Focus Representation and Backward Underspecification in Dependent Type Semantics

Transcript

1. 19, Nov, 2023 LENLS 20 Focus Representation and Backward Underspecification in Dependent Type Semantics 1 Hayate Funakura Kyoto University
2. Agenda • Background and motivation • Empirical scope • Proposal • Focus context • Backward underspecified term • How the related examples are derived • Unsolved issues 2
3. Background and Motivation • Main topics: FOCUS and QUESTION-ANSWER CONGRUENCE • central in question semantics • (important for logic-guided chatbots) 3
4. Background and Motivation • Main topics: FOCUS and QUESTION-ANSWER CONGRUENCE • central in question semantics • (important for logic-guided chatbots) • Proposals: A method to represent focus information and an analysis of English wh-questions in Dependent Type Semantics 4
5. Background and Motivation • Dependent Type Semantics [Bekki 2014, etc.] • NL semantics based on Martin-Löf type theory • Key item: underspecified terms (UTs) 5
6. Background and Motivation • Dependent Type Semantics [Bekki 2014, etc.] • NL semantics based on Martin-Löf type theory • Key item: underspecified terms (UTs) 6 John knows that Susan danced. ↦ know(j, dance(s), @) in Tanaka+ ( 2 0 1 7 ) Presup. Susan danced. Previous context requires the previous context to entail @ dance(s)
7. Background and Motivation • In DTS, questions are addressed by Watanabe+ 2019, 
 but focus is not covered. • (mention-some) wh-questions are represented as weak- sigma types Who danced? • Informally, a response which entails Someone danced is predicted to be a felicitous answer, regardless of focus ↦ (x : entity) ⊕ dance(x) 7
8. Empirical scope • Single-wh • Who does John like? • John likes [Mary]F. • Multiple-wh • Who likes whom? • [John]F likes [Mary]F. 8 • Phrasal focus • What did John do? • John [met Mary]F. • Answers with anaphoric expressions • John likes [him]F.
9. Empirical scope • Out of scopes • Answers with quantificational expressions / coordination • John likes [everyone]F. • John likes [Mary and Taro]F. • Adjunct wh-questions (when, where, how, etc.) • Polar/alternative questions • Other focus-related phenomena • Comparison with model-theoretical approaches 9
10. Background and Motivation • Alternative Semantics [Rooth 1992, etc.] is a standard approach to focus in formal semantics 10
11. Background and Motivation • Alternative Semantics [Rooth 1992, etc.] is a standard approach to focus in formal semantics • Two options: • Translate Alternative Semantics into DTS language • Explore a unique approach to DTS 11
12. Background and Motivation • Alternative Semantics [Rooth 1992, etc.] is a standard approach to focus in formal semantics • Two options: • Translate Alternative Semantics into DTS language • Explore a unique approach to DTS • The latter seems more challenging 12
13. Proposal • Focus contexts (FCs) Sequences of type assignments which represent 
 focus information • Backward underspecified terms (backward UTs) Gaps in wh-questions which are expected to be filled 
 by an answer 13
14. Proposal • Focus contexts (FCs) Sequences of type assignments which represent 
 focus information • Backward underspecified terms (backward UTs) Gaps in wh-questions which are expected to be filled 
 by an answer 14
15. Focus contexts • FCs are sequences of type assignments which correspond to focused elements • [John]F likes Mary. SR: FC: • John [likes Mary]F. SR: FC: • FCs for each sentence are obtained in parallel with semantic composition (i.e., CCG derivation) like(j, m) j : e like(j, m) like : e → e → 𝚝 𝚢 𝚙 𝚎 , m : e 15
16. Focus contexts • To derive FCs, I add lexical FC to CCG lexical entries • Each lexicon is assigned different FCs depending on whether it appears in a focused constituent or not 16
17. Focus contexts A CCG derivation for “[John]F likes Mary” 17
18. Focus contexts A CCG derivation for “[John]F likes Mary” 18 Assigned at the lexical level Merged in line with the derivation
19. • A case of phrasal focus • Since “met” and “Mary” are focused, we obtain a sequence of type assignments for these words Focus contexts 19
20. Proposal • Focus contexts (FCs) Sequences of type assignments which represent 
 focus information • Backward underspecified terms (backward UTs) Gaps in wh-questions which are expected to be filled 
 by an answer 20
21. Backward underspecified terms • idea: • The meaning of wh-questions has an unsolved part • Backward UTs represent that unsolved part • Not an alternative to ordinary underspecified terms, 
 but an additional item 21 Who does John like? } unsolved
22. Backward underspecified terms 22 Sentence Who does John like? like(j, @B) SR FC @B : e • is a backward underspecified term • For a SR which contains a backward UT, 
 the type-checking is postponed until the focus context of a response fills the gap. @B
23. SR 23 like(j, @B) Response “John likes [Mary]F” SR FC like(j, m) Question “Who does John like?” m : e FC @B : e Backward underspecified terms
24. 24 Response “John likes [Mary]F” 1. search a proof term of type e Question “Who does John like?” SR like(j, @B) SR FC like(j, m) m : e FC @B : e Backward underspecified terms
25. 25 Response “John likes [Mary]F” 1. search a proof term of type e Question “Who does John like?” SR like(j, @B) SR FC like(j, m) m : e FC @B : e 2. -elimination @B like(j, m) Backward underspecified terms
26. 26 Response “John likes [Mary]F” 1. search a proof term of type e Question “Who does John like?” SR like(j, @B) SR FC like(j, m) m : e FC @B : e 2. -elimination @B like(j, m) 3. entailment? Backward underspecified terms
27. QA congruence in DTS 27
28. How the related examples are derived: single wh-questions 28 Question Who does John like? Response [John]F likes [Mary]F. An example of overfocusing
29. How the related examples are derived: single wh-questions 29 Question Who does John like? like(j, @B) SR Response [John]F likes [Mary]F. like(j, m) SR FC An example of overfocusing FC @B : e m : e j : e
30. How the related examples are derived: single wh-questions 30 Question Who does John like? like(j, @B) SR Response [John]F likes [Mary]F. like(j, m) SR FC 1. proof search OK 2. -elimination @B like(j, m) An example of overfocusing FC @B : e m : e j : e
31. How the related examples are derived: single wh-questions 31 Question Who does John like? like(j, @B) SR Response [John]F likes [Mary]F. like(j, m) SR FC 1. proof search OK prediction: incongruent observation: incongruent 2. -elimination @B like(j, m) An example of overfocusing FC @B : e m : e j : e
32. How the related examples are derived: multiple wh-questions 32 Question Who likes whom? Response [John]F likes [Mary]F. An example of a single-pair answer
33. How the related examples are derived: multiple wh-questions 33 Question Who likes whom? like(@B 1 , @B 2 ) SR FC @B 1 : e Response [John]F likes [Mary]F. SR FC @B 2 : e like(j, m) An example of a single-pair answer m : e j : e
34. How the related examples are derived: multiple wh-questions 34 Question Who likes whom? like(@B 1 , @B 2 ) SR FC @B 1 : e Response [John]F likes [Mary]F. SR FC 1. proof search OK prediction: congruent @B 2 : e 3. entailment observation: congruent like(j, m) 2. -elimination @B like(j, m) An example of a single-pair answer (other eliminations are possible, but ommited) m : e j : e
35. How the related examples are derived: anaphora 35 Question Who does John like? An example of answers with anaphoric expressions Response John likes [him]F. SR FC @ : e like(j, @)
36. How the related examples are derived: single wh-questions 36 Question Who does John like? An example of answers with anaphoric expressions Response John likes [him]F. SR FC @ : e like(j, @) Previous context 1. proof search
37. How the related examples are derived: single wh-questions 37 Question Who does John like? An example of answers with anaphoric expressions Response John likes [him]F. SR FC @ : e like(j, @) 2. -elimination @ SR FC Previous context 1. proof search t : e like(j, t)
38. How the related examples are derived: single wh-questions 38 Question Who does John like? An example of answers with anaphoric expressions Response John likes [him]F. SR FC @ : e like(j, @) 2. -elimination @ SR FC t : e like(j, t) Previous context 1. proof search The remaining procedures are the same as non-anaphoric examples
39. Problematic cases 39
40. 40 Question Who likes whom? Response [John]F likes [Mary]F, and [Taro]F likes [Susan]F. prediction: incongruent observation: congruent The current analysis cannot capture a pair-list answer Problematic cases (undergeneration) (pointed out by Daiki Matsuoka)
41. 41 Question Who likes whom? like(@B 1 , @B 2 ) SR FC @B 1 : e Response [John]F likes [Mary]F, and [Taro]F likes [Susan]F. like(j, m) ∧ like(m, s) SR FC prediction: incongruent @B 2 : e observation: congruent The current analysis cannot capture a pair-list answer Problematic cases (undergeneration) m : e j : e s : e t : e
42. 42 Question Who likes whom? like(@B 1 , @B 2 ) SR FC @B 1 : e Response [John]F likes [Mary]F, and [Taro]F likes [Susan]F. like(j, m) ∧ like(m, s) SR FC prediction: incongruent @B 2 : e observation: congruent The current analysis cannot capture a pair-list answer Problematic cases (undergeneration) m : e j : e s : e t : e -elimination @B like(j, m) proof search OK (others ommited)
43. 43 Question Who does John like? Response John likes Mary, and [Mary]F is tall. prediction: congruent observation: incongruent FCs lacks positional information Problematic cases (overgeneration)
44. 44 Question Who does John like? Response John likes Mary, and [Mary]F is tall. prediction: congruent observation: incongruent FCs lacks positional information Problematic cases (overgeneration) like(j, @B) SR FC @B : e like(j, m) ∧ tall(m) SR FC m : e
45. Summary • Poposal: • Focus contexts Sequences of type assignments which represent 
 focus information • Backward underspecified terms Gaps in wh-questions which are expected to be filled 
 by an answer • Future tasks: Avoiding over/undergeneration, comparison with other systems, … 45
46. References [Bekki 2014] “Representing anaphora with dependent types”. In: International conference on logical aspects of computational linguistics. Springer. 2014. [Rooth 1992] “A theory of focus interpretation”. In: Natural language semantics 1.1 (1992). [Watanabe+ 2019] “Questions in Dependent Type Semantics”. In: Proceedings of the Sixth Workshop on Natural Language and Computer Science. Gothenburg, Sweden: Association for Computational Linguistics, May 2019. 46
47. Halliday’s generalization (Halliday, 1976) “An appropriate answer to a wh-question must have F marking on the constituent corresponding to the wh-phrase.” 47