Graduate studies at Western
Journal of Philosophical Logic 38 (6):681 - 710 (2009)
|Abstract||The Lambek-Grishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of type-forming operations (product and residual left and right division) with a dual family: coproduct, left and right difference. Interaction between these two families is provided by distributivity laws. These distributivity laws have pleasant invariance properties: stability of interpretations for the Curry-Howard derivational semantics, and structure-preservation at the syntactic end. The move to symmetry thus offers novel ways of reconciling the demands of natural language form and meaning.|
|Keywords||Categorial grammar Lambek calculus Lambda calculus Curry-Howard correspondence Substructural logic|
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