A tableau algorithm for description logics with concrete domains and general TBoxes

Journal of Automated Reasoning

Volumn 38, Issue 1-3, 2007, Pages 227-259

  Lutz, Carsten ^a   Miličić, Maja ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Concrete domains; Decidability; Description logic; Tableau algorithm

Indexed keywords

ALGORITHMS; COMPUTABILITY AND DECIDABILITY;

CONCRETE DOMAINS; DESCRIPTION LOGIC; TABLEAU ALGORITHM;

FORMAL LOGIC;

EID: 33847663341     PISSN: 01687433     EISSN: 15730670     Source Type: Journal    
DOI: 10.1007/s10817-006-9049-7     Document Type: Conference Paper

References (34)

1. Allen, J.: Maintaining knowledge about temporal intervals. Commun. ACM 26(11), 832-843 (1983)
2. Baader, F., Hanschke, P.: A scheme for integrating concrete domains into concept languages. In: Proceedings of the 12th International Joint Conference on Artificial Intelligence, IJCAI-91, pp. 452-457. Sydney, Australia (1991)
3. Baader, F., Horrocks, I., Sattler, U.: Description logics as ontology languages for the semantic web. In: Hutter, D., Stephan, W. (eds.) Festschrift in Honor of Jörg Siekmann (2003a)
4. Baader, F., McGuiness, D.L., Nardi, D., Patel-Schneider, P.: The Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, Cambridge, UK (2003b)
5. Balbiani, P., Condotta, J.-F.: Computational complexity of propositional linear temporal logics based on qualitative spatial or temporal reasoning. In: Frontiers of Combining Systems (FroCoS), pp. 162-176 (2002)
6. Bennett, B.: Modal logics for qualitative spatial reasoning. J. Interest Group in Pure and Applied Logic 4(1), 1-20 (1997)
7. Calvanese, D.: Reasoning with inclusion axioms in description logics: algorithms and complexity. In: Proceedings of the Twelfth European Conference on Artificial Intelligence (ECAI-96), pp. 303-307 (1996)
8. Calvanese, D., Lenzerini, M., Nardi, D.: Description logics for conceptual data modeling. In: Chomicki, J., Saake, G. (eds.) Logics for Databases and Information Systems, Chap. 8, pp. 229-263. Kluwer, Norwell, MA (1998)
9. Egenhofer, M. J., Franzosa, R.: Point-set topological spatial relations. Int. J. Geogr. Inf. Syst. 5(2), 161-174 (1991)
10. Frank, A.: Qualitative spatial reasoning: cardinal directions as an example. Int. J. Geogr. Inf. Syst. 10(3), 269-290 (1996)
11. Gabbay, D.M., Kurucz, A., Wolter, F., Zakharyaschev, M.: Many-dimensional Modal Logics: Theory and Applications, No. 148 in Studies in Logic and the Foundations of Mathematics. Elsevier, Amsterdam, The Netherlands (2003)
12. Haarslev, V., Möller, R.,: RACER system description. In: Goré, R., Leitsch, A., Nipkow, T. (eds.) Proceedings of the First International Joint Conference on Automated Reasoning (IJCAR'01), pp. 701-705 (2001)
13. R+ extended with concrete domains: a practically motivated approach. In: Goré, R., Leitsch, A., Nipkow, T. (eds.) Proceedings of the First International Joint Conference on Automated Reasoning IJCAR'01, pp. 29-44 (2001)
14. Horrocks, I.: Using an expressive description logic: fact or fiction? In: Proceedings of the Sixth International Conference on the Principles of Knowledge Representation and Reasoning (KR98), pp. 636-647 (1998)
15. Horrocks, I., Patel-Schneider, P.F.: Optimising description logic subsumption. J. Log. Comput. 9(3), 267-293 (1999)
16. Horrocks, I., Sattler, U.: A description logic with transitive and inverse roles and role hierarchies. J. Log. Comput. 9(3) (1999)
17. Horrocks, I., Sattler, U.: Ontology reasoning in the SHΟQ(D) description logic. In: Nebel, B. (ed.) Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence (IJCAI'01), pp. 199-204 (2001)
18. Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for expressive description logics. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) Proceedings of the 6th International Conference on Logic for Programming and Automated Reasoning (LPAR'99), pp. 161-180 (1999)
19. Lutz, C.: Complexity of terminological reasoning revisited. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) Proceedings of the 6th International Conference on Logic for Programming and Automated Reasoning (LPAR'99), pp. 181-200 (1999)
20. Lutz, C.: Adding numbers to the SHIQ description logic - first results. In: Proceedings of the Eighth International Conference on Principles of Knowledge Representation and Reasoning (KR2002), pp. 191-202 (2002a)
21. Lutz, C.: PSPACE reasoning with the description logic AℒCℱ(D). Log. J. IGPL 10(5), 535-568 (2002b)
22. Lutz, C.: Reasoning about entity relationship diagrams with complex attribute dependencies. In: Horrocks, I., Tessaris, S. (eds.) Proceedings of the International Workshop in Description Logics 2002 (DL2002), pp. 185-194 (2002c)
23. Lutz, C.: Description logics with concrete domains - a survey. In: Advances in Modal Logics Volume 4, pp. 265-296 (2003)
24. Lutz, C.: Combining interval-based temporal reasoning with general TBoxes. Artif. Intell. 152(2), 235-274 (2004a)
25. Lutz, C.: NExpTime-complete description logics with concrete domains. ACM Trans. Comput. Log. 5(4), 669-705 (2004b)
26. Lutz, C., Milicic, M.: A tableau algorithm for description logics with concrete domains and GCIs. In: Proceedings of the 14th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods TABLEAUX 2005. Koblenz, Germany, pp. 201-216 (2005)
27. Lutz, C., Wolter, F.: Modal logics of topological relations. In: Proceedings of Advances in Modal Logics, 2004
28. Nebel, B., Bürckert, H.-J.: Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra. Journal of the ACM 42(1), 43-66 (1995)
29. Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Nebel, B., Rich, C., Swartout, W. (eds.) Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning (KR'92), pp. 165-176 (1992)
30. Renz, J., Nebel, B.: On the complexity of qualitative spatial reasoning: a maximal tractable fragment of the region connection calculus. Artif. Intell. 108(1-2), 69-123 (1999)
31. Russell, S.J., Norvig, P.: Artificial Intelligence: A Modern Approach. Prentice Hall, Upper Saddle River, NJ (1995)
32. Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artif. Intell. 48(1), 1-26 (1991)
33. Vilain, M., Kautz, H.: Constraint propagation algorithms for temporal reasoning. In: National Conference on Artificial Intelligence of the American Association for AI (AAAI 86), pp. 377-382 (1986)
34. Vilain, M., Kautz, H., van Beek, P.: Constraint propagation algorithms for temporal reasoning: a revised report. In: Readings in qualitative reasoning about physical systems. Morgan Kaufmann, San Francisco, CA, pp. 373-381 (1990)