Section: New Results

Decision procedures for intuitionistic propositional logic

Participant : Stéphane Graham-Lengrand.

Provability in intuitionistic propositional logic is decidable and, as revealed by the works of, e.g., Vorobev  [72], Hudelmaier  [51] and Dyckhoff  [42], proof theory can provide natural decision procedures, which have been implemented in various software. More precisely, a decision procedure is obtained by performing direct root-first proof-search in (different variants of) a sequent calculus system called LJT (aka G4ip); termination is ensured by a property of the sequent calculus called depth-boundedness.

Independently from this, Claessen and Rosen  [40] recently proposed a decision procedure for the same logic, based on a methodology used in the field of Satisfiability-Modulo-Theories (SMT). Their implementation clearly outperforms the sequent-calculus-based implementations.

In 2018 we managed to establish of formal connection between the G4ip sequent calculus and the algorithm from  [40], revealing the features that they share and the features that distinguish them. This connection is interesting because it gives a proof-theoretical light on SMT-solving techniques, and it opens the door to the design of an intuitionistic version of the CDCL algorithm used in SAT-solvers, which decides provability in classical logic.