Reasoning in Infinitely Valued G-IALCQ

TL;DR

This paper extends decidability results for infinitely valued G"odel-based fuzzy description logics to include qualified number restrictions, combining crispification and automata techniques for improved reasoning.

Contribution

It introduces a novel approach that merges crispification and automata methods to handle qualified number restrictions in G-IALC, enhancing reasoning capabilities.

Findings

Decidability is extended to G-IALC with number restrictions.

The combined approach improves reasoning efficiency.

The method removes limitations of previous techniques.

Abstract

Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable in the presence of a negation constructor and general concept inclusion axioms. One exception to this negative result are FDLs whose semantics is based on the infinitely valued G\"odel t-norm (G). In this paper, we extend previous decidability results for G-IALC to deal also with qualified number restrictions. Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and the automata-based procedure originally developed for reasoning in G-IALC. The proposed approach combines the advantages of these two methods, while removing their respective drawbacks.