SAT-Based Decision Procedure for Analytic Pure Sequent Calculi

We identify a wide family of analytic sequent calculi for propositional non-classical logics whose derivability problem can be uniformly reduced to SAT. The proposed reduction is based on interpreting these calculi using non-deterministic semantics. Its time complexity is polynomial, and, in fact, linear for a useful subfamily. We further study an extension of such calculi with Next operators, and show that this extension preserves analyticity and is subject to a similar reduction to SAT. A particular interesting instance of these results is a HORNSATbased linear-time decision procedure for Gurevich and Neeman’s primal infon logic and several natural extensions of it.