Substructural Logic for Orientable and Non-Orientable Surfaces

Christophe Fouqueré (1) , Virgile Mogbil (1) , Gabriele Pulcini (2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 Department of Philosophy, University of Chieti-Pescara

We present a generalization of Permutative logic (PL) which is a non-commutative variant of Linear logic suggested by some topological investigations on the geometry of linear proofs. The original logical status based on a variety-presentation framework is simplified by extending the notion of q-permutation to the one of pq-permutation. Whereas PL is limited to orientable structures, we characterize the whole range of topological surfaces, orientable as well as non-orientable. The system we obtain is a surface calculus that enjoys both cut elimination and focussing properties and comes with a natural phase semantics whenever explicit context is considered.

Mots clés: Permutative logic; Sequent Calculus for Surfaces; Orientable and non-orientable surfaces; Phase Semantic; Relaxation

Domaines: Logique en informatique [cs.LO]

Christophe Fouqueré, Virgile Mogbil, Gabriele Pulcini. Substructural Logic for Orientable and Non-Orientable Surfaces. 2011. ⟨hal-00586978⟩