Specifying syntactic structures
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
JELIA '90 Proceedings of the European Workshop on Logics in AI
Lambek calculus is NP-complete
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Continuation semantics for symmetric categorial grammar
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Continuation semantics for the Lambek--Grishin calculus
Information and Computation
Continuation semantics for symmetric categorial grammar
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Extraction in the Lambek-Grishin calculus
ESSLLI'08/09 Proceedings of the 2008 international conference on Interfaces: explorations in logic, language and computation
The calculus of responsibility and commitment
Ludics, dialogue and interaction
The generative capacity of the lambek-grishin calculus: a new lower bound
FG'09 Proceedings of the 14th international conference on Formal grammar
Covert movement in logical grammar
Logic and grammar
The product-free Lambek-Grishin calculus is NP-complete
LACL'11 Proceedings of the 6th international conference on Logical aspects of computational linguistics
The Lambek-Grishin calculus is NP-Complete
FG'10/FG'11 Proceedings of the 15th and 16th international conference on Formal Grammar
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In this paper, we explore the Lambek-Grishin calculus LG: a symmetric version of categorial grammar based on the generalizations of Lambek calculus studied in Grishin [1]. The vocabulary of LG complements the Lambek product and its left and right residuals with a dual family of type-forming operations: coproduct, left and right difference. The two families interact by means of structure-preserving distributivity principles. We present an axiomatization of LG in the style of Curry's combinatory logic and establish its decidability. We discuss Kripke models and Curry-Howard interpretation for LG and characterize its notion of type similarity in comparison with the other categorial systems. From the linguistic point of view, we show that LG naturally accommodates non-local semantic construal and displacement -- phenomena that are problematic for the original Lambek calculi.