Monads and composable continuations
Lisp and Symbolic Computation
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Call-by-value is dual to call-by-name
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Control categories and duality: on the categorical semantics of the lambda-mu calculus
Mathematical Structures in Computer Science
Linguistic side effects
Types as Graphs: Continuations in Type Logical Grammar
Journal of Logic, Language and Information
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Continuation semantics for symmetric categorial grammar
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Symmetries in natural language syntax and semantics: the Lambek-Grishin calculus
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Relational semantics for the Lambek-Grishin calculus
MOL'07/09 Proceedings of the 10th and 11th Biennial conference on The mathematics of language
Explanation in natural language of λμμ-Terms
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Relational semantics for the Lambek-Grishin calculus
MOL'07/09 Proceedings of the 10th and 11th Biennial conference on The mathematics of language
Polarized classical non-associative Lambek calculus and formal semantics
LACL'11 Proceedings of the 6th international conference on Logical aspects of computational linguistics
SDRT and continuation semantics
JSAI-isAI'10 Proceedings of the 2010 international conference on New Frontiers in Artificial Intelligence
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Categorial grammars in the tradition of Lambek are asymmetric: sequent statements are of the form @C@?A, where the succedent is a single formula A, the antecedent a structured configuration of formulas A"1,...,A"n. The absence of structural context in the succedent makes the analysis of a number of phenomena in natural language semantics problematic. A case in point is scope construal: the different possibilities to build an interpretation for sentences containing generalized quantifiers and related expressions. In this paper, we explore a symmetric version of categorial grammar, based on work by Grishin [14]. In addition to the Lambek product, left and right division, we consider a dual family of type-forming operations: coproduct, left and right difference. Communication between the two families is established by means of structure-preserving distributivity principles. We call the resulting system LG. We present a Curry-Howard interpretation for LG derivations, based on Curien and Herbelin's lambda mu comu calculus. We discuss continuation-passing-style (CPS) translations mapping LG derivations to proofs/terms of Intuitionistic Multiplicative Linear Logic - the categorial system LP which serves as the logic for natural language meaning assembly. We show how LG, thus interpreted, associates sentences with quantifier phrases with the appropriate range of meanings, thus overcoming the expressive limitations of asymmetric categorial grammars in this area.