Answers, Exhaustivity, and Presupposition of wh-questions in Dependent Type Semantics

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1. Hayate Funakura Graduate School of Human and Environmental Studies, Kyoto University Answers, Exhaustivity, and Presupposition 
 of wh-questions in Dependent Type Semantics -&/-4
   /PWFNCFS
   
   
2. Contents • Overview • Dependent Type Semantics • Desiderata • Different levels of answers (w.r.t direct questions) • Exhaustivity (w.r.t. embedded questions) • Existential Presupposition (w.r.t. embedded questions) • Proposal • Limitations and future work 
3. Overview 
4. Overview • I have provided an analysis of who/which-questions in Dependent Type Semantics. • Preceding analysis [Watanabe et al. 2019]: • Analyzes who, polar, and alternative questions. • Only direct questions are considered. • This study analyzes both direct and embedded questions and defines semantic composition. • It captures a few facts, including question-answer relationships, presupposition, and exhaustivity (to be explained later). • For embedded questions, only factive predicates such as know are considered. 
5. Dependent Type Semantics 
6. DTS [Bekki 2014, Bekki&Mineshima 2017] • A semantic framework that is an extension of Dependent Type Theory 
 [Martin-Löf 1984]. • Underspecified terms ( , asperand) • Inference-driven accounts • The meaning of natural language is represented by types. • types: etc. 
 @ (x : A) × B (x : A) → B A ⊎ B  ∃x : A . B ∀x : A . B A ∨ B ≡ ≡ ≡ …Corresponding propositions
7. DTS • Accounts for anaphora and presupposition in a unified way. • The key item is underspecified terms. • If a semantic representation contains an underspecified term , for to be well-formed ( ), a proof term of the same type as must be constructed from the preceding context. • For example … R @ R R : 𝚝 𝚢 𝚙 𝚎 @ 
8. DTS • John knows that Susan danced. presupposes Susan danced. • John knows that Susan danced. (Tanaka et al. 2017, slightly modified) • The semantic representation contains the underspecified term . Therefore, for to be well-formed, a proof term of the same type as must be constructed from the preceding context. • Through the type checking for , it is shown that has the type . • a proof term of must be constructed from the preceding context. CCG ↦ know(j)(dance(s))(@) know(j)(dance(s))(@) @ know(j)(dance(s))(@) @ know(j)(dance(s))(@) @ dance(s) dance(s) 
9. Desiderata 
10. Different levels of answers • There are at least three levels of answers to a wh-question depending on contexts.  • A: Who danced? • B: John danced. (Mention-some answer) • B: John and Mary danced. (Weakly exhaustive answer) • B: John and Susan danced, and Mary didn’t dance. (Strongly exhaustive answer) John danced. Susan danced. Mary didin’t dance. 4& 8& .4
11. Different levels of answers • Most approaches, including [Watanabe et al. 2019], have attempted to capture these answer levels by assuming the ambiguity of interrogatives. • Who danced? (MS) • Who danced? (SE) • The proposed analysis captures the variety of answers based on a single semantic representation of each interrogative. ↦ (x : entity) ⊕ d(x) ↦ (x : entity) → d(x) ⊎ ¬d(x)  [Watanabe et al. 2019]
12. Exhaustivity • There is ambiguity about exhaustivity in question-embedded sentences. • Annie knows who danced. • There is a p ∈ {John danced, Susan danced} s.t. Annie knows p. (MS reading) • For all p ∈ {John danced, Susan danced}, Annie knows p. (WE reading) • For all p ∈ {John danced, Susan danced}, Annie knows p, and 
 for all q ∈ {Mary didn’t dance}, Annie knows q. (SE reading) 
13. Exhaustivity • A related example: John knows who danced. (Strongly exhaustive reading) Mary didn’t dance. ———————————————————————— ∴ John knows that Mary didn’t dance. • A natural application of (Watanabe et al. 2019) to that of factive predicates (Tanaka et al. 2017) yields the following analysis: • • This representation doesn’t capture the above inference unless some additional axiom is added. know(j)((x : entity) → d(x) ⊎ ¬d(x))(@) 
14. Existential presupposition • Factive predicates that take a wh-complement trigger an existential presupposition. • John knows who danced. presupposes Someone danced. • It is also widely known that factive predicates trigger a factive presupposition. • John knows that Sue smokes. presupposes Sue smokes. 
15. Existential presupposition • Factive predicates that take a wh-complement trigger an existential presupposition. • John knows who danced. presupposes Someone danced. • It is also widely known that factive predicates trigger a factive presupposition. • John knows that Sue smokes. presupposes Sue smokes. • The declarative-taking and interrogative-taking know have the same meaning because a single know can take both interrogative and declarative. • Alice knows who danced and that John hosted the dance party. 
16. Goal • Find an analysis that captures the following phenomena: • Different levels of answers • Exhaustivity • Existential presupposition 
17. Goal • Find an analysis that captures the following phenomena: • Different levels of answers • Exhaustivity • Existential presupposition  not attributed to the ambiguity of know
18. Goal • Find an analysis that captures the following phenomena: • Different levels of answers • Exhaustivity • Existential presupposition • As for the semantic representation of know, I adopt the one presented by [Tanaka et al. 2017]. know := λp . λx . know(x)(p)(@)  not attributed to the ambiguity of know
19. Proposal 
20.  • I analyse root questions as -types, • Who danced? • Which student danced? • To derive these representations, I define the following lexical entries: Σ ↦ (x : e) × d(x) ↦ (x : e) × (s(x) × d(x)) Proposal
21. Proposal • And I define answerhood via entailment. • Simply put: If entails or contradicts , is an answer to . SA SQ SA SQ 
22. Proposal • And I define answerhood via entailment. • Simply put: If entails or contradicts , is an answer to . SA SQ SA SQ  John danced. d(j) John and Susan danced. 
 d(j) × d(s) Nobody danced. 
 (x : e) → ¬d(x) Bill ran. r(b) Who danced? 
 (x : e) × d(x) entailment entailment contradiction neither
23. Proposal • Composition • Who danced? • A wh-word creates a -abstract. • (null Q) is combined with the abstract into a -type. • The wh-as-lambda strategy allows for a fine-grained analysis of embedded questions. CCG ↦ (x : e) × d(x) λ ∅ 𝖰 Σ 
24. Proposal • Embedded questions • For embedded questions, I define three empty operators , , and . • The ambiguity about exhaustivity is reduced to the choice of these operators. • E.g., the strongly exhaustive reading ∅ 𝖬 𝖲 ∅ 𝖶 𝖤 ∅ 𝖲 𝖤 
25. Proposal • Embedded questions • For embedded questions, I define three empty operators , , and . • The ambiguity about exhaustivity is reduced to the choice of these operators. • E.g., the strongly exhaustive reading ∅ 𝖬 𝖲 ∅ 𝖶 𝖤 ∅ 𝖲 𝖤  This part presupposes Someone danced.
26. Proposal • Embedded questions • For embedded questions, I define three empty operators , , and . • The ambiguity about exhaustivity is reduced to the choice of these operators. • E.g., the strongly exhaustive reading ∅ 𝖬 𝖲 ∅ 𝖶 𝖤 ∅ 𝖲 𝖤  This part evokes inferences about exhaustivity.
27. Proposal • An inference about exhaustivity: John knows who danced. (Strongly exhaustive reading) Mary didn’t dance. ———————————————————————— ∴ John knows that Mary didn’t dance. 
28. 
29.  John knows who danced. (SE reading) Mary didn’t dance. John knows that Mary didn’t dance.
30. Future tasks 
31. Limitations and future work • Untouched tasks: I need to • Analyze other types of interrogatives (when, where, polar, alternative, etc.) • Compare with other frameworks (e.g., inquisitive semantics 
 [Ciardelli et al. 2019]) • Consider intermediate exhaustivity [Spector 2005] • Predicates of Relevance, selection restriction, etc. 
32. Limitations and future work • Toward a hybrid theory • The proposed theory can be seen as a hybrid theory that encompasses two different approaches to question semantics. • Propositional-answer-oriented: 
 Hamblin-Karttunen semantics, inquisitive semantics, etc. • Short-answer-oriented: Structured meaning approach, etc. “Question meanings are functions that, when applied to the meaning of the answer, yield a proposition.” [Krifka 2001] 
33. Limitations and future work  • “Question meanings are functions that, when applied to the meaning of the answer, yield a proposition.” [Krifka 2001] • But this version of the analysis can only handle the simplest cases (e.g., “John").
34. Appendix 
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