A non-monotonic Description Logic for reasoning about typicality

  • Authors:

  • L. Giordano;V. Gliozzi;N. Olivetti;G. L. Pozzato

  • Affiliations:

  • DISIT, Universití del Piemonte Orientale "A. Avogadro", viale Teresa Michel, 11, 15121 Alessandria, Italy;Dipartimento di Informatica, Universití degli Studi di Torino, C.So Svizzera, 185, 10149 Torino, Italy;Aix-Marseille Université, CNRS, LSIS UMR 7296, Campus de Saint Jérôme, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France;Dipartimento di Informatica, Universití degli Studi di Torino, C.So Svizzera, 185, 10149 Torino, Italy

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2013

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Abstract

In 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"m"i"n, 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)@?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"m"i"n, 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"m"i"n we are able to infer defeasible properties of (explicit or implicit) individuals. We also present a tableau calculus for deciding ALC+T"m"i"n entailment that allows to give a complexity upper bound for the logic, namely that query entailment is in co-NExp^N^P.