Propositional syntax and semantics induced knowledge re-structuring in a fuzzy logic network for ad hoc reasoning

Abstract

Traditional approaches to fuzzy reasoning usually employ Generalized Modus Ponens, Generalized Modus Tollens and Generalized Hypothetical Syllogisms to derive fuzzy inferences from a given set of fuzzy observations/facts and fuzzy if-then rules. However, the above approaches occasionally fail to generate inferences, although semantically plausible fuzzy inferences follow as a natural consequence of the given set of rules and fuzzy facts/observations. This paper serves to fill this void. It extends propositional syntax and semantics in the context of fuzzy reasoning to transform/re-structure individual rules to a suitable form (by negating and transposing propositions from antecedent to consequent and vice-versa), so as to get the propositions present in the antecedent (consequent) instantiated (refuted) by positive (negative) facts to enable the rules for forward (backward) firing. Next fuzzy compositional rule of inference is used to perform forward/backward reasoning. Consequently, when the rules are embedded in a fuzzy Petri net like structure, the rules apparently fire randomly in forward or backward direction without maintaining any topological order in transition-firing. Such random firing of rules in distributed parts of the network is referred to as ad hoc reasoning. Here, we transform such randomly ordered forward/backward firing sequence of transitions in the network into a fixed topological order of transition-firing in forward direction only by replacing backward firing transitions into equivalent forward firing transitions. The proposed method of automated reasoning has successfully been applied in diagnostic application of an electronic rectifier circuit, and the results are appealing.