SAT and SMT technology for many-valued logics

Abstract

© 2014 Old City Publishing, Inc. We propose to use the SAT and SMT technology to deal with manyvalued logics. Our approach is twofold. Firstly, we focus on finitelyvalued logics, and extend the language of signed CNF formulas with linear integer arithmetic constraints. This way, we get a simple modeling language in which a wide range of practical combinatorial problems admit compact and natural encodings. We then define efficient translations from our language into the SAT and SMT formalisms, and propose to use SAT and SMT solvers for finding solutions. Secondly, we show how we can use the SMT technology to build efficient automated theorem provers for infinitely-valued logics, taking Lukasiewicz infinitely-valued logic as a case study.