Long-distance dependencies in continuation grammar Cara Su-Yi Leong & Michael Yoshitaka Erlewine cara@u.nus.edu mitcho@nus.edu.sg National University of Singapore PACLIC 33 Future University Hakodate, September 2019
Introduction Barker & Shan (B&S) develop a Combinatory Categorial Grammar which uses the notion of continuations for semantic scope-taking. One hallmark of B&S is their explanatory account of crossover efgects (Shan and Barker 2006). Today: We critically evaluate the B&S framework, based on the behavior of long-distance dependencies . • Data from quantifjer scope-taking and long-distance dependencies motivate some refjnements to the B&S theory... • ...but these necessary refjnements then result in undoing their positive predictions for crossover efgects. B&S, but their scope-taking behavior is empirically difgerent. We show that the B&S framework has fundamental diffjculties modeling such behavior. 2 � Quantifjers, pronouns, and gaps all “take scope” in the same way for
Introduction Barker & Shan (B&S) develop a Combinatory Categorial Grammar which uses the notion of continuations for semantic scope-taking. One hallmark of B&S is their explanatory account of crossover efgects (Shan and Barker 2006). Today: We critically evaluate the B&S framework, based on the behavior of long-distance dependencies . • Data from quantifjer scope-taking and long-distance dependencies motivate some refjnements to the B&S theory... • ...but these necessary refjnements then result in undoing their positive predictions for crossover efgects. B&S, but their scope-taking behavior is empirically difgerent. We show that the B&S framework has fundamental diffjculties modeling such behavior. 2 � Quantifjers, pronouns, and gaps all “take scope” in the same way for
Introduction Barker & Shan (B&S) develop a Combinatory Categorial Grammar which uses the notion of continuations for semantic scope-taking. One hallmark of B&S is their explanatory account of crossover efgects (Shan and Barker 2006). Today: We critically evaluate the B&S framework, based on the behavior of long-distance dependencies . • Data from quantifjer scope-taking and long-distance dependencies motivate some refjnements to the B&S theory... • ...but these necessary refjnements then result in undoing their positive predictions for crossover efgects. B&S, but their scope-taking behavior is empirically difgerent. We show that the B&S framework has fundamental diffjculties modeling such behavior. 2 � Quantifjers, pronouns, and gaps all “take scope” in the same way for
§2 Background: Barker & Shan’s continuation- based grammar 3
B&S: CCG with continuations likes likes j m John likes Mary S j John Barker and Shan (Barker 2002; Shan 2004, 2007; Shan and Barker 2006; DP likes m Mary DP We refer to these works collectively as B&S . Barker and Shan 2006, 2008, 2014) develop a CCG using continuations . 4 ( DP \ S ) / DP ← syntactic type = ← surface form ← denotation
B&S: CCG with continuations likes likes j m John likes Mary S j John Barker and Shan (Barker 2002; Shan 2004, 2007; Shan and Barker 2006; DP likes m Mary DP We refer to these works collectively as B&S . Barker and Shan 2006, 2008, 2014) develop a CCG using continuations . 4 ( DP \ S ) / DP ← syntactic type = ← surface form ← denotation
Continuations Continuations refer to the “computational future of an expression” (Shan and Barker 2006: 95), i.e. the procedures that will later apply to the expression. B&S use continuation-passing to implement semantic scope. Informally, following B&S (2014: 6): 5 In addition to common \ and / type constructors for left and right composition, B&S introduce � and � for continuation-passing. • A � B would be a B if we could add an A inside it; • C � D would be a C if we could add a surrounding D .
Continuations Continuations refer to the “computational future of an expression” (Shan and Barker 2006: 95), i.e. the procedures that will later apply to the expression. B&S use continuation-passing to implement semantic scope. Informally, following B&S (2014: 6): 5 In addition to common \ and / type constructors for left and right composition, B&S introduce � and � for continuation-passing. • A � B would be a B if we could add an A inside it; • C � D would be a C if we could add a surrounding D .
Multi-level towers B&S introduce multi-level towers with the interpretation in ( ?? ), where higher levels of the towers represent continuation-passing. (1) C B A expression a expression 6 C � ( A � B ) := f [ ] λκ . f ( κ ( a ))
Composition of towers E Notice that adjacent types on the higher levels have to match. left-exp right-exp B E C f Composing two expressions: right-exp D x left-exp A D C (2) 7 A \ B = g [ ] h [ ] g ( h [ ]) f ( x )
Composition of towers E Notice that adjacent types on the higher levels have to match. left-exp right-exp B E C f Composing two expressions: right-exp D x left-exp A D C (2) 7 A \ B = g [ ] h [ ] g ( h [ ]) f ( x )
Scope-taking and type-shifters Scope-taking expressions like quantifjers have two-level denotations. y everyone DP S S likes likes x someone DP S S 8 ( DP \ S ) / DP ∃ x . [ ] ∀ y . [ ]
Scope-taking and type-shifters Scope-taking expressions like quantifjers have two-level denotations. composition. We use lift ( ?? ) to match non-scope-taking expressions for y everyone DP S S likes likes S S x someone DP S S 8 ( DP \ S ) / DP ∃ x . [ ] [ ] ∀ y . [ ]
Scope-taking and type-shifters likes likes y x someone likes everyone S S S y everyone DP S Scope-taking expressions like quantifjers have two-level denotations. S likes S S x someone DP S S 8 ( DP \ S ) / DP = ∃ x . [ ] [ ] ∀ y . [ ] ∃ x . ∀ y . [ ]
Scope-taking and type-shifters S We then lower ( ?? ) the expression at the end. someone likes everyone S = likes y x someone likes everyone S S S y Scope-taking expressions like quantifjers have two-level denotations. DP everyone S x S S DP someone likes 8 S S likes ( DP \ S ) / DP = ∃ x . [ ] [ ] ∀ y . [ ] ∃ x . ∀ y . [ ] ↓ ⇒ ∃ x . ∀ y . likes y x
Scope-taking and type-shifters S y everyone DP S S S S likes likes We can also derive inverse scope using multi-level towers. 9 S someone S S S S S DP x S ( DP \ S ) / DP [ ] [ ] ∀ y . [ ] ∃ x . [ ] [ ] [ ] We use “internal lift ” to raise ∀ to a higher level.
Scope-taking and type-shifters likes likes y x someone likes everyone S S S S S y everyone DP S S S We can also derive inverse scope using multi-level towers. S 9 S likes S S S S x S S S someone DP ( DP \ S ) / DP = [ ] [ ] ∀ y . [ ] ∀ y . [ ] ∃ x . [ ] [ ] [ ] ∃ x . [ ]
Scope-taking and type-shifters S S We can also derive inverse scope using multi-level towers. DP everyone y S S S S S someone likes everyone likes y x = = S someone likes everyone S S likes S S S S S DP someone x 9 S S likes S ( DP \ S ) / DP = [ ] [ ] ∀ y . [ ] ∀ y . [ ] ∃ x . [ ] [ ] [ ] ∃ x . [ ] ↓↓ ⇒ ∀ y . ∃ x . likes y x
Pronouns pronoun of category A , for example: S DP he x Pronouns are represented as inherently multi-level towers, meaning that they are also scope-taking expressions. 10 The syntactic category A ▷ B represents a B that contains an unbound DP ▷ S λ x . [ ]
Pronouns said We apply bind ( ?? ) to John for it to bind the pronoun to its right. cried cried S S x he DP S said j 11 in the expression until it is bound (hypothetically). John DP The DP ▷ S type propagates to the left, denoting an open pronoun exists DP ▷ S DP ▷ S DP ▷ S DP ▷ S DP ▷ S ( DP \ S ) / S DP / S [ ] [ ] λ x . [ ] [ ]
Pronouns said We apply bind ( ?? ) to John for it to bind the pronoun to its right. cried cried S S x he DP S said j 11 in the expression until it is bound (hypothetically). S John DP The DP ▷ S type propagates to the left, denoting an open pronoun exists DP ▷ S DP ▷ S DP ▷ S DP ▷ S ( DP \ S ) / S DP / S [ ] j [ ] λ x . [ ] [ ]
Movement Continuation-passing provides an in-situ account of movement dependencies using gaps. S DP x 12 Gaps introduce a variable and λ binder like pronouns: DP � S λ x . [ ] Similarly, DP � S propagates to the left to get bound.
Crossover One advertised feature of B&S’s proposal is its explanation for crossover efgects (Postal 1971) using linear evaluation. ( ?? ) a. ? ( ?? ) i 13 Which girl i did John introduce to her i second cousin? b. ?? Which girl i did John introduce her i second cousin to a. ✓ wh i ... i ... pro i b. * wh i ... pro i ...
Crossover One advertised feature of B&S’s proposal is its explanation for crossover efgects (Postal 1971) using linear evaluation. ( ?? ) a. ? ( ?? ) i 13 Which girl i did John introduce to her i second cousin? b. ?? Which girl i did John introduce her i second cousin to a. ✓ wh i ... i ... pro i b. * wh i ... pro i ...
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