On Expressive Description Logics with Composition of Roles in Number Restrictions
Description Logics are knowledge representation formalisms which have been used in a wide range of application domains. Owing to their appealing expressiveness, we consider in this paper extensions of the well-known concept language ALC allowing for number restrictions on complex role expressions. These have been first introduced by Baader and Sattler as ALCN(M) languages, with the adoption of role constructors M ⊆ ◯,-,⊔,⊓.
In particular, as far as languages equipped with role composition are concerned, they showed in 1999 that, although ALCN(◯) is decidable, the addition of other operators may easily lead to undecidability: in fact, ALCN(◯,⊓) and ALCN(◯,-,⊔) were proved undecidable. In this work, we further investigate the computational properties of the ALCN family, aiming at narrowing the decidability gap left open by Baader and Sattler’s results. In particular, we will show that ALCN(◯) extended with inverse roles both in number and in value restrictions becomes undecidable, whereas it can be safely extended with qualified number restrictions without losing decidability of reasoning.
KeywordsDescription Logic Concept Description Atomic Concept Semistructured Data Role Chain
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- 1.A. Artale and E. Franconi. Temporal ER Modeling with Description Logics. In Proc. Intl’ Conf. on Conceptual Modeling (ER’99), pages 81–95, 1999.Google Scholar
- 2.F. Baader, D. McGuinness, D. Nardi, and P.F. Patel-Schneider, editors. The Decsription Logic Handbook: Theory, implementation and applications. Cambridge University Press, 2002 (to appear).Google Scholar
- 5.R. Berger. The Undecidability of the Dominoe Problems. Mem. Amer. Mathematical Society, 66:1–72, 1966.Google Scholar
- 7.A. Borgida and M. Jarke. Knowledge Representation and Reasoning in Software Engineering. IEEE Transactions on Software Engineering, 18(6):449–450, 1992.Google Scholar
- 9.D. Calvanese, G. De Giacomo, and M. Lenzerini. Description Logics: Foundations for Class-based Knowledge Representation. In Proc. of IEEE Symposium on Logic in Computer Science (LICS’99), 2002.Google Scholar
- 10.D. Calvanese, G. De Giacomo, M. Lenzerini, and D. Nardi. Reasoning in Expressive Description Logics. In Handbook of Automated Reasoning, pages 1581–1634. Elsevier, 2001.Google Scholar
- 11.D. Calvanese, G. De Giacomo, M. Lenzerini, D. Nardi, and R. Rosati. Description Logic Framework for Information Integration. In Proc. of Intl’ Conf. on the Principles of Knowledge Representation and Reasoning (KR’98), 1998.Google Scholar
- 12.D. Calvanese, M. Lenzerini, and D. Nardi. Description Logics for Conceptual Data Modeling. In Logics for Databases and Information Systems, pages 229–263. Kluwer Academic Publishers, 1998.Google Scholar
- 13.G. De Giacomo and M. Lenzerini. TBox and ABox Reasoning in Expressive Description Logics. In Proc. of Intl’ Conf. on the Principles of Knowledge Representation and Reasoning (KR’96), pages 348–353, 1996.Google Scholar
- 15.E. Franconi, F. Grandi, and F. Mandreoli. A Semantic Approach for Schema Evolution and Versioning in Object-Oriented Databases. In Proc. Intl’ Conf. on Deductive and Object-Oriented Databases (DOOD 2000), pages 1048–1062, 2000.Google Scholar
- 16.C.A. Goble and C. Haul and S. Bechhofer. Describing and Classifying Multimedia Using the Description Logic GRAIL. In Proc. of Storage and Retrieval for Image and Video Databases (SPIE), 1996.Google Scholar
- 17.E. Grädel, M. Otto, and E. Rosen. Two-variable Logic with Counting is Decidable. In Proc. Annual IEEE Symp. on Logic in Computer Science (LICS’97), pages 306–317, 1997.Google Scholar
- 18.F. Grandi. On Expressive Number Restrictions in Description Logics. In Proc. of Intl’ Workshop on Description Logics (DL’01), 2001.Google Scholar
- 19.F. Grandi. On Expressive Description Logics with Composition of Roles in Number Restrictions. Technical Report CSITE-01-02, CSITE-CNR Bologna, 2002. (URL ftp://ftp-db.deis.unibo.it/pub/fabio/TR/CSITE-01-02.pdf)
- 20.B. Hollunder and F. Baader. Qualifying Number Restrictions in Concept Languages. In Proc. of 2nd International Conference on Principles of Knowledge Representation and Reasoning, KR-91, pages 335–346, 1991.Google Scholar
- 21.B. Hollunder, W. Nutt, and M. Schmidt-Schauß. Subsumption Algorithms for Concept Description Languages. In Proc. of Europ. Conf. on Artificial Intelligence (ECAI’90), pages 335–346, 1990.Google Scholar
- 22.I. Horrocks and U. Sattler. Ontology Reasoning in the SHOQ(D) Description Logic. In Proc. of Intl’ Joint Conf. on Artificial Intelligence (IJCAI’01), 2001.Google Scholar
- 23.L. Pacholski, W. Szwast, and L. Tendera. Complexity of Two-variable Logic with Counting. In Proc. Annual IEEE Symp. on Logic in Computer Science (LICS’97), pages 318–327, 1997.Google Scholar
- 26.S. Tobies. Complexity Results and Practical Algorithms for Logics in Knowledge Representation. PhD thesis, RWTH Aachen, Germany, 2001.Google Scholar