Polyhedral semantics and the tractable approximation of Łukasiewicz infinitely-valued logic

Abstract

Abstract In this work, we present polyhedral semantics as a means to tractably approximate Łukasiewicz infinitely-valued logic (Ł$_{\infty}$). As Ł$_{\infty}$ is an expressive multivalued propositional logic whose decision problem is NP-complete, we show how to to obtain an approximation for this problem providing a family of multivalued logics over the same language as Ł$_{\infty}$. Each element of the family is associated to a polynomial-time linear program, thus providing a tractable way of deciding each intermediate step. We also investigate properties of the logic system derived from polyhedral semantics and the details of an algorithm for the approximation process.