Abstract
This paper investigates a Description Logic, namely \(\mathcal{SHI}_+\), which extends \(\mathcal{SHI}\) by adding transitive closure of roles. The resulting logic \(\mathcal{SHI}_+\) allows transitive closure of roles to occur not only in concept inclusion axioms but also in role inclusion axioms. We show that \(\mathcal{SHI}_+\) is decidable by devising a terminating, sound and complete algorithm for deciding satisfiability of concepts in \(\mathcal{SHI}_+\) with respect to a set of concept and role inclusion axioms.
Chapter PDF
Similar content being viewed by others
References
Aho, A.V., Ullman, J.D.: Universality of data retrieval languages. In: Proceedings of the 6th of ACM on Principles of Programming Language (1979)
Baader, F.: Augmenting concept languages by transitive closure of roles: An alternative to terminological cycles. In: Proceedings of the Twelfth International Joint Conference on Artificial Intelligence (1991)
Baader, F., Sattler, U.: Tableau algorithms for description logics. In: Dyckhoff, R. (ed.) TABLEAUX 2000. LNCS(LNAI), vol. 1847, p. 118. Springer, Heidelberg (2000)
de Giacomo, G., Lenzerini, M.: Boosting the correspondence between description logics and propositional dynamic logics. In: Proceedings of the 12th National conference on Artificial Intelligence, pp. 205–212 (1994)
de Giacomo, G., Lenzerini, M.: What’s in an aggregate: Foundations for description logics with tuples and sets. In: Proceedings of the Fourteenth International Joint Conference On Intelligence Artificial 1995 (IJCAI 1995) (1995)
de Giacomo, G., Massacci, F.: Combining deduction and model checking into tableaux and algorithms for converse-PDL. Information and Computation (1) (1998)
Horrocks, I., Sattler, U.: A tableau decision procedure for \(\mathcal{SHOIQ}\). Journal Of Automated Reasoning 39(3), 249–276 (2007)
Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for expressive description logics. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol. 1705. Springer, Heidelberg (1999)
ISO. Standard ISO 8807: LOTOS, a formal description technique based on temporal ordering of observational behaviour (1988)
Patel-Schneider, P., Hayes, P., Horrocks, I.: OWL web ontology language semantics and abstract syntax. W3C Recommendation (2004)
Sattler, U.: A concept language extended with different kinds of transitive roles. In: Proceedings of the 20th German Annual Conf. on Artificial Intelligence (KI 2001), vol. 1137, pp. 199–204. Springer, Heidelberg (2001)
Tobies, S.: The complexity of reasoning with cardinality restrictions and nominals in expressive description logics. Journal of Artificial Intelligence Research 12, 199–217 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Le Duc, C. (2009). Decidability of \(\mathcal{SHI}\) with Transitive Closure of Roles. In: Aroyo, L., et al. The Semantic Web: Research and Applications. ESWC 2009. Lecture Notes in Computer Science, vol 5554. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02121-3_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-02121-3_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02120-6
Online ISBN: 978-3-642-02121-3
eBook Packages: Computer ScienceComputer Science (R0)