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 , Hudelmaier  and Dyckhoff , 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  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 , 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.