SAT-Based Decision Procedure for Analytic Pure Sequent Calculi

• Published in: Automated Reasoning pp. 76 - 90
• Main Authors: Lahav, Ori, Zohar, Yoni
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing 2014
• Series: Lecture Notes in Computer Science
• ISBN: 9783319085869; 3319085867
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-08587-6_6

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 HORNSAT-based linear-time decision procedure for Gurevich and Neeman’s primal infon logic and several natural extensions of it.