Fuzzy Reasoning and the Logics of Uncertainty

This paper is concerned with the foundations of fuzzy reasoning and its relationships with other logics of uncertainty. The definitions of fuzzy logics are first examined and the role of fuzzification discussed. It is shown that fuzzification of PC gives a known multivalued logic but with inappropriate semantics of implication and various alternative forms of implication are discussed. In the main section the discussion is broadened to other logics of uncertainty and it is argued that there are close links, both formal and semantic, between fuzzy logic and probability logics. A basic multivalued logic is developed in terms of a truth function over a lattice of propositions that encompasses a wide range of logics of uncertainty. Various degrees of truth functionality are then defined and used to derive specific logics including probability logic and Lukasiewicz infinitely valued logic. Quantification and modal operators over the basic logic are introduced. Finally, a semantics for the basic logic is introduced in terms of a population (of events, or people, or neurons) and the semantic significance of the constraints giving rise to different logics is discussed.