Towards a Rational Closure for Expressive Description Logics:the Case of SHIQ

Laura Giordano (1) , Valentina Gliozzi (2) , Nicola Olivetti (3, 4, 5)

1 DISIT - Dipartimento di Scienze e Innovazione Tecnologica [Alessandria]
2 UNITO - Università degli studi di Torino = University of Turin
3 AMU - Aix Marseille Université
4 LIS - Laboratoire d'Informatique et Systèmes
5 LIRICA - Logique, Interaction, Raisonnement et Inférence, Complexité, Algèbre

We explore the extension of the notion of rational closure to logics lacking the finite model property, considering the logic SHIQ. We provide a semantic characterization of rational closure in SHIQ in terms of a preferential semantics, based on a finite rank characterization of minimal models. We show that the rational closure of a KB can be computed in EXPTIME based on a polynomial encoding of the rational extension of SHIQ into entailment in SHIQ. We discuss the extension of rational closure to more expressive description logics.

Keywords: Description Logics; Nonmonotonic reasoning

Domains: Computer Science [cs]; Computer Science [cs]; Artificial Intelligence [cs.AI]; Computer Science [cs]; Logic in Computer Science [cs.LO]

Laura Giordano, Valentina Gliozzi, Nicola Olivetti. Towards a Rational Closure for Expressive Description Logics:the Case of SHIQ. Fundamenta Informaticae, 2018, 159 (1-2), pp.95-122. ⟨10.3233/FI-2018-1659⟩. ⟨hal-02079796⟩