Abstract
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles, role hierarchies, and qualifying number restrictions. Early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSpace. Finally, we investigate the limits of decidability for this family of DLs.
Part of this work was carried out while being a guest at IRST, Trento.
This work was supported by the Esprit Project 22469 — DWQ and the DFG, Project No. GR 1324/3-1.
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References
F. Baader. Augmenting concept languages by transitive closure of roles: An alternative to terminological cycles. In Proc. of IJCAI-91, 1991.
F. Baader, M. Buchheit, and B. Hollunder. Cardinality restrictions on concepts. Artificial Intelligence, 88(1–2):195–213, 1996.
F. Baader, H.-J. Bürckert, B. Nebel, W. Nutt, and G. Smolka. On the expressivity of feature logics with negation, functional uncertainty, and sort equations. J. of Logic, Language and Information, 2:1–18, 1993.
R. Berger. The undecidability of the dominoe problem. Mem. Amer. Math. Soc., 66, 1966.
F. Baader and U. Sattler. Number restrictions on complex roles in description logics. In Proc. of KR-96, pages 328–339, 1996.
D. Calvanese, G. De Giacomo, and M. Lenzerini. On the decidability of query containment under constraints. In Proc. of the 17th ACM SIGAGT SIGMOD SIGART Sym. on Principles of Database Systems (PODS’98), pages 149–158, 1998.
D. Calvanese, G. De Giacomo, M. Lenzerini, D. Nardi, and R. Rosati. Source integration in data warehousing. In Proc. of DEXA-98. IEEE Computer Society Press, 1998.
D. Calvanese, G. De Giacomo, and M. Lenzerini. Reasoning in expressive description logics with fixpoints based on automata on infinite trees. In Proc. of the 16th Int. Joint. Conf. on Artificial Intelligence (IJCAI’99), 1999.
D. Calvanese, G. De Giacomo, and R. Rosati. A note on encoding inverse roles and functional restrictions in ALC knowledge bases. In Proc. of DL’ 98, 1998.
Diego Calvanese, Maurizio Lenzerini, and Daniele Nardi. A unified framework for class based representation formalisms. Proc. of KR-94, pages 109–120. M. Kaufmann, Los Altos.
G. De Giacomo and M. Lenzerini. What’s in an aggregate: Foundations for description logics with tuples and sets. In Proc. of IJCAI-95, 1995.
G. De Giacomo and M. Lenzerini. Tbox and Abox reasoning in expressive description logics. In Proc. of KR-96, pages 316–327. M. Kaufmann, Los Altos, 1996.
F. Donini, M. Lenzerini, D. Nardi, and W. Nutt. The complexity of concept languages. In Proc. of KR-91, Boston, MA, USA, 1991.
F. M. Donini, M. Lenzerini, D. Nardi, and A. Schaerf. Reasoning in description logics. In G. Brewka, editor, Foundation of Knowledge Representation. CSLI Publication, Cambridge University Press, 1996.
G. De Giacomo and F. Massacci. Combining deduction and model checking into tableaux and algorithms for Converse-PDL. Information and Computation, 1998. To appear.
B. Hollunder, W. Nutt, and M. Schmidt-Schauss. Subsumption algorithms for concept description languages. In ECAI-90, Pitman Publishing, London, 1990.
I. Horrocks. Using an expressive description logic: FaCT or fiction? In Proc. of KR-98, pages 636–647, 1998.
I. Horrocks and U. Sattler. A description logic with transitive and inverse roles and role hierarchies. J. of Logic and Computation, 1999. To appear.
I. Horrocks, U. Sattler, and S. Tobies. A PSpace-algorithm for deciding ALCI R+-satisfiability. Technical Report 98-08, LuFg Theoretical Computer Science, RWTH Aachen, 1998. See http://www-lti.informatik.rwth-aachen.de/Forschung/Papers.html.
I. Horrocks, U. Sattler, and S. Tobies. A description logic with transitive and converse roles, role hierarchies and qualifying number restrictions. LTCS-Report 99-08, LuFg Theoretical Computer Science, RWTH Aachen, Germany, 1999.
U. Sattler. A concept language extended with different kinds of transitive roles. In 20. Deutsche Jahrestagung für KI, LNAI 1137. Springer-Verlag, 1996.
K. Schild. A correspondence theory for terminological logics: Preliminary report. In Proc. of IJCAI-91, pages 466–471, Sydney, 1991.
M. Schmidt-Schauß and G. Smolka. Attributive concept descriptions with complements. Artificial Intelligence, 48(1):1–26, 1991.
S. Tobies. A PSpace algorithm for graded modal logic. In Proc. of CADE-16, LNCS. Springer, 1999.
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Horrocks, I., Sattler, U., Tobies, S. (1999). Practical Reasoning for Expressive Description Logics. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds) Logic for Programming and Automated Reasoning. LPAR 1999. Lecture Notes in Computer Science(), vol 1705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48242-3_11
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DOI: https://doi.org/10.1007/3-540-48242-3_11
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