On Multi-step Fuzzy Inference in Goedel Logic

Abstract

This paper addresses the logical and computational foundations of multi-step fuzzy inference using the Mamdani-Assilian type of fuzzy rules by implementing such inference in Goedel logic with truth constants. We apply the results achieved in the development of a hyperresolution calculus for this logic. We pose three fundamental problems: reachability, stability, the existence of a k-cycle in multi-step fuzzy inference and reduce them to certain deduction and unsatisfiability problems. The corresponding unsatisfiability problems may be solved using hyperresolution.