https://hal-amu.archives-ouvertes.fr/hal-01479546Giordano, LauraLauraGiordanoGliozzi, ValentinaValentinaGliozziOlivetti, NicolaNicolaOlivettiLSIS - Laboratoire des Sciences de l'Information et des Systèmes - AMU - Aix Marseille Université - UTLN - Université de Toulon - Arts et Métiers Paristech ENSAM Aix-en-Provence - CNRS - Centre National de la Recherche ScientifiquePozzato, GianGianPozzatoA non-monotonic Description Logic for reasoning about typicalityHAL CCSD2013[INFO] Computer Science [cs]Domingues Vinhas, William2017-02-28 20:38:572023-03-24 14:53:042017-02-28 20:38:57enJournal articles10.1016/j.artint.2012.10.0041In this paper we propose a non-monotonic extension of the Description Logic ALC for reasoning about prototypical properties and inheritance with exceptions. The resulting logic, called ALC + T-min, is built upon a previously introduced (monotonic) logic ALC + T that is obtained by adding a typicality operator T to ALC. The operator T is intended to select the "most normal" or "most typical" instances of a concept, so that knowledge bases may contain subsumption relations of the form T(C) subset of D ("T(C) is subsumed by D"), expressing that typical C-members are instances of concept D. From a knowledge representation point of view, the monotonic logic ALC + T is too weak to perform inheritance reasoning. In ALC + T-min, in order to perform non-monotonic inferences, we define a "minimal model" semantics over ALC + T. The intuition is that preferred or minimal models are those that maximize typical instances of concepts. By means of ALC + T-min we are able to infer defeasible properties of (explicit or implicit) individuals. We also present a tableau calculus for deciding ALC + T-min entailment that allows to give a complexity upper bound for the logic, namely that query entailment is in co-NExp(NP)