On Rational Closure in Description Logics of Typicality

TL;DR

This paper introduces a rational closure semantics for Description Logics with a typicality operator, extending existing frameworks to better model typicality and normality, with formal semantics and an algorithm for Abox reasoning.

Contribution

It defines a rational closure for ALC+T Description Logics, extending the concept to Abox, and provides a sound, complete ExpTime algorithm for reasoning.

Findings

Semantic characterization of rational closure via minimal models

Extension of rational closure to Abox reasoning

Development of an ExpTime reasoning algorithm

Abstract

We define the notion of rational closure in the context of Description Logics extended with a tipicality operator. We start from ALC+T, an extension of ALC with a typicality operator T: intuitively allowing to express concepts of the form T(C), meant to select the "most normal" instances of a concept C. The semantics we consider is based on rational model. But we further restrict the semantics to minimal models, that is to say, to models that minimise the rank of domain elements. We show that this semantics captures exactly a notion of rational closure which is a natural extension to Description Logics of Lehmann and Magidor's original one. We also extend the notion of rational closure to the Abox component. We provide an ExpTime algorithm for computing the rational closure of an Abox and we show that it is sound and complete with respect to the minimal model semantics.