Hyperresolution for Multi-step Fuzzy Inference in Goedel Logic

TL;DR

This paper advances the computational methods for multi-step fuzzy inference in Goedel logic, specifically by developing a hyperresolution calculus to efficiently solve related deduction and unsatisfiability problems.

Contribution

It introduces an adapted hyperresolution calculus for multi-step fuzzy inference in Goedel logic, building on previous translations of fuzzy rules to improve computational reasoning.

Findings

Successful implementation of hyperresolution calculus

Enhanced efficiency in solving fuzzy inference problems

Improved translation of fuzzy rules to logical formulae

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.