A new continuous propositional logic

Abstract

In this paper we present Minimal Polynomial Logic (MPL), a generalisation of classical propositional logic which allows truth values in the continuous interval [0, 1] and in which propositions are represented by multi-variate polynomials with integer coefficients.The truth values in MPL are suited to represent the probability of an assertion being true, as in Nilsson's Probabilistic Logic, but can also be interpreted as the degree of truth of that assertion, as in Fuzzy Logic. However, unlike fuzzy logic MPL respects all logical equivalences, and unlike probabilistic logic it does not require explicit manipulation of possible worlds.In the paper we describe the derivation and the properties of this new form of logic and we apply it to solve and better understand several practical problems in classical logic, such as satisfiability.