CRISSP lecture 3 of 3, October 2015, Brussels 3/42 Sluicing as anaphora to a scope remnant Chris Barker, NYU Richard Montague Robert May Synopsis: I argue that sluicing is anaphora to a continuation, that is, to a constituent missing a piece. When a DP takes scope over a clause, it creates the right kind of antecedent. The prediction is that sluicing is sensitive to scope islands, but not to overt-movement islands. Today’s question: How to incorporate QR into a genuine logic? 2/42 4/42 Quantifier Raising: a logical inference? Lambek’s substructural logic NL for natural language Without Exchange, ‘ → ’ splits into ‘ \ ’ and ‘ / ’ • Montague 1973: Quantifying In: (2661 citations) • Formulas: F = DP | S | F \ F | F / F • May 1978,1985: Quantifier Raising (QR): (2866 citations) • Structures: S = F | S · S • Sequents: S ⊢ F everyone ( λ x . Ann saw x ) ⊢ S Montague ↓ ↑ May = = = = = = = = = = = = = = = = = = = = Ann saw everyone ⊢ S • Logical rules: S Γ ⊢ A Σ [ B ] ⊢ C \ L A · Γ ⊢ B \ R Γ ⊢ A \ B Σ [ Γ · A \ B ] ⊢ C everyone · S λ x S Γ ⊢ A Σ [ B ] ⊢ C / L Γ · A ⊢ B / R ≡ Σ [ B / A · Γ ] ⊢ C Γ ⊢ B / A Ann VP Ann VP saw everyone saw x Structural rules: none! (Cut baked in)
5/42 7/42 How context notation works in inference rules • Capital Greek letters ( ∆ , Γ , Σ ) stand for complete structures • ‘ Σ [ ∆ ] ’ ≡ Σ containing a distinguished instance of ∆ • ‘ Σ [ Γ · A \ B ] ’ matches the structure below in two ways: – [Ann · DP \ S] · (and ((the · man) · cried)) – (Ann · left) · (and · [(the · man) · DP \ S]) · · · DP DP \ S S \ ( S / S ) · Ann left and · DP \ S DP / n cried n the man Joachim Lambek 6/42 8/42 An example derivation of Ann saw Bill Adding a structural rule for QR Associativity: p · ( q · r ) ≡ ( p · q ) · r · · DP ⊢ DP S ⊢ S \ L DP ⊢ DP DP · DP \ S ⊢ S / L (1) p · · r ≡ DP · (( DP \ S ) / DP · DP ) ⊢ S lex Ann · ( saw · Bill ) ⊢ S q r p q Quantifier Raising: Σ [ ∆ ] ≡ ∆ · λ x Σ [ x ] S · DP DP \ S everyone · Ann ( DP \ S ) / DP DP · λ x · saw Bill (2) ≡ Ann · Ann · (3) a. Curry-Howard: L rules correspond to function application saw everyone saw x b. saw ( bill )( ann )
9/42 11/42 NL QR : NL with Quantifier Raising Scope-taking as a syntactic mode of combination • Variables: = | | | ... V x y z • Formulas: = DP | S | F \ F | F / F F • Structures: = | S · S | | λ V S S F V • Sequents: S ⊢ F • Logical rules: A · Γ ⊢ B \ R Γ ⊢ A Σ [ B ] ⊢ C \ L Σ [ Γ · A \ B ] ⊢ C Γ ⊢ A \ B Γ · A ⊢ B / R Γ ⊢ A Σ [ B ] ⊢ C / L Σ [ B / A · Γ ] ⊢ C Γ ⊢ B / A • Structural rule: Σ [ ∆ ] ≡ QR ∆ · λ x Σ [ x ] Michael Moortgat Linear: !1 var per lambda; x chosen fresh 10/42 12/42 Works great! Two modes of syntactic combination · · · Ann · ( saw · DP ) ⊢ S • → (4) ⊢ qr DP · λ x ( Ann · ( saw · x )) ⊢ S \ R A \ B A B λ x ( Ann · ( saw · x )) ⊢ DP \ S S ⊢ S / L S / ( DP \ S ) · λ x ( Ann · ( saw · x )) ⊢ S lex • ← (5) ⊢ everyone · λ x ( Ann · ( saw · x )) ⊢ S qr B / A A B Ann · ( saw · everyone ) ⊢ S ...including the Curry-Howard labeling for the semantics: · · · ⊢ ◦ A � B (6) ↑ ann · ( saw · y ) ⊢ saw y ann A qr y ◦ λ x ( ann · ( saw · x )) ⊢ saw y ann \ R B λ x ( ann · ( saw · x )) ⊢ λ y . saw y ann p ⊢ p / L Q ◦ λ x ( ann · ( saw · x )) ⊢ Q ( λ y . saw y ann ) ⊢ ◦ ↓ (7) lex everyone ◦ λ x ( ann · ( saw · x )) ⊢ everyone ( λ y . saw y ann ) qr � A B ann · ( saw · everyone ) ⊢ everyone ( λ y . saw y ann ) B Compare with tangram diagrams in Moortgat 1996b
13/42 15/42 Parasitic scope: sentence-internal same Parasitic scope in schematic format (8) a. The same waiter served everyone. [Stump, Heim] b. There is a (unique) waiter x such that x served everyone. · · · ( the · ( a · waiter )) · ( served · DP ) ⊢ S λ DP ◦ λ x (( the · ( a · waiter )) · ( served · x )) ⊢ S � R λ x (( the · ( a · waiter )) · ( served · x )) ⊢ DP � S λ (9) a ◦ λ y λ x (( the · ( y · waiter )) · ( served · x )) ⊢ DP � S � R λ y λ x (( the · ( y · waiter )) · ( served · x )) ⊢ a � ( DP � S ) DP � S ⊢ DP � S � L A � ( B � C ) ( DP � S ) � ( a � ( DP � S )) ◦ λ y λ x (( the · ( y · waiter )) · ( served · x )) ⊢ DP � S lex same ◦ λ y λ x (( the · ( y · waiter )) · ( served · x )) ⊢ DP � S S ⊢ S � L S � ( DP � S ) ◦ ( same ◦ λ y λ x (( the · ( y · waiter )) · ( served · x )) ⊢ S lex A everyone ◦ ( same ◦ λ y λ x (( the · ( y · waiter )) · ( served · x )) ⊢ S λ B everyone ◦ λ x (( the · ( same · waiter )) · ( served · x )) ⊢ S λ ( the · ( same · waiter )) · ( served · everyone ) ⊢ S Grey constituent ∼ string with two points of discontinuity Details in Barker 2007; not derivable in MM96 14/42 16/42 Parasitic scope in tree format Other phenomena with a parasitic scope analysis (10) a. Anaphora: Morrill, Fadda & Valent´ ın 2011 ◦ b. he : ( DP � S ) � ( DP � ( DPS )) c. Everyone thinks he is smart. everyone ◦ d. everyone ◦ ( he ◦ λ y λ x ( x · ( thinks · ( y · ( is · smart ))))) ⊢ S ◦ (11) a. Average : Kennedy and Stanley 2009 same ◦ b. The average American has 2.3 kids. everyone ◦ c. 2.3 ◦ ( avg ◦ λ f λ n (( the · ( f · Am’n )) · ( has · ( n · kids )))) ◦ λ f (12) a. Fancy coordination: Kubota & Levine (various papers) · λ x λ x · b. I said the same thing to Terry on Mon and to Kim on Tue. c. � = I said the same thing to Terry on Monday and I said the same · · · · thing to Kim on Tuesday. the · served x (13) a. Remnant comparatives: Pollard and Smith 2013 the · served x b. Ann owes Bill more than Clara. same waiter f waiter Kubota and Levine’s workshop in week 2!
17/42 19/42 Recursive scope Three comparison analyses: structured silence? Some analyses of sluicing assume that the sluice ellipsis site contains a (14) a. Solomon 2009 silent object that has internal structure: b. Ann and Bill know [some of the same people]. c. There is a set of people X such that Ann knows some of X and • LF copying : Chung, Ladusaw and McCloskey 1995 Bill knows some of X . – Re-use (“recycle”) the Logical Form of the antecedent d. No guarantee that Ann and Bill know anyone in common! – Builds silent structure inside sluicegap e. Solomon: same : (( DP � S ) � ( DP � ( DP � S ))) � ( a � DP ) • PF Deletion : Merchant 2001 they ◦ (( same ◦ λ x ( some · ( of · ( the · ( x · people ))))) ◦ λ zy ( y · ( know · z ))) ⊢ S λ – Build any IP you want to. Move the WH out; delete the re- they ◦ λ y ( y · ( know · ( same ◦ λ x ( some · ( of · ( the · ( x · people ))))))) ⊢ S λ mainder if there is a certain kind of semantic equivalence with (15) they · ( know · ( same ◦ λ x ( some · ( of · ( the · ( x · people )))))) ⊢ S λ the antecedent they · ( know · ( some · ( of · ( the · ( same · people ))))) ⊢ S Other analyses propose that sluicing is a kind of anaphora: • Anaphora : J¨ ager 2005 – Antecedent: clause containing an indefinite – No internal structure to silence lancet liver fluke (Dicrocoelium dendriticum) 18/42 20/42 Sluicing as anaphora to an anti-constituent Three puzzles to use for comparing analyses Case matching : the case of the WH element in the sluice (1) Someone left, but I don’t know [who ]. must match the case of the inner antecedent. (4) Er will jemandem schmeicheln, aber sie wissen nicht, { *wen / wem } . (2) [Someone inner antecedent left] outer antecedent , he wants someone. dat flatter but they know not { who. acc / who. dat } but I don’t know [who wh sluicegap ] sluice . ‘He wants to flatter someone, but they don’t know who.’ (5) Er will jemanden loben, aber sie wissen nicht, { wen / *wem } . he wants someone. acc praise but they know not { who. acc / who. dat } sluice = wh-phrase +( antecedent-clause − inner-antecedent ) ‘He wants to praise someone, but they don’t know who.’ Island insensitivity : the inner antecedent can be embedded = who +([ someone left ] − someone ) within an island for WH-movement. = who +[ left ] (6) He wants a detailed list, but I don’t know how detailed [he wants a list] (* if pronounced) • The outer antecedent with the inner antecedent removed (7) Bo talked to the people who discovered something, • The remnant of the outer antecedent after the inner antecedent but we don’t know what has taken scope (i.e., a nuclear scope) [Bo talked to the people who discovered ]. • The complement of the inner antecedent with respect to the outer Sprouting : sometimes there is no overt inner antecedent antecedent, i.e., an anti-constituent (10) John left, but I don’t know when. • The delimited continuation of the inner antecedent wrt to the outer antecedent
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