Connection-based proof search in intuitionistic logic from transitive closure of constraints

Didier Galmiche (1) , Daniel Mery (1)

1 TYPES - Logic, proof Theory and Programming

We present a constraint-based calculus for intuitionistic propositional logic (IPL) which gives rise to a new connection-based characterization of intuitionistic provability. Compared to other free-variable tableaux or connectionbased systems, our calculus replaces so-called prefixes by labels and constraints derived directly from the standard Kripke semantics for IPL. In order to characterize intuitionistic provability, using label constraints instead of prefixes allows to drop prefix-uni cation algorithms in favor of a more direct and simple transitive closure operation on label constraints. We show the soundness and the completeness of the system, give arguments for its termination.

Domaines: Logique en informatique [cs.LO]

Didier Galmiche, Daniel Mery. Connection-based proof search in intuitionistic logic from transitive closure of constraints. International Workshop on Automated Deduction: Decidability, Complexity, Tractability - ADDCT'07, Jul 2007, Bremen, Germany. pp.15. ⟨hal-00580308⟩