Proof nets for the Lambek-Grishin calculus

Abstract

Grishin's generalization of Lambek's Syntactic Calculus combines a non-commutative multiplicative conjunction and its residuals (product, left and right division) with a dual family: multiplicative disjunction, right and left difference. Interaction between these two families takes the form of linear distributivity principles. We study proof nets for the Lambek-Grishin calculus and the correspondence between these nets and unfocused and focused versions of its sequent calculus.

Revised version to appear as a chapter in E. Grefenstette, C. Heunen, and M. Sadrzadeh (eds.) 'Compositional Methods in Physics and Linguistics', Oxford University Press

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