Rewritings for Polarized Multiplicative and Exponential Proof Structures

Christophe Fouqueré (1) , Virgile Mogbil (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

We study conditions for a concurrent construction of proof-nets in the framework of linear logic following Andreoli's works. We define specific correctness criteria for that purpose. We first study the multiplicative case and show how the correctness criterion given by Danos and decidable in linear time, may be extended to closed modules (i.e. validity of polarized proof structures). We then study the exponential case. This has natural applications in (concurrent) logic programming as validity of partial proof structures may be interpreted in terms of validity of a concurrent execution of clauses in an environment.

Mots clés: linear logic; proof-nets; logic programming; focalization; concurrent execution

Domaines: Logique en informatique [cs.LO]; Calcul parallèle, distribué et partagé [cs.DC]

Christophe Fouqueré, Virgile Mogbil. Rewritings for Polarized Multiplicative and Exponential Proof Structures. Electronic Notes in Theoretical Computer Science, 2008, pre-proceedings version, 203 (1), pp. 109-121. ⟨10.1016/j.entcs.2008.03.037⟩. ⟨hal-00143929⟩