A procedure for automatic proof nets construction

Didier Galmiche (1, 2) , Guy Perrier (2, 1)

1 UHP - Université Henri Poincaré - Nancy 1
2 Prograis

In this paper, we consider multiplicative linear logic (MLL) from an automated deduction point of view. Linear logic is more expressive than classical and intuitionistic logic and has an undirectional character due to the particular treatment of negation and the absence of structural rules. Considering this new logical framework to make logic programming or programming with proofs (extracting programs from proofs), a better comprehension of proofs in MLL (proof nets) is necessary and automated deduction has to be studied. Knowing that the multiplicative part of linear logic is decidable, we propose a new algorithm to construct automatically a proof net for a given sequent in MLL with proofs of termination, correctness and completeness. It can be considered as a more direct and implementation oriented way to consider automated deduction in linear logic.

Mots clés: Linear Logic; Proof nets

Domaines: Informatique et langage [cs.CL]

Didier Galmiche, Guy Perrier. A procedure for automatic proof nets construction. Conference on Logic Programming and Automated Reasoning, LPAR'92, 1992, St-Petersburg, Russia. pp.42-53. ⟨hal-01297750⟩