The complexity of circumscription in description logic

Journal of Artificial Intelligence Research

Volumn 35, Issue , 2009, Pages 717-773

  Bonatti, Piero A ^a   Lutz, Carsten ^b   Wolter, Frank ^c  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b UNIVERSITY OF BREMEN   (Germany)

^c UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DATA DESCRIPTION; FORMAL LANGUAGES; FORMAL LOGIC;

DEFAULT LOGIC; DEFAULT RULE; DESCRIPTION LOGIC; FIRST ORDER LOGIC; NONMONOTONIC; UNDECIDABILITY;

COMPUTER CIRCUITS;

EID: 77953963653     PISSN: 10769757     EISSN: None     Source Type: Journal    
DOI: 10.1613/jair.2763     Document Type: Article

References (63)

1. Areces, C., Blackburn, P., & Marx, M. (1999). A road-map on complexity for hybrid logics. In Proceedings of the Eighth Annual Conference of the EACSL (CSL99), No. 1683 in Lecture Notes in Computer Science, pp. 307–321. Springer-Verlag.
2. Areces, C., Blackburn, P., & Marx, M. (2000). The computational complexity of hybrid temporal logics. Logic Journal of the IGPL, 8(5), 653–679.
3. Baader, F., Brandt, S., & Lutz, C. (2005a). Pushing the EL envelope. In Kaelbling, L. P., & Saffiotti, A. (Eds.), Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI05), pp. 364–369. Professional Book Center.
4. Baader, F., Milicic, M., Lutz, C., Sattler, U., & Wolter, F. (2005b). Integrating description logics and action formalisms for reasoning about web services. LTCS-report LTCS-05-02, Chair for Automata Theory, Institute for Theoretical Computer Science, Dresden University of Technology, Germany. See http://lat.inf.tudresden.de/research/reports.html.
5. Baader, F., & Hollunder, B. (1995a). Embedding defaults into terminological knowledge representation formalisms.. Journal of Automated Reasoning, 14(1), 149–180.
6. Baader, F., & Hollunder, B. (1995b). Priorities on defaults with prerequisites, and their application in treating specificity in terminological default logic.. Journal of Automated Reasoning, 15(1), 41–68.
7. Baader, F., McGuiness, D. L., Nardi, D., & Patel-Schneider, P. (2003). The Description Logic Handbook: Theory, implementation and applications. Cambridge University Press.
8. Baader, F., & Sattler, U. (2000). Tableau algorithms for description logics. In Dyckhoff, R. (Ed.), Proceedings of the International Conference on Automated Reasoning with Tableaux and Related Methods (Tableaux2000), Vol. 1847 of Lecture Notes in Artificial Intelligence, pp. 1–18. Springer-Verlag.
9. Berger, R. (1966). The undecidability of the dominoe problem. Memoirs of the American Mathematical Society, 66.
10. Blackburn, P., & van Benthem, J. (2007). Modal logic: a semantic perspective. In Handbook of Modal Logic. Elsevier.
11. Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge University Press.
12. Bonatti, P., Faella, M., & Sauro, L. (2009). Defeasible inclusions in low-complexity DLs: Preliminary notes. In Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI09). AAAI Press.
13. Bonatti, P., Lutz, C., & Wolter, F. (2006). Expressive non-monotonic description logics based on circumscription. In Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning (KR06), pp. 400–410. AAAI Press.
14. Bonatti, P. A., & Eiter, T. (1996). Querying disjunctive databases through nonmonotonic logics.. Theoretical Computer Science, 160(1&2), 321–363.
15. Bonatti, P. A., & Samarati, P. (2003). Logics for authorization and security. In Logics for Emerging Applications of Databases, pp. 277–323. Springer-Verlag.
16. Borgida, A. (1996). On the relative expressiveness of description logics and predicate logics. Artificial Intelligence, 82(1 - 2), 353–367.
17. Brewka, G. (1987). The logic of inheritance in frame systems. In Proceedings of the 10th International Joint Conference on Artificial Intelligence (IJCAI87), pp. 483–488. Morgan Kaufmann.
18. Brewka, G. (1994). Adding priorities and specificity to default logic.. In Proceedings of Logics in Artificial Intelligence (JELIA94), Vol. 838 of Lecture Notes in Computer Science, pp. 247–260. Springer-Verlag.
19. Cadoli, M., Donini, F., & Schaerf, M. (1990). Closed world reasoning in hybrid systems. In Proceedings of the 6th International Symposium on Methodologies for Intelligent Systems (ISMIS’90), pp. 474–481. Elsevier.
20. Calvanese, D., Giacomo, G. D., Lembo, D., Lenzerini, M., & Rosati, R. (2007). Tractable reasoning and efficient query answering in description logics: The DL-lite family. Journal of Automated Reasoning, 39(3), 385–429.
21. Cote, R., Rothwell, D., Palotay, J., Beckett, R., & Brochu, L. (1993). The systematized nomenclature of human and veterinary medicine. Tech. rep., SNOMED International, Northfield, IL: College of American Pathologists.
22. de Kleer, J., & Konolige, K. (1989). Eliminating the fixed predicates from circumscription. Artificial Intelligence, 39(3), 391–398.
23. Donini, F. M., Lenzerini, M., Nardi, D., Nutt, W., & Schaerf, A. (1998). An epistemic operator for description logics.. Artificial Intelligence, 100(1-2), 225–274.
24. Donini, F. M., Nardi, D., & Rosati, R. (1997). Autoepistemic description logics. In Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence (IJ-CAI97), pp. 136–141. Morgan Kaufmann.
25. Donini, F. M., Nardi, D., & Rosati, R. (2002). Description logics of minimal knowledge and negation as failure. ACM Transactions on Computational Logic, 3(2), 177–225.
26. Eiter, T., Gottlob, G., & Mannila, H. (1997). Disjunctive Datalog. ACM Transactions on Database Systems, 22(3), 364–418.
27. Eiter, T., Lukasiewicz, T., Schindlauer, R., & Tompits, H. (2004). Combining answer set programming with description logics for the semantic web. In Proceedings of the Ninth International Conference on the Principles of Knowledge Representation and Reasoning (KR 2004), pp. 141–151.
28. Giordano, L., Gliozzi, V., Olivetti, N., & Pozzato, G. L. (2008). Reasoning about typicality in preferential description logics. In Proceedings of Logics in Artificial Intelligence (JELIA08), Vol. 5293 of Lecture Notes in Computer Science, pp. 192–205. Springer-Verlag.
29. Goldblatt, R. (2003). Mathematical modal logic: A view of its evolution. Journal of Applied Logic, 1, 309–392.
30. Grädel, E., Otto, M., & Rosen, E. (1997). Two-Variable Logic with Counting is Decidable. In Proceedings of Twelfth IEEE Symposium on Logic in Computer Science (LICS’97), pp. 306–317. IEEE Computer Society Press.
31. Grimm, S., & Hitzler, P. (2008). Defeasible inference with circumscriptive OWL ontologies. In Proceedings of the Workshop on Advancing Reasoning on the Web: Scalability and Commonsense, No. 350 in CEUR-WS (http://ceur-ws.org/).
32. Horrocks, I., Sattler, U., & Tobies, S. (2000). Practical reasoning for very expressive description logics. Logic Journal of the IGPL, 8(3), 239–264.
33. Horty, J. F. (1994). Some direct theories of nonmonotonoc inheritance. In Handbook of Logic in Artificial Intelligence and Logic Programming-Nonmonotonic Reasoning and Uncertain Reasoning(Volume 3), pp. 111–187. Clarendon Press.
34. Janhunen, T. (1999). On the intertranslatability of non-monotonic logics. Annals of Mathematics in Artificial Intelligence, 27(1-4), 79–128.
35. Kagal, L., Finin, T., & Joshi, A. (2003). A policy language for a pervasive computing environment. In Fourth IEEE International Workshop on Policies for Distributed Systems and Networks (POLICY2003).
36. Knorr, M., Alferes, J. J., & Hitzler, P. (2007). A well-founded semantics for hybrid MKNF knowledge bases. In Proceedings of the 2007 International Workshop on Description Logics (DL2007), No. 250 in CEUR-WS (http://ceur-ws.org/).
37. Konev, B., Lutz, C., Walther, D., & Wolter, F. (2008). Semantic modularity and module extraction in description logics. In Proceedings of 18th European Conference on Artificial Intelligence (ECAI), pp. 55–59.
38. Lambrix, P., Shahmehri, N., & Wahlloef, N. (1998). A default extension to description logics for use in an intelligent search engine. In : Proceedings of the Thirty-First Annual Hawaii International Conference on System Sciences (HICSS98)-Volume 5, p. 28–35. IEEE Computer Society.
39. Lifschitz, V. (1985). Computing circumscription. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence (IJCAI85), pp. 121–127. Morgan Kaufmann.
40. Lifschitz, V. (1993). Circumscription. In The Handbook of Logic in AI and Logic Programming 3, pp. 298–352. Oxford University Press.
41. Lifschitz, V. (1995). Nested abnormality theories. Artificial Intelligence, 74(2), 351–365.
42. McCarthy, J. (1980). Circumscription: a form of nonmonotonic reasoning. Artificial Intelligence, 13, 27–39.
43. McCarthy, J. (1986). Applications of circumscription in formalizing common sense knowledge. Artificial Intelligence, 28, 89–116.
44. Minsky, M. (1975). A framework for representating knowledge. In Winston, P. H. (Ed.), The Psychology of Computer Vision, pp. 211–277. McGraw-Hill.
45. Moore, R. C. (1985). Semantical considerations on nonmonotonic logics. Artificial Intelligence, 25, 75–94.
46. Motik, B., & Rosati, R. (2007). A Faithful Integration of Description Logics with Logic Programming. In Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI2007), pp. 477–482. Morgan Kaufmann.
47. Pacholski, L., Szwast, W., & Tendera, L. (2000). Complexity results for first-order two-variable logic with counting. SIAM Journal on Computing, 29(4), 1083–1117.
48. Padgham, L., & Zhang, T. (1993). A terminological logic with defaults: A definition and an application. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence (IJCAI93), pp. 662–668. Morgan Kaufmann.
49. Pratt-Hartmann, I. (2005). Complexity of the two-variable fragment with counting quantifiers. Journal of Logic, Language, and Information, 14(3), 369–395.
50. Quillian, M. R. (1968). Semantic memory. In Semantic Information Processing, pp. 227–270. MIT Press.
51. Rector, A. (2004). Defaults, context, and knowledge: Alternatives for OWL-indexed knowledge bases. In Proceedings of the Pacific Symposium on Biocomputing (PSB04), pp. 226–237. World Scientific.
52. Rector, A., & Horrocks, I. (1997). Experience building a large, re-usable medical ontology using a description logic with transitivity and concept inclusions. In Proceedings of the Workshop on Ontological Engineering, AAAI Spring Symposium. AAAI Press.
53. Reiter, R. (1980). A logic for default reasoning. Artificial Intelligence, 13, 81–132.
54. Stevens, R., Aranguren, M. E., Wolstencroft, K., Sattler, U., Drummond, N., Horridge, M., & Rector, A. (2005). Using OWL to model biological knowledge. International Journal of Man-Machine Studies, 65(7), 583–594.
55. Stewart, I. A. (1991). Complete problems involving Boolean labelled structures and projection transactions. Journal of Logic and Computation, 1(6), 861–882.
56. Straccia, U. (1993). Default inheritance reasoning in hybrid KL-ONE-style logics.. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence (IJCAI93), pp. 676–681. Morgan Kaufmann.
57. Thomason, S. (1975a). The logical consequence relation of propositional tense logic. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 21, 29–40.
58. Thomason, S. (1975b). Reduction of second-order logic to modal logic. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 21, 107–114.
59. Tobies, S. (2000). The complexity of reasoning with cardinality restrictions and nominals in expressive description logics. Journal of Artificial Intelligence Research, 12, 199–217.
60. Tonti, G., Bradshaw, J. M., Jeffers, R., Montanari, R., Suri, N., & Uszok, A. (2003). Semantic web languages for policy representation and reasoning: A comparison of KAoS, Rei, and Ponder. In Proceedings of the Second International Semantic Web Conference (ISWC03), Vol. 2870 of Lecture Notes in Computer Science, pp. 419–437. Springer-Verlag.
61. Uszok, A., Bradshaw, J. M., Johnson, M., Jeffers, R., Tate, A., Dalton, J., & Aitken, S. (2004). KAoS policy management for semantic web services. IEEE Intelligent Systems, 19(4), 32–41.
62. Wolter, F., & Zakharyaschev, M. (2007). Modal decision problems. In Handbook of Modal Logic. Elsevier.
63. Y. Ding, V. H., & Wu, J. (2007). A new mapping from ALCI to ALC. In In Proceedings of the 2007 International Workshop on Description Logics (DL2007), No. 250 in CEUR-WS (http://ceur-ws.org/).