Theoretical Foundations of Defeasible Description Logics

TL;DR

This paper extends description logics with non-monotonic reasoning, introducing defeasible subsumption, and provides semantics, properties, and an efficient algorithm for defeasible reasoning.

Contribution

It introduces a semantic framework for defeasible subsumption in DLs, links it to KLM properties, and presents an algorithm for rational closure with complexity comparable to classical DL reasoning.

Findings

Semantic constructions satisfy KLM properties

Algorithm computes rational closure efficiently

Reasoning complexity remains on par with classical DLs

Abstract

We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in DLs. Indeed, we also analyse the problem of non-monotonic reasoning in DLs at the level of entailment and present an algorithm for the computation of rational closure of a defeasible ontology. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of reasoning in the underlying classical DL ALC.