An interval fuzzy truth-value approach to the generalized modus ponens

One of the desirable properties of generalized modus ponens in fuzzy logic is: if X is A/spl rarr/Y is B, and X is not A, then Y is unknown. From a truth-value viewpoint, "unknown" can be represented as the interval [0,1]. However most existing fuzzy reasoning mechanisms use the truth value 1 to represent "unknown". In this paper, we propose a new approach to fuzzy reasoning based on a possible world approach. We show that our approach obtains the desired interval truth valve [0,1] when the the antecedent is known to be false. We also compare our approach to Baldwin's (1979) and Godo's (1989) approaches and discuss the impact of the proposed approach to other desired properties of generalized modus ponens and generalized modus tollens.