Connectives: Conjunctions, Disjunctions and Negations

Abstract

In fuzzy logic, the law of contradiction and the law of excluded middle are, in general, false. However, because of their intuitive appeal, it is reasonable to study fuzzy logical systems, where these laws hold. In this chapter, we give a full description of consistent conjunction, disjunction, and negation triples in such systems. We also introduce additional negation operators that naturally define thresholds for better modeling of human thinking. The results of this chapter form the basis for constructing fuzzy logical systems that can later, in Chap. 9, be represented by neural-network transformations. This representation will assist the natural language interpretation of machine learning methods.