Satisfiability Degree Analysis and Deductive Reasoning

Abstract

There are many situations that common logic models aren't capable of representing, so nonclassical logic systems have emerged to compensate for their inability to express uncertainty. This article introduces the satisfiability degree for propositional logic. It's a new means of describing the extent to which a proposition is satisfied, and it employs deterministic logic rather than probabilistic or fuzzy logic. The independent formula-pair and incompatible formula-pair of the propositions are discussed. Some properties of the satisfiability degree are given with a conditional satisfiability degree. The weighted satisfiability degree is defined and the properties are proven. Deductive reasoning methods based on the satisfiability degree are established. The formula reasoning and semantic checking are given by the conditional satisfiability degree. Finally, calculations of the satisfiability degree for the circuit logic diagram and Bayesian attack graphs are given.