Hyperresolution for Multi-step Fuzzy Inference in Goedel Logic

Abstract

This paper is a continuation of our work concerning the logical and computational foundations of multi-step fuzzy inference. We bring further results on the implementation of the Mamdani-Assilian type of fuzzy rules and inference in Goedel logic with truth constants. In our previous work, we have provided translation of Mamdani-Assilian fuzzy rules to formulae of Goedel logic, and subsequently, to suitable clausal form. Moreover, we have outlined a class of problems regarding general properties of fuzzy inference and shown its reduction to a class of deduction/unsatisfiability problems. We now focus on solving such problems using an adapted hyperresolution calculus.