ABSTRACT
Reasoning in expert systems in the presence of imprecision and inconsistency of the database and uncertainty of a knowledge base, is itself a complex problem, and becomes intractable when the knowledge base has an explicit self reference to itself A self referential knowledge base, if instantiated with appropriate data elements, gives rise to formation of cycles in the reasoning space. The chapter presents a structured approach to fuzzy reasoning using Petri nets to handle all the above problems of inexactness of data and knowledge by a unified approach.
A structural analysis of the model has been undertaken to examine its properties with respect to ‘reachability of places’ in the network for subsequent applications in the detection of cycles. A behavioral analysis of the model, with special reference to stability, reciprocity and duality, has also been presented. The results of the above analysis have been applied to fuzzy reasoning of a diverse nature including Modus Ponens, Modus Tollens, Abduction and non-monotonism.
