-question. Jonathan Ginzburg, King’s College London Sem & Int in Dialogue: lec. 1












Resolving Answerhood Answerhood in the aboutness sense is clearly distinct from a highly restricted notion of answerhood, that of being a proposition that resolves or constitutes exhaustive information about a question. This latter sense of answerhood has been explored in great detail in the formal semantics literature, since it is a key ingredient in explicating the behaviour of interrogatives embedded by resolutive predicates such as ‘know’, ‘tell’ and ‘discover’. (42)

I wondered about who/when/why Bo left, so I asked. Mo told me . . . , so now I know who/when/why Bo left. a. An important issue is what we should do next. We’ve been discussing this in some detail. But the issue hasn’t been resolved as yet.





Resolving Answerhood One useful semantic notion of resolvedness is strong exhaustiveness, due originally to Groenendijk and Stokhof 1984, which approximates resolvedness in cases involving fairly transparent interaction taking place in a familiar domain: (43)

p is a strongly exhaustive answer to q iff p is true and entails every pi which is a simple answer to q.

The characterization in (43) seems to straightforwardly capture the resolvedness conditions for a polar question: (44)

Bo knows whether p (whether Mo is asleep). Hence, either Jo knows p (that Mo is asleep) or Jo knows ¬p (that Mo is not asleep).





Resolving Answerhood

The situation with wh-questions is far more complicated. As discussed in inter alia Boër and Lycan 1985, Ginzburg, 1995, Asher and Lacarides, 1998, Van Rooy, 2003 there are various pragmatic factors which seem to come into the picture when evaluating whether a proposition resolves a question, in a given context. These include the goals associated with the interaction and the knowledge states of the CPs. (See next lecture for a bit more discussion.).





Resolving Answerhood To be strongly exhaustive for a question like (45a), a proposition p needs to entail all true positive instantiations of the question, as well as the true negative instantiations: (45) Who attended the lecture? a. Names... b. Some logicians and linguists. For this to be plausible, one needs to ensure that the set of true, simple answers is not too large. Two factors play a role in this: on the one hand, domain selection and on the other hand, it should be relatively ‘difficult’ for negative propositions to be true. Once again, the importance of constructive logical frameworks is significant. Jonathan Ginzburg, King’s College London




Querying The fact is though that in interaction, questions get posed and successfully responded to, without an exhaustive answer being communicated. In (46(4)) Bill’s response is entirely cooperative—it provides Jill with the information she is after—and yet it does not seem to allow disquotation as (46b,c), which I take to be a criterion of whether the answer is resolving in context: (46) a. Jill(1): Who is coming tonight? Bill(2): Why do you ask? Jill(3): Well after the last party and my antics there I’m anxious. Bill(4): Oh well, no cause for worry: few people who saw you at the last party. Jonathan King’s College London Sem & Int in lec. 1 Jill who was b. Ginzburg, (as report of the dialogue): #Dialogue: Bill told



Querying querying involves a course of events where the responder poses a question in the belief that the response offered will be sufficient, given what she believes she knows, to bring about her goal G. Given that she has actually posed the question q, rather than some other question, this forces on her the pretense of being someone that expects to be provided with information about q, and it is indeed somewhat hard to defeat this expectation: (47) a. [Context: Jill wants to get onto the next train to Edinburgh but does not see where the queue for that train is. She goes to a guard and asks:] excuse me, could you please tell me—why can’t I find the queue to the Edinburgh train? b. As follow up: # Not that I care about that. All I want is to find the queue.





Querying A responder who believes he has figured out the querier’s goal can cut the exchange to a minimum and respond directly, providing information that fulfills the goal and ignores the question asked By associating as part of the force of a query the querier’s commitment to requesting information about the question she asks, we also have some account of why information that is more than sufficient to fulfill the goal is often provided, as in (48c): (48) a. A: When is the Middlesborough train leaving? b. B: Go now to platform 12. c. B2: 5:04, platform 12. Jonathan Ginzburg, King’s College London




Querying The role of aboutness in this picture is relatively straightforward: it provides the range of possible contents to be conveyed. But in many contexts, as we have seen, the answer by the querier need not involve resolving the question asked. Where does resolvedness come into the picture? Although this is not evident in most AI work on planning, many goals are naturally described as questions to be resolved, as in (49b): (49) a. A: I’d like to know where Jill lives nowadays. B: Why do you ask? b. A: Oh. I’m curious what city she’s chosen to live in. Jonathan Ginzburg, King’s College London




Querying

In this respect, the prototypical query is one where someone asks a question desiring an answer that resolves the question. The fact that this is not always so reflects the potential ‘indirectness’ or lack of transparency characteristic of human/human interaction. In other words, these are cases where the question asked and the underlying goal are distinct.




Why use TTR? Basics of TTR Ontological summary

Where we are now 1


2


3


4






Type Theory with Records as logical framework Use Type Theory with Records (TTR) (Cooper, 2005) to build the semantic ontology. Type Theory with Records: a framework that allows —Dynamic semantic techniques à la DRT —Constraint-based Grammar à la HPSG —Dialogue Analysis à la KOS TTR notationally similar to Type Feature Structures, but substantively different —TTR has token type distinction: crucial for dealing with grounding/clarification potential of utterances —TTR contains λ-calculus: crucial for doing semantics Jonathan Ginzburg, King’s College London




Fundamental notion The most fundamental notion of CTT is the typing judgement a : T classifying an object a as being of type T . (50a-c) are typing judgements that presuppose the existence of types SIT, IND, REL. (50d) is the direct analogue of the ST statement p |= hhRUN; b, tii; here run(b,t) is a type (of a proof) (= ‘observation’ or even ‘situation’ etc.) (50) a. s : SIT b. b: IND c. run : REL d. s : run(b,t) Jonathan Ginzburg, King’s College London




Records and Record Types A record is is an ordered tuple of the form (51), where crucially each successive field can depend on the values of the preceding fields:   (51) a. li = ki   li+1 = ki+1 . . .  li+j = ki+j   b. x = a   y = b  prf = p





Records and Record Types

Together with records come record types. A record type is simply an ordered tuple of the form (52), where again each successive type can depend on its predecessor types within the record:   (52) li : T i   li+1 : Ti+1 . . .  li+j : Ti+j





Records and Record Types Record types allow us to place constraints on records: the basic typing mechanism assumed is that a record r is of type RT if all the typing constraints imposed by RT are satisfied by r . If a1 : T1 , a2 : T2 (a1 ), . . . , an : Tn (a1 , a2 , . . . , an−1 ), the  record:   l1 = a1 l1 : T1  l2   = a l : T2 (l1 ) 2    2  ...  is of type:  . . . ln = an ln : Tn (l1 , l2 , . . . , ln−1 ) Crucially, not all the fields in r need to be ‘disciplined’ by RT . Jonathan Ginzburg, King’s College London


   



Records and Record Types

The record     is of the type runner : Ind runner = bo     time = 2pm, Dec 20 time : Time  place = batumi place : Loc h i " # and of the type runner : Ind and of the type runner : Ind time : Time hi and of the type , the type that imposes no constraints.





Ontology in Type Theory Type Theoretic World (Cooper 2004, simplified): TYPE = h Typen , BasicType, ProofTypen , RecTypen , hA, F n i, i Typen is the set of types of order n, built up recursively using type construction operations. BasicType: IND, TIME, LOC, LEX . . . ProofTypen (“interface with external reality”): tuples consisting of entities [from the model] and predicates. RecTypen : set of records, record types defined with respect to a set of objects used as labels. hA, F n i is a model (assigning entities to BasicType, and tuples to ProofTypen ). Jonathan Ginzburg, King’s College London




Ontology in Type Theory

The universe is connected to the real world via the proof types and the model. The model grounds the basic types. From these beginnings, arise structured objects via two recursive mechanisms: type construction and record cutting.





An event Proof types play a role akin to (atomic) situation types (SOAs) in situation semantics, serving as the smallest particles of external reality. The model will determine (via the function F n ) whether e.g. a : IND and the witnesses for the proof type woman(a); Assuming the existence of basic types TIME and LOC(ation), one could offer (53) as the most rudimentary notion of situation, namely that it is a record which carries information about spatio-temporal extent: (53) " # SIT =def time : TIME loc:LOC Jonathan Ginzburg, King’s College London












An event The type of a situation witha woman riding a bicycle would    then be a record . . . of type x: IND     x = a   c1: woman(x)     c1 = p1    c2: bicycle(x)         y = b  y: IND       c2 = p2    time : TIME     time = t0   loc:LOC         loc = l0  c3: ride(x,y,time,loc)     c3 = p3    ... such that: a:IND; c1: woman(a); b: IND; p2: bicycle(b); t0 : TIME; l0 : LOC;p3: ride(a,b,t0,l0); Jonathan Ginzburg, King’s College London




Type Constructors In order to do semantics, we need to have available various type construction operations, which allow for a recursive building up of the type theoretic universe. (56) a. function types: if T1 and T2 are types, then so is (T1 → T2 ), the type of functions from elements of type T1 to elements of type T2 . f:(T1 → T2 ) iff {a|a : T1 } is a subset of the domain of f and the range of f is a subset of {a|a : T2 } b. The type of lists: if T is a type, [T], the type of lists each of whose members is a : T, is a type. c. The unique type: if T is a type and x : T , then Tx is a type. a : Tx iff a = x. Jonathan Ginzburg, King’s College London




Simultaneous abstraction with restrictions Function types allow one to model abstraction. Given the existence of record typing, this allows for a simple modelling of simultaneous, restricted abstraction— multiple (incl none) entities get ‘abstracted over’ simultaneously, while encoding restrictions. The simultaneous abstract in (57a) can be modelled as the function in (57b), which has the type in (57c): (57) a. λ{x1 , . . . , xk }φ(x1 , . . . , xk ) [ψ1 (x1 , . .. , xn1 ), . . . , ψk (xk , . . . , xnk )]  b. x1 = a1 7→ φ(a1 , . . . , ak )   . . .    x = a   k k    c1 =King’s p1 College London Jonathan  Ginzburg, Sem & Int in Dialogue: lec. 1 



Simultaneous abstraction with restrictions

  → φ(r .x1 , . . . , r .xk ) (58) a. r : x1 : T1   . . .    x : T    k k   c1 : ψ1 (a1 , . . . , an1 )     . . .   ck : ψk (ak , . . . , ank )





Simultaneous abstraction with restrictions

A simplified analysis of the meaning of the sentence ‘I see Bo’:   (59) a. context-assgn: α = x : Ind   t : Time    p1: speak(x,t)    y: Ind    p2: named(Bo,y) b. h cont : see(context-assgn.x,context-assgn.t,context-assgn





Simultaneous abstraction with restrictions (60) (c) context-assgn:α → RecType (the type of) functions from records of type α into record types. A function of this type maps contexts specified to be a record of the   following form— . . . , where x0 : Ind,t0 : Time, c1:   x = x0    t = t0      p1 = c1   y = y0    p2 = c2   ... speak(x0 ,t0 ),h y0 : Ind, and c2: named(Bo,y0), into a i record type cont : see(x0 ,t0 ,y0 ) Jonathan Ginzburg, King’s College London




Vacuous abstraction A vacuous abstract is a constant function of some kind—where implementation varies is the domain of the function. If we think of a unary abstract as involving a domain type with one field which directly influences the ‘value’ of the function, a binary abstract as one whose domain type contains two such fields etc, then the domain type of a 0-ary type would simply be the empty type []. hence: a 0-ary abstract a constant function from the universe of all records (since every record is of the type [].). An alternative implementation is to arbitrarily choose some fixed entity as the domain of vacuous abstracts. For instance, we could take the domain type to be the type [][] whose sole member is [].





Vacuous abstraction: an example

hi (61) a. r: α = h i b. ρ: cont: run(a,t,l) hi c. r: 7→ ρ: function from records of type α into records types.





Propositions One of the cornerstones of standard type theory is a conflation of propositions with types. There are, however, a variety of linguistic considerations, exemplified in the little inference pattern in (62), that suggest we need to treat propositions as individuals (‘data elements’) that can be arguments of predicates. (62) a. The claim is that Bo left. Mike believes that claim. Hence, Mike believes that Bo left. This is one feature that distinguishes the situation theoretic treatment, where propositions are first class citizens, from the standard CTT one. Jonathan Ginzburg, King’s College London




Propositions The situation theoretic ontology, as motivated in Ginzburg and Sag 2000, provides a sharp distinction between propositions and situation types. Situation types are potential properties of (real world) situations, whereas propositions are the bearers of truth. TTR offers a straightforward way for us to model propositions using records. A proposition is a record of the form in (63a). The type of propositions is the record type (63b): sit = r0 (63) a. sit-type = p0 sit : Record b. sit-type : RecType Jonathan Ginzburg, King’s College London




Propositions

Truth: (64)

A proposition

sit sit-type


= =

r0 p0

is true iff r0 : p0




Logic We can now import an essentially intuitionist logic to underpin the Boolean structure of our space of propositions. The following are the operations on types typically assumed in TTR: (65) a. ¬T0 is the type T0 → ⊥: the type ¬T0 is witnessed if one can show that every situation of type T0 is also of type ⊥. b. T1 ∧ T2 : to show that T1 ∧ T2 is witnessed, one needs a pair < p1, p2 > where p1 is of type T1 and p2 is of type T2 . c. T 1 ∨ T 2: a witness for T 1 ∨ T 2 is an entity p0 where p0 is of type T1 or p0 is of type T2 . Given this, simple to define the requisite Boolean operations on propositions.





Outcomes

The class of outcomes was introduced in Ginzburg and Sag 2000, following ?, to describe goals and serve as the denotata of imperatives, subjunctives and (certain uses of) infinitives, as in (66): (66) a. Sit! b. Bo demands that Mo sit. c. Mo’s goal is to leave.





Outcomes Outcomes are closely related to propositions, with the main difference being temporal—outcomes are intrinsically futurate, but with a temporal dimension which is typically unanchored (at speech time), which makes them useful theoretical entities for reasoning about future action. (67) illustrates the futurity and the fact that an outcome can remain unfulfilled: (67) a. Go home. You can then take a nap. b. Mo requested Bo to resign. He never did.





Outcomes Truth is not applicable to such entities, what is applicable is the notion of being fulfilled. We can explicate this in an Austinian fashion—as records whose fields are a situation and a situation type–abstract, of which a temporal argument has been abstracted away. We define the type Irrealis—temporal abstracts over the class of record types: h i (68) Irrealis =def ( t : Time )RType





Outcomes Truth is not applicable to such entities, what is applicable is the notion of being fulfilled. We can explicate this in an Austinian fashion—as records whose fields are a situation and a situation type–abstract, of which a temporal argument has been abstracted away. We define the type Irrealis—temporal abstracts over the class of record types: h i (69) Irrealis =def ( t : Time )RType





Outcomes An outcome will be a record of the form in (70a), the type Outcome given in (70b): sit = r0 (70) a. irr-sit-type = p0 sit : Record b. Outcome =def irr-sit-type : Irrealis The fulfilledness conditions of an outcome sit = s0 involve the existence of a situation irr-sit-type = p0 s1 which is situated temporally after s0 such that s1 witnesses an instantiation of p0 . This is the sense in which outcomes are ‘futurate’: Jonathan Ginzburg, King’s College London




Outcomes (71)

# " For an outcome o1 = sit = s0 irr-sit-type = p0 Fulfillers(o1) =def   s1 : Record   fulfill − time : Time    c1 : anterior (s0 , s1 )    " #     sit = s 1 p = : True sit-type = p0 (fulfill-time)





Outcomes (72) Mo: Bo, leave!   spkr : Ind   addr : Ind    utt-time : Time          sit = s0   h i h i   o = : Outcome   irr-sit-type = (r : t : Time ) c1: leave(b,r.t)     c2 : ∀f : Fulfillers(o) ¬[utt-time = f.fulfill-time : Time ]    cont : Command(spkr,addr,utt-time,o)





Questions in TTR

Given the existence of sitsemian-like propositions, a proposition/situation-type-like distinction, and a theory of λ-abstraction, it is relatively straightforward to develop a theory of questions as propositional abstracts in TTR. One could alternatively develop a theory of questions in TTR which took Question as a type, arising from a constructor ? operating on functions (see Cooper (in prep)). Avoids prop/sit-type distinction.





Questions: some simple examples A question will be a function from records into propositions: (73) a. Did Bo run TTR   representation—( r : = r1 h i sit i . That is, a ) sit-type = h c : run(b) hi function that maps records r : T0 = into  propositions of the form  sit = r1  sit-type = h i c : run(b) Jonathan Ginzburg, King’s College London




Questions: some simple examples (74) a. who ran

x rest 

: :

Ind person(x)

)

TTR representation—(r :  sit = r1  sit-type = h i  That is, a function that c : run(r.x) x : Ind maps records r : Twho = into rest : person(x)   sit = r1 i propositions of the form  sit-type = h c : run(r.x) Jonathan Ginzburg, King’s College London




Questions: some simple examples

(75)

a. who touched what 3 2 3 Ind sit = r1 person(x) 7 7)4 sit-type h i 5 = 5 Ind c : touch(r.x,r.y) thing(y) 2 3 x : Ind 6 rest1 : person(x) 7 6 7 That is, a function that maps records r : Twho,what =4 5 y : Ind rest2 : thing(y) 2 3 sit = r1 h i 5 = into propositions of the form 4 sit-type c : touch(r.x,r.y) 2

x 6 rest1 TTR representation—(r : 6 4 y rest2

: : : :





Fixing the type of questions

Recall that one of the stumbling blocks facing QPA as implemented in the late 1970s was the the distinctness of types associated with interrogatives. This problem does not arise here due to the following elementary fact: Fact Function type subsumption For any types A, A0 , B if A v A0 , then (A0 → B) v (A → B).





Fixing the type of questions h i For example: Let f = r : x : ind 7→ run(r.x). So: f : h i ( x : Ind )Prop " # " # Take r0 = x = a . Now r0 : x : Ind , hence also r0 : y =b y : Ind h i x : Ind , hence f is defined on r0 (mapping it to run(a)). So " # f : ( x : Ind )Prop. y : Ind





Questions: some simple examples Now the types which can be associated with the above questions satisfy the subtype hierarchy in (76a). Given this and Fact 1, we get a correspondingly inverted hierarchy for the function types in (76b): (76) a. Twho,what v Twho v T0 b. (T0 → Prop) v (Twho → Prop) v (Twho,what → Prop) Can be generalized to accommodate arbitrarily complex questions. (See Ginzburg, J. of Logic&Computation, 2005). Alternative more general strategy use partial function spaces. Jonathan Ginzburg, King’s College London




Answerhood Abstracts can be used to underspecify answerhood. This is important given that NL requires a variety of answerhood notions, not merely exhaustive answerhood or notions straightforwardly definable from it. Moreover answerhood needs to be explicable theory — internally, not merely metatheoretically. This is because answerhood figures as a constituent relation of the lexical entries of resolutive verbs e.g. ‘know’, ‘discover’, and ‘tell’. When such a verb embeds an interrogative complement I which denotes a question q the semantic argument of the verb is coerced to denote a fact that resolves q. Also in rules regulating felicitous responses in dialogue management. For current purposes this means that we need to be able to define notions of answerhood as types.















Answerhood The simplest notion of answerhood I will define on the basis of an abstract is simple answerhood. A simple answer is an instantiation of the abstract or negation thereof. (77)

Given a question q : (A → B): a.  AtomAns(q) =def  shortans : A   compoundans = q(shortans) : Prop   propans : Prop    c : Conj*(propans,compoundans)





Answerhood

(78)

"SimpleAns(q) =def # at : AtomAns(q) simpleans = at.propans ∨ ¬at.propans : Prop





Simple Answerhood A simple way to enrich simple answerhood is by closing simple answerhood under disjunction: (79)


simpans is a field for a list of simple answers, disjans is a field for their disjunction, given a function that maps a list of records of type SimpleAns(q) to the disjunction of the simpleans fields of these records, propans is a proposition that entails this disjunction:





Answerhood

(80)

Given a question q : (A → B): a.  Aboutness(q) =def  h i simpanslist : SimpleAns(q)   W   disjans = simpleans simpanslist : Prop   propans : Prop    c : →(propans,disjans)





Answerhood

Given that for any question, the class of simple answers always contains at least one proposition p and its negation ¬p, the definition is (79) is restrictive only within a logical framework in which the law of the excluded middle fails. (81)


Both situation theory and TTR are such settings.





Strong exhaustiveness

(82)

p is a strongly exhaustive answer to q iff p is true and entails every pi which is a true simple answer to q.

(83)

StrongExhAns(q) =def  exhans : Prop #  "  h i  r : SimpleAns(q) c : c2 : →(exhans,r.simpleans)  0 c1 : r.simpleans





Strong exhaustiveness

(84)

Anders: I wanted to get to Josè’s house on the Tube. So I asked Werner where Josè’s house is. Werner told me that the house is near Pimlico station. So now I know where Josè’s house is. An analysis of resolvedness needs to integrate semantic constraints that derive directly from the question with agent-relative information:





Strong exhaustiveness (85)

For a question q = (a : A)p(a) ResolvingAnswers(q) =def (p resolves q relative to B’s desired outcome o)   p : Prop ∧ True   B: Ind    a: A    o : outcome      p1 = q(a) ∨ p1 = ∀x : A¬q(x) : Prop   c2 : entails(p,p1)      c3: want(B,o)  c4 : ep-sufficient(p,B, o) Jonathan Ginzburg, King’s College London




Strong exhaustiveness In (86), this latter is cashed out in terms of a relation, not further analysed here, epistemically-sufficient that holds between a proposition, an agent, and an outcome. This relation is intended to represent a proposition providing information to an agent that is sufficient for an outcome to be fulfilled. The semantic constraints in (86) concerning the question are essentially a type theoretic reformulation of the relation potential resolvedness from Ginzburg and Sag 2000: they involve a proposition p entailing either an instantiation of the question or the negative universal. For polar questions this h ireduces to the characterization in (??), given that a polar question ( )p has the sole instantiation p and so the corresponding negative universal is ¬p.





Ontological summary The ontology satisfies the following requirements: It is intentional: providing entities such as propositions and questions which can be shared across participants and languages and enabling us to develop a theory of event anaphora. It is fine-grained: does not run into logical omniscience or Soames’ puzzle. It is not too fine grained, so it allows for identity of content across translation or synonymous reformulation, leaving an account of, for instance, clarification potential to a theory of locutionary propositions (see Chapter 5). It allows for distinctions to be made between various kinds of ‘informational entities’, including events, situation types, propositions, questions, and outcomes. At the same time, commonalities between these entities can be captured.















Ontological summary

It can be implemented computationally in a transparent way. It provides for a theory of abstraction which allows for null, unary, and multiple restricted abstracts, all interpreted as families over a record type. Questions are propositional abstracts and can be used to underspecify answerhood.





Ontological summary






Ontological summary





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Commentary on Pickering and Garrod’s paper, Behavioural and Brain Sciences 27



Semantics and Interaction in Dialogue

Semantics and Interaction in Dialogue

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