Proofs nets and the categorial flow of information

Michael Moortgat (1) , Richard Moot (2)

1 UiL OTS - Utrecht Institute of Linguistics OTS
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

The Lambek-Grishin calculus (LG) is a multiple-conclusion extension of Lambek's categorial type logic with dual families of fusion ('merge') and fission operations, and linear distributivity principles relating these two. Thanks to the distributivity principles, LG captures dependency patterns beyond context-free, both in syntax and semantics. In this paper we represent the information flow in categorial derivations in terms of a proof net graphical calculus. We study the correspondence between the composition graphs for these nets and the terms associated with focused sequent derivations.

Mots clés: Proof nets; Proof theory; Lambek-Grishin calculus; Continuation Passing Translation

Domaines: Informatique et langage [cs.CL]

Michael Moortgat, Richard Moot. Proofs nets and the categorial flow of information. Logic and Interactive Rationality, 2012, Amsterdam, Netherlands. ⟨hal-00759906⟩