Affiliations: Dipartimento di Informatica Università del Piemonte
Orientale "A. Avogadro" viale Teresa Michel, 11 -
15121, Alessandria, Italy. E-mail: laura@mfn.unipmn.it | LSIS-UMR CNRS 6168 Université
"Paul Cézanne" Aix en Provence, France.
E-mail: nicola.olivetti@univ-cezanne.fr | Dipartimento di Informatica Università degli Studi di
Torino c.so Svizzera 185, 10145 Torino, Italy. E-mail: {gliozzi,pozzato}@di.unito.it
Abstract: We extend the Description Logic ALC with a
"typicality" operator T that allows us to reason about
the prototypical properties and inheritance with exceptions. The resulting
logic is called ALC + T. The typicality operator is intended to select the
"most normal" or "most typical" instances of a concept. In our framework, knowledge
bases may then contain, in addition to ordinary ABoxes and TBoxes, subsumption
relations of the form "T(C) is subsumed by P",
expressing that typical C-members have the property P. The semantics of a
typicality operator is defined by a set of postulates that are strongly related
to Kraus-Lehmann-Magidor axioms of preferential logic P. We first show that T
enjoys a simple semantics provided by ordinary structures equipped with a
preference relation. This allows us to obtain a modal interpretation of the
typicality operator. We show that the satisfiability of anALC+Tknowledge base
is decidable and it is precisely EXPTIME. We then present a tableau calculus
for deciding satisfiability of ALC + T knowledge bases. Our calculus gives a
(suboptimal) nondeterministic-exponential time decision procedure for ALC + T.
We finally discuss how to extend ALC + T in order to infer defeasible
properties of (explicit or implicit) individuals. We propose two alternatives:
(i) a nonmonotonic completion of a knowledge base; (ii) a "minimal
model" semantics for ALC + T whose intuition is that minimal
models are those that maximise typical instances of concepts.
