Measuring Formula-Variable Relevance in Four-Valued Logic by Forgetting

Abstract

This paper discusses an approach to evaluate the relevance between a formula and a variable in it under the four-valued semantics. In the existing literature, for the classical two-valued propositional logic, there are definitions of whether a variable is independent to a certain formula. These definitions are based on forgetting, which is an operation to maintain and manage knowledge bases. Forgetting has its semantic connections with relevance. In the previous work in which the authors of this paper participated, an approach of quantitatively defining formula-variable relevance in two-valued propositional logic was proposed, which not only gave the judgement of relevant or not, but also gave a measurement of how relevant they are (i.e., the degree of relevance), also using the tool of variable forgetting. In this paper, we adapt the method to four-valued logic. Because forgetting has not been defined in four-valued logic yet, our first step is to define forgetting in four-valued logic. Then we will define formula-variable relevance quantitatively in four-valued logic. It will be a tool for the management of the knowledge bases under four-valued logic.