Abstract
Previously, we have investigated both standard and non-standard inferences in the presence of terminological cycles for the description logic \(\mathcal{EL}\), which allows for conjunctions, existential restrictions, and the top concept. The present paper is concerned with two problems left open by this previous work, namely the instance problem and the problem of computing most specific concepts w.r.t. descriptive semantics, which is the usual first-order semantics for description logics. We will show that—like subsumption—the instance problem is polynomial in this context. Similar to the case of the least common subsumer, the most specific concept w.r.t. descriptive semantics need not exist, but we are able to characterize the cases in which it exists and give a decidable sufficient condition for the existence of the most specific concept. Under this condition, it can be computed in polynomial time.
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References
Baader, F.: Using automata theory for characterizing the semantics of terminological cycles. Ann. of Mathematics and Artificial Intelligence 18, 175–219 (1996)
Baader, F.: Computing the least common subsumer in the description logic EL w.r.t. terminological cycles with descriptive semantics. In: Proceedings of the 11th International Conference on Conceptual Structures. LNCS (LNAI), Springer, Heidelberg (2003)
Baader, F.: The instance problem and the most specific concept in the description logic EL w.r.t. terminological cycles with descriptive semantics. LTCS-Report LTCS-03-01, Chair for Automata Theory, Institute for Theoretical Computer Science, Dresden University of Technology, Germany (2003), See http://lat.inf.tudresden.de/research/reports.html
Baader, F.: Least common subsumers and most specific concepts in a description logic with existential restrictions and terminological cycles. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence (2003) (to appear)
Baader, F.: Terminological cycles in a description logic with existential restrictions. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence (2003) (to appear)
Baader, F., Küsters, R.: Computing the least common subsumer and the most specific concept in the presence of cyclic ALN-concept descriptions. In: Herzog, O. (ed.) KI 1998. LNCS, vol. 1504, pp. 129–140. Springer, Heidelberg (1998)
Baader, F., Küsters, R., Molitor, R.: Computing least common subsumers in description logics with existential restrictions. In: Proc. of the 16th Int. Joint Conf. on Artificial Intelligence (IJCAI 1999), pp. 96–101 (1999)
Haarslev, V., Möller, R.: High performance reasoning with very large knowledge bases: A practical case study. In: Proc. of the 17th Int. Joint Conf. on Artificial Intelligence, IJCAI 2001 (2001)
Henzinger, M.R., Henzinger, T.A., Kopke, P.W.: Computing simulations on finite and infinite graphs. In: 36th Annual Symposium on Foundations of Computer Science, Milwaukee, Wisconsin, pp. 453–462. IEEE Computer Society Press, Los Alamitos (1995)
Horrocks, I.: Using an expressive description logic: FaCT or fiction? In: Proc. of the 6th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 1998), pp. 636–647 (1998)
Küsters, R.: Non-standard Inferences in Description Logics. In: Küsters, R. (ed.) Non-Standard Inferences in Description Logics. LNCS (LNAI), vol. 2100, p. 33. Springer, Heidelberg (2001)
Nebel, B.: Reasoning and Revision in Hybrid Representation Systems. LNCS, vol. 422. Springer, Heidelberg (1990)
Nebel, B.: Terminological cycles: Semantics and computational properties. In: Sowa, J.F. (ed.) Principles of Semantic Networks, pp. 331–361. Morgan Kaufmann, Los Altos (1991)
Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artificial Intelligence 48(1), 1–26 (1991)
Spackman, K.A.: Normal forms for description logic expressions of clinical concepts in SNOMED RT. J. of the American Medical Informatics Association, 627–631 (2001), Symposium Supplement
Spackman, K.A., Campbell, K.E., Cote, R.A.: SNOMED RT: A reference terminology for health care. J. of the American Medical Informatics Association, 640–644 (1997), Fall Symposium Supplement
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Baader, F. (2003). The Instance Problem and the Most Specific Concept in the Description Logic \(\mathcal{EL}\) w.r.t. Terminological Cycles with Descriptive Semantics. In: Günter, A., Kruse, R., Neumann, B. (eds) KI 2003: Advances in Artificial Intelligence. KI 2003. Lecture Notes in Computer Science(), vol 2821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39451-8_6
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DOI: https://doi.org/10.1007/978-3-540-39451-8_6
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