Reasoning with Very Expressive Fuzzy Description Logics

TL;DR

This paper extends fuzzy Description Logics to more expressive forms with transitive roles, inverse roles, hierarchies, and number restrictions, proving their decidability and providing reasoning procedures.

Contribution

It introduces fuzzy SHIN DL, proves its decidability, and develops decision procedures for knowledge base satisfiability, advancing expressive fuzzy DL reasoning.

Findings

Decidability of fuzzy-SI and fuzzy-SHIN DLs established.

Decision procedures for knowledge base satisfiability developed.

Handling transitive roles in fuzzy interpretations addressed.

Abstract

It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN.