Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca PozzatoIn our recent research we have proposed a nonmonotonic extension ALC + Tmin of the Description Logic ALC for reasoning about prototypical properties and inheritance with exception. The logic ALC+Tmin is built upon a previously introduced (monotonic) logic ALC + T [1], 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) is subsumed by P”, expressing that typical C-members have the property P. In order to perform nonmonotonic inferences, we define a “minimal model” semantics ALC +Tmin for ALC +T. The intuition is that preferred, or minimal models are those that maximise typical instances of concepts. By means of ALC +Tmin we are able to infer defeasible properties of (explicit or implicit) individuals. We are able to provide a decision procedure for checking satisfiability and va- lidity in ALC +Tmin. Our decision procedure has the form of tableaux calculus, with a two-step tableau construction. The idea is that the top level construc- tion generates open branches that are candidates to represent minimal models, whereas the auxiliary construction checks whether a candidate branch represents indeed a minimal model. Our procedure can be used to determine constructively an upper bound of the complexity of ALC+Tmin. Namely we obtain that check- ing query entailment for ALC + Tmin is in co-NExp ^{NP}.pdf@Inproceedings{GiordanoEtAl, author = {Laura Giordano and Valentina Gliozzi and Nicola Olivetti and Gian Luca Pozzato}, title ={Reasoning About Typicality in Description Logics: the Logic ALC + Tmin}, year = {2008}, editor = {Marco Gavanelli and Toni Mancini}, booktitle = {R.i.C.e.R.c.A. 2008: RCRA Incontri E Confronti}, } |