Abstract
Mathematical Fuzzy Logics [51, 60] have a long tradition with roots going back to the many-valued logics of Łukasiewicz, Gödel, and Kleene [57, 68, 73] and the Fuzzy Set Theory of Zadeh [111]. Their purpose is to model vagueness or imprecision in the real world, by introducing new degrees of truth as additional shades of gray between the Boolean true and false. For example, one can express the distinction between a person x having a high fever or a low fever as the degree of truth of the logical statement Fever (x). One of the central properties of fuzzy logics is truth functionality—the truth degree of a complex logical formula is uniquely determined by the truth degrees of its subformulas. This is a fundamental difference to other quantitative logics like probabilistic or possibilistic logics [56, 83].