On Multi-step Fuzzy Inference in Goedel Logic

TL;DR

This paper explores the logical and computational foundations of multi-step fuzzy inference in Goedel logic, proposing methods to address key problems like reachability, stability, and cycles using hyperresolution calculus.

Contribution

It introduces a hyperresolution calculus for multi-step fuzzy inference in Goedel logic, addressing fundamental problems through deduction and unsatisfiability reductions.

Findings

Reduction of reachability, stability, and cycle problems to deduction and unsatisfiability.

Application of hyperresolution calculus to solve these problems.

Establishment of a formal framework for 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.