Wh -items quantify over polymorphic sets Yimei Xiang May 27, 2017 - PowerPoint PPT Presentation

Wh -items quantify over polymorphic sets Yimei Xiang May 27, 2017 Harvard University yxiang@fas.harvard.edu Chicago Linguistics Society (CLS) 53

Overview What we know: Wh -words are existential quantifiers. Yimei Xiang Overview: May 27, 2017 2 / 24

Overview What we know: Wh -words are existential quantifiers. Cross-linguistically, wh -words behave like ∃ -indefinites in non-interrogatives. Yimei Xiang Overview: May 27, 2017 2 / 24

Overview What we know: Wh -words are existential quantifiers. Cross-linguistically, wh -words behave like ∃ -indefinites in non-interrogatives. Example (1) Yuehan haoxiang jian-le shenme-ren . John perhaps meet- perf what-person ‘Perhaps John met someone .’ Yimei Xiang Overview: May 27, 2017 2 / 24

Overview What we know: Wh -words are existential quantifiers. Cross-linguistically, wh -words behave like ∃ -indefinites in non-interrogatives. Example (1) Yuehan haoxiang jian-le shenme-ren . John perhaps meet- perf what-person ‘Perhaps John met someone .’ What we don’t know: What do wh -words quantify over? Yimei Xiang Overview: May 27, 2017 2 / 24

Overview The traditional view A wh -phrase existentially quantifies over the set of individuals denoted by the wh -complement. (Karttunen 1977) (2) a. � which NP � = λ P � e , t � . ∃ x ∈ � NP � [ P ( x )] Yimei Xiang Overview: May 27, 2017 3 / 24

Overview The traditional view A wh -phrase existentially quantifies over the set of individuals denoted by the wh -complement. (Karttunen 1977) (2) a. � which NP � = λ P � e , t � . ∃ x ∈ � NP � [ P ( x )] = � some NP � Yimei Xiang Overview: May 27, 2017 3 / 24

Overview The traditional view A wh -phrase existentially quantifies over the set of individuals denoted by the wh -complement. (Karttunen 1977) (2) a. � which NP � = λ P � e , t � . ∃ x ∈ � NP � [ P ( x )] = � some NP � b. Be ( � which NP � ) = � NP � ( Be converts an ∃ -quantifier to its quantification domain. (Partee 1987)) Yimei Xiang Overview: May 27, 2017 3 / 24

Overview The traditional view A wh -phrase existentially quantifies over the set of individuals denoted by the wh -complement. (Karttunen 1977) (2) a. � which NP � = λ P � e , t � . ∃ x ∈ � NP � [ P ( x )] = � some NP � b. Be ( � which NP � ) = � NP � ( Be converts an ∃ -quantifier to its quantification domain. (Partee 1987)) Example (3) With only two considered kids a and b , we have: Yimei Xiang Overview: May 27, 2017 3 / 24

Overview The traditional view A wh -phrase existentially quantifies over the set of individuals denoted by the wh -complement. (Karttunen 1977) (2) a. � which NP � = λ P � e , t � . ∃ x ∈ � NP � [ P ( x )] = � some NP � b. Be ( � which NP � ) = � NP � ( Be converts an ∃ -quantifier to its quantification domain. (Partee 1987)) Example (3) With only two considered kids a and b , we have: a. Be ( � which kid � ) = � kid � = { a , b } Yimei Xiang Overview: May 27, 2017 3 / 24

Overview The traditional view A wh -phrase existentially quantifies over the set of individuals denoted by the wh -complement. (Karttunen 1977) (2) a. � which NP � = λ P � e , t � . ∃ x ∈ � NP � [ P ( x )] = � some NP � b. Be ( � which NP � ) = � NP � ( Be converts an ∃ -quantifier to its quantification domain. (Partee 1987)) Example (3) With only two considered kids a and b , we have: a. Be ( � which kid � ) = � kid � = { a , b } b. Be ( � which kids � ) = � kids � = { a , b , a ⊕ b } Yimei Xiang Overview: May 27, 2017 3 / 24

Overview The traditional view A wh -phrase existentially quantifies over the set of individuals denoted by the wh -complement. (Karttunen 1977) (2) a. � which NP � = λ P � e , t � . ∃ x ∈ � NP � [ P ( x )] = � some NP � b. Be ( � which NP � ) = � NP � ( Be converts an ∃ -quantifier to its quantification domain. (Partee 1987)) Example (3) With only two considered kids a and b , we have: a. Be ( � which kid � ) = � kid � = { a , b } b. Be ( � which kids � ) = � kids � = { a , b , a ⊕ b } My view Some wh -items have a richer quantification domain: it contains not only individuals , but also generalized quantifiers that are conjunctions or disjunctions over these individuals. Yimei Xiang Overview: May 27, 2017 3 / 24

Overview (4) a. � Andy and Billy � = a ⊕ b b. � Andy and Billy � = a ¯ ∧ b = λ P � e , t � [ P ( a ) ∧ P ( b )] Yimei Xiang Overview: May 27, 2017 4 / 24

Overview (4) a. � Andy and Billy � = a ⊕ b b. � Andy and Billy � = a ¯ ∧ b = λ P � e , t � [ P ( a ) ∧ P ( b )] Generalized conjunction (5) a. For any two items a and b of type τ : a ¯ ∧ b = λ P � τ , t � [ P ( a ) ∧ P ( b )] b. For any non-empty set α of type � τ , t � : ¯ � α = λ P � τ , t � . ∀ x ∈ α [ P ( x )] Yimei Xiang Overview: May 27, 2017 4 / 24

Overview (4) a. � Andy and Billy � = a ⊕ b b. � Andy and Billy � = a ¯ ∧ b = λ P � e , t � [ P ( a ) ∧ P ( b )] Generalized conjunction (5) a. For any two items a and b of type τ : a ¯ ∧ b = λ P � τ , t � [ P ( a ) ∧ P ( b )] b. For any non-empty set α of type � τ , t � : ¯ � α = λ P � τ , t � . ∀ x ∈ α [ P ( x )] Generalized disjunction (6) a. For any two items a and b of type τ : a ¯ ∨ b = λ P � τ , t � [ P ( a ) ∨ P ( b )] b. For any non-empty set α of type � τ , t � : ¯ � α = λ P � τ , t � . ∃ x ∈ α [ P ( x )] Yimei Xiang Overview: May 27, 2017 4 / 24

Roadmap Yimei Xiang Overview: May 27, 2017 5 / 24

Roadmap Setting up the relation between questions and answers 1 Yimei Xiang Overview: May 27, 2017 5 / 24

Roadmap Setting up the relation between questions and answers 1 Defining the wh -determiner 2 Yimei Xiang Overview: May 27, 2017 5 / 24

Roadmap Setting up the relation between questions and answers 1 Defining the wh -determiner 2 Deriving the individual and higher-order readings of wh -questions 3 Yimei Xiang Overview: May 27, 2017 5 / 24

1. Wh -questions and their answers Yimei Xiang Wh -questions and their answers: May 27, 2017 6 / 24

Wh -questions and their answers full answers vs. short answers (7) Which boy came? a. John came. (full answer) b. John. (short answer) Yimei Xiang Wh -questions and their answers: May 27, 2017 7 / 24

Wh -questions and their answers full answers vs. short answers (7) Which boy came? a. John came. (full answer) b. John. (short answer) A categorial approach of question semantics ◮ I define questions as topical properties . Yimei Xiang Wh -questions and their answers: May 27, 2017 7 / 24

Wh -questions and their answers full answers vs. short answers (7) Which boy came? a. John came. (full answer) b. John. (short answer) A categorial approach of question semantics ◮ I define questions as topical properties . ◮ Topical properties are λ -abstracts ranging over propositions. A topical property maps a short answer to a propositional answer. (8) Which boy came? a. P = λ x [ boy @ ( x ) = 1 . ˆ came ( x )] b. P ( j ) = ˆ came ( j ) Yimei Xiang Wh -questions and their answers: May 27, 2017 7 / 24

Wh -questions and their answers full answers vs. short answers (7) Which boy came? a. John came. (full answer) b. John. (short answer) A categorial approach of question semantics ◮ I define questions as topical properties . ◮ Topical properties are λ -abstracts ranging over propositions. A topical property maps a short answer to a propositional answer. (8) Which boy came? a. P = λ x [ boy @ ( x ) = 1 . ˆ came ( x )] b. P ( j ) = ˆ came ( j ) Dom( P ) boy @ the set of possible short answers Yimei Xiang Wh -questions and their answers: May 27, 2017 7 / 24

Wh -questions and their answers full answers vs. short answers (7) Which boy came? a. John came. (full answer) b. John. (short answer) A categorial approach of question semantics ◮ I define questions as topical properties . ◮ Topical properties are λ -abstracts ranging over propositions. A topical property maps a short answer to a propositional answer. (8) Which boy came? a. P = λ x [ boy @ ( x ) = 1 . ˆ came ( x )] b. P ( j ) = ˆ came ( j ) Dom( P ) boy @ the set of possible short answers { P ( α ) : α ∈ Dom ( P ) } { ˆ came ( x ) : x ∈ boy @ } the set of possible full answers Yimei Xiang Wh -questions and their answers: May 27, 2017 7 / 24

Wh -questions and their answers Why pursing a categorial approach? Yimei Xiang Wh -questions and their answers: May 27, 2017 8 / 24

Wh -questions and their answers Why pursing a categorial approach? ◮ The individual specified by a short answer must be in the quantification domain of the wh -item (Jacobson 2016): (9) Which linguist did Mary invite? Yimei Xiang Wh -questions and their answers: May 27, 2017 8 / 24

Wh -questions and their answers Why pursing a categorial approach? ◮ The individual specified by a short answer must be in the quantification domain of the wh -item (Jacobson 2016): (9) Which linguist did Mary invite? a. Mary invited Andy, Yimei Xiang Wh -questions and their answers: May 27, 2017 8 / 24