Denotational semantics Object language Operational semantics 1 - PowerPoint PPT Presentation

Denotational semantics Object language Operational semantics 1

Cheating? State passing save , load Add register 1

Cheating? State passing save , load set! Add register 1

Cheating? Continuation passing reset catch , throw , both , shift someone, everyone abort Add metacontext 1

The rest of this course Multi-level continuations Day 3 Day 4 reset Donkey anaphora: shift Day 5 scope and binding Quotation 1

Donkey anaphora is in-scope binding Chris Barker and Chung-chieh Shan ESSLLI, 6 August 2008 Semantics and Pragmatics 1(1):1–42, 2008 2

Donkey anaphora If a donkey eats, it sleeps. Every farmer who owns a donkey beats it. 3

Donkey anaphora If a donkey eats, it sleeps. Every farmer who owns a donkey beats it. A donkey pronoun is a pronoun that lies outside the antecedent of a conditional (or the restrictor of a quantifier) yet covaries with an indefinite (or some other quantifier) inside it. 3

Donkey anaphora If a donkey eats, it sleeps. Every farmer who owns a donkey beats it. A donkey pronoun is a pronoun that lies outside the antecedent of a conditional (or the restrictor of a quantifier) yet covaries with an indefinite (or some other quantifier) inside it. 3

Donkey anaphora is in-scope binding If a donkey eats, it sleeps. Every farmer who owns a donkey beats it. A donkey pronoun is a pronoun that lies outside the antecedent of a conditional (or the restrictor of a quantifier) yet covaries with an indefinite (or some other quantifier) inside it. Our claim: the indefinite takes scope over and binds the donkey pronoun as usual . Every boy loves his mother. 3

Why not? Quantifier scope is clause-bound? But not indefinites. A donkey eats. It sleeps. 4

Why not? Quantifier scope is clause-bound? But not indefinites. A donkey eats. It sleeps. Binding requires c-command? Just evaluation order. Every boy’s mother loves him. 4

Why not? Quantifier scope is clause-bound? But not indefinites. A donkey eats. It sleeps. Binding requires c-command? Just evaluation order. Every boy’s mother loves him. How to get the right truth conditions? � � not ∃ d . ( donkey d ) ∧ ( eats d ) → ( sleeps d ) 4

Why not? Quantifier scope is clause-bound? But not indefinites. A donkey eats. It sleeps. Binding requires c-command? Just evaluation order. Every boy’s mother loves him. How to get the right truth conditions? � � not ∃ d . ( donkey d ) ∧ ( eats d ) → ( sleeps d ) ¬∃ d . ( donkey d ) ∧ ( eats d ) ∧¬ ( sleeps d ) but A donkey takes scope over the entire conditional but under if . A donkey sleeps if it eats. 4

Our account Compositional truth conditions: if , every , most , usually , strong/weak. Key: multiple levels of continuations Plan: Everyone loves someone. (surface scope) Everyone loves his mother. If a donkey eats, it sleeps. 5

Our account Compositional truth conditions: if , every , most , usually , strong/weak. Key: multiple levels of continuations Plan: Everyone loves someone. (surface scope) Everyone loves his mother. If a donkey eats, it sleeps. Everyone loves someone. (inverse scope) If a farmer owns a donkey, he beats it. Every farmer who owns a donkey beats it. Most farmers who own a donkey beat it. 5

� ( A � B ) A Lift B = ⇒ expression expression λ c . c ( x ) x 6

� ( A � B ) A Lift B = ⇒ expression expression λ c . c ( x ) x � ( ( A / B ) � D ) � ( B � E ) � ( A � E ) C D C left right = ⇒ left right λ c . L ( λ f . R ( λ x . c ( fx ))) L R 6

� ( A � B ) A Lift B = ⇒ expression expression λ c . c ( x ) x � ( ( A / B ) � D ) � ( B � E ) � ( A � E ) C D C left right = ⇒ left right λ c . L ( λ f . R ( λ x . c ( fx ))) L R � ( B � D ) � ( ( B \ A ) � E ) � ( A � E ) C D C = ⇒ left right left right L R λ c . L ( λ x . R ( λ f . c ( fx ))) 6

� ( A � B ) � ( S � S ) A Lift B A Lower A = ⇒ = ⇒ expression expression expression expression λ c . c ( x ) F ( λ x . x ) x F � ( ( A / B ) � D ) � ( B � E ) � ( A � E ) C D C left right = ⇒ left right λ c . L ( λ f . R ( λ x . c ( fx ))) L R � ( B � D ) � ( ( B \ A ) � E ) � ( A � E ) C D C = ⇒ left right left right L R λ c . L ( λ x . R ( λ f . c ( fx ))) 6

Linear notation Tower notation B C � ( A � C ) B A S S S � ( DP � S ) DP 7

Linear notation Tower notation B C � ( A � C ) B A S S S � ( DP � S ) DP f [ ] λ c . f [ c ( x )] x ¬∃ x . [ ] λ c . ¬∃ x . c ( mother x ) mother x 7

� ( A � B ) � ( S � S ) A Lift B A Lower A = ⇒ = ⇒ expression expression expression expression λ c . c ( x ) F ( λ x . x ) x F � ( ( A / B ) � D ) � ( B � E ) � ( A � E ) C D C left right = ⇒ left right λ c . L ( λ f . R ( λ x . c ( fx ))) L R � ( B � D ) � ( ( B \ A ) � E ) � ( A � E ) C D C = ⇒ left right left right L R λ c . L ( λ x . R ( λ f . c ( fx ))) 8

B B A S A Lift A S Lower A = ⇒ = ⇒ expression expression expression expression [ ] f [ ] f [ x ] x x x C D D E C E A / B B A left right = ⇒ left right g [ ] h [ ] g [ h [ ]] f ( x ) f x C D D E C E B \ A B A = ⇒ left right left right g [ ] h [ ] g [ h [ ]] x f f ( x ) 8

B B A S A Lift A S Lower A = ⇒ = ⇒ expression expression expression expression [ ] f [ ] f [ x ] x x x C D D E C E A / B B A left right = ⇒ left right g [ ] h [ ] g [ h [ ]] f ( x ) f x C D D E C E DP ⊲ B B B \ A B A DP = ⇒ left right left right he g [ ] h [ ] g [ h [ ]] λ y . [ ] x f f ( x ) y 8

B B A S A Lift A S Lower A = ⇒ = ⇒ expression expression expression expression [ ] f [ ] f [ x ] x x x C D D E C E A B A DP ⊲ B A / B B A DP Bind DP left right = ⇒ left right expression = ⇒ expression g [ ] h [ ] g [ h [ ]] f [ ] f ([ ] x ) f ( x ) f x x x C D D E C E DP ⊲ B B B \ A B A DP = ⇒ left right left right he g [ ] h [ ] g [ h [ ]] λ y . [ ] x f f ( x ) y 8

B B A S A Lift A S Lower A = ⇒ = ⇒ expression expression expression expression [ ] f [ ] f [ x ] x x x C D D E C E A B A DP ⊲ B A / B B A DP Bind DP left right = ⇒ left right expression = ⇒ expression g [ ] h [ ] g [ h [ ]] f [ ] f ([ ] x ) f ( x ) f x x x C D D E C E DP ⊲ B B S S B \ A ( S / S ) / S B A DP = ⇒ left right left right he if g [ ] h [ ] g [ h [ ]] λ y . [ ] ¬ [ ] x f f ( x ) y λ p λ q . p ∧¬ q 8

Every farmer who owns a donkey beats it S S N farmer who owns a donkey ∃ y . ( donkey y ) ∧ [ ] λ z . ( farmer z ) ∧ ( owns y z ) 9

Every farmer who owns a donkey beats it S DP ⊲ S N farmer who owns a donkey ∃ y . ( donkey y ) ∧ ([ ] y ) λ z . ( farmer z ) ∧ ( owns y z ) 9

Every farmer who owns a donkey beats it   S S � S S S DP ⊲ S     N   DP N     every farmer who owns a donkey     ¬∃ x . [ ] ∃ y . ( donkey y ) ∧ ([ ] y )     λ P . Px ∧¬ [ ] λ z . ( farmer z ) ∧ ( owns y z )     x 9

Every farmer who owns a donkey beats it   DP ⊲ S S S S � S S S DP ⊲ S S S     N   DP \ S DP N     every farmer who owns a donkey beats it     ¬∃ x . [ ] ∃ y . ( donkey y ) ∧ ([ ] y ) λ w . [ ]     λ P . Px ∧¬ [ ] λ z . ( farmer z ) ∧ ( owns y z )   [ ]   x beats w 9

Every farmer who owns a donkey beats it   DP ⊲ S S S S � S S S DP ⊲ S S S     N   DP \ S DP N     every farmer who owns a donkey beats it     ¬∃ x . [ ] ∃ y . ( donkey y ) ∧ ([ ] y ) λ w . [ ]     λ P . Px ∧¬ [ ] λ z . ( farmer z ) ∧ ( owns y z )   [ ]   x beats w ¬∃ x ∃ y . donkey y ∧ (( farmer x ∧ owns y x ) ∧¬ ( beats y x )) 9

Most farmers who own a donkey beat it S S S S � N DP most MOST ( λ x λ p . [ ]) λ P . Px ∧ ( p ∨ [ ]) x � # { x | F ( x )( FALSE ) } � 1 MOST ( F ) = > # { x | F ( x )( TRUE ) } 2 10

Most farmers who own a donkey beat it (weak) S S S S � N DP most MOST ( λ x λ p . [ ]) λ P . Px ∧ ( p ∨ [ ]) x � # { x | F ( x )( FALSE ) } � 1 MOST ( F ) = > # { x | F ( x )( TRUE ) } 2 10

Most farmers who own a donkey beat it (strong) S S S S � N DP most MOST ( λ x λ p . [ ]) λ P . Px ∧ ( p ∨¬ [ ]) x � # { x | F ( x )( FALSE ) } � 1 MOST ( F ) = < # { x | F ( x )( TRUE ) } 2 10