SAT-Based Proof Search in Intermediate Propositional Logics

Abstract

We present a decision procedure for intermediate logics relying on a modular extension of the SAT-based prover $$\texttt {intuitR} $$ intuitR for $$\mathrm {IPL} $$ IPL (Intuitionistic Propositional Logic). Given an intermediate logic L and a formula $$\alpha $$ α , the procedure outputs either a Kripke countermodel for $$\alpha $$ α or the instances of the characteristic axioms of L that must be added to $$\mathrm {IPL} $$ IPL in order to prove $$\alpha $$ α . The procedure exploits an incremental SAT-solver; during the computation, new clauses are learned and added to the solver.