Symmetric categorial grammar

Journal of Philosophical Logic 38 (6):681 - 710 (2009)
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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Joachim Lambek (1968). The Mathematics of Sentence Structure. Journal of Symbolic Logic 33 (4):627-628.

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