Truth-Functional Logic and Fuzzy Logic

Abstract

Generally speaking, all fuzzy logics considered so far arise from the fiizzification of notions having a metalogic character (see Section 10 in Chapter 3). By contrast, in this chapter we will investigate several fuzzy logics directly arising from “fuzzy worlds”, i.e., worlds whose properties can be vague and therefore whose truth-value assignments can be graded. This leads to truth-functional semantics, i.e., semantics in which the truth value of a composite sentence is determined by the truth-values of its constituents. More precisely, we consider a language by starting from

• an infinite set VAR = {p ₁, ... , p _n , ...} of propositional variables,

• a set of logical connectives containing the usual connectives, namely ∧ , ∨ , ¬.