Answering Fuzzy Queries over Fuzzy DL-Lite Ontologies

TL;DR

This paper explores how to answer fuzzy queries over fuzzy DL-Lite ontologies, revealing complexity results and providing an effective reduction method for G"odel t-norms, thus advancing reasoning in fuzzy description logics.

Contribution

It introduces a rewriting approach for fuzzy DL-Lite query answering, analyzing complexity and semantics dependence, and offers a reduction method for G"odel t-norms.

Findings

Threshold query answering remains in AC_0 data complexity.

Conjunctive query answering depends on the chosen triangular norm.

Effective reduction method for G"odel t-norms is proposed.

Abstract

A prominent problem in knowledge representation is how to answer queries taking into account also the implicit consequences of an ontology representing domain knowledge. While this problem has been widely studied within the realm of description logic ontologies, it has been surprisingly neglected within the context of vague or imprecise knowledge, particularly from the point of view of mathematical fuzzy logic. In this paper we study the problem of answering conjunctive queries and threshold queries w.r.t. ontologies in fuzzy DL-Lite. Specifically, we show through a rewriting approach that threshold query answering w.r.t. consistent ontologies remains in $AC_0$ in data complexity, but that conjunctive query answering is highly dependent on the selected triangular norm, which has an impact on the underlying semantics. For the idempodent G\"odel t-norm, we provide an effective method based on a reduction to the classical case. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).