\(\mathcal{ALC}^{u}_{\mathbb{P}}\): An Integration of Description Logic and General Rules

  • Jing Mei
  • Zuoquan Lin
  • Harold Boley
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4524)


A unifying logic is built on top of ontologies and rules for the revised Semantic Web Architecture. This paper proposes \(\mathcal{ALC}^{u}_{\mathbb{P}}\), which integrates a description logic (DL) that makes a unique names assumption with general rules that have the form of Datalog ℙrograms permitting default negation in the body. An \(\mathcal{ALC}^{u}_{\mathbb{P}}\) knowledge base (KB) consists of a TBox \(\mathcal{T}\) of subsumptions, an ABox \(\mathcal{A}\) of assertions, and a novel PBox ℙ of general rules that share predicates with DL concepts and DL roles. To model open answer set semantics, extended Herbrand structures are used for interpreting DL concepts and DL roles, while open answer sets hold for general rules. To retain decidability, a well-known weak safeness condition is employed. We develop DL tableaux-based algorithms for decision procedures of the KB satisfiability and the query entailment problems.


Description Logic Conjunctive Query Negation Normal Form Datalog Program Completion Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Antoniou, G., Damasio, C.V., Grosof, B., Horrocks, I., Kifer, M., Maluszynski, J., Patel-Schneider, P.F.: Combining Rules and Ontologies - A survey. Deliverables I3-D3, REWERSE (March 2005),
  2. 2.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.: The Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  3. 3.
    Berners-Lee, T.: AAAI-06 Invited Talk: Artificial Intelligence and the Semantic Web,
  4. 4.
    Calvanese, D., De Giacomo, G., Lenzerini, M.: Conjunctive Query Containment in Description Logics with n-ary Relations. In: Proceedings of International Workshop on Description Logics, vol. 410 of URA-CNRS (1997)Google Scholar
  5. 5.
    de Bruijn, J., Eiter, T., Polleres, A., Tompits, H.: On Representational Issues About Combinations of Classical Theories with Nonmonotonic Rules. In: Lang, J., Lin, F., Wang, J. (eds.) KSEM 2006. LNCS (LNAI), vol. 4092, pp. 1–22. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    de Bruijn, J., Pearce, D., Polleres, A., Valverde, A.: A Logic for Hybrid Rules. In: Proceedings of RuleML 2006 Workshop: Ontology and Rule Integration (November 2006)Google Scholar
  7. 7.
    Donini, F.M., Lenzerini, M., Nardi, D., Schaerf, A.: AL-log: Integrating Datalog and Description Logics. Journal of Intelligent Information Systems (JIIS) 10(3), 227–252 (1998)CrossRefGoogle Scholar
  8. 8.
    Eiter, T., Ianni, G., Schindlauer, R., Tompits, H.: Effective Integration of Declarative Rules with External Evaluations for Semantic-Web Reasoning. In: Sure, Y., Domingue, J. (eds.) ESWC 2006. LNCS, vol. 4011, pp. 273–287. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Eiter, T., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining Answer Set Programming with Description Logics for the Semantic Web. In: Proceedings of the 9th KR, pp. 141–151. AAAI Press, Stanford (2004)Google Scholar
  10. 10.
    Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programming. In: Proceedings of the 5th International Conference and Symposium on Logic Programming (ICLP/SLP), pp. 1070–1080. MIT Press, Cambridge (1988)Google Scholar
  11. 11.
    Grosof, B.N., Horrocks, I., Volz, R., Decker, S.: Description Logic Programs: Combining Logic Programs with Description Logic. In: Proceedings of the 12th International World Wide Web Conference, pp. 48–57. ACM Press, New York (2003)Google Scholar
  12. 12.
    Heymans, S.: Decidable Open Answer Set Programming. Phd thesis, Theoretical Computer Science Lab (TINF), Vrije Universiteit Brussel (February 2006)Google Scholar
  13. 13.
    Horrocks, I., Sattler, U., Tobies, S.: A Description Logic with Transitive and Converse Roles, Role Hierarchies and Qualifying Number Restrictions. LTCS-Report 99–08, RWTH Aachen, Germany (1999)Google Scholar
  14. 14.
    Horrocks, I., Sattler, U., Tobies, S.: Reasoning with Individuals for the Description Logic SHIQ. In: McAllester, D. (ed.) Automated Deduction - CADE-17. LNCS, vol. 1831, pp. 482–496. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Hustadt, U., Motik, B., Sattler, U.: Reducing SHIQ-Description Logic to Disjunctive Datalog Programs. In: Proceedings of the 9th KR, pp. 152–162. AAAI Press, Stanford (2004)Google Scholar
  16. 16.
    Levy, A.Y., Rousset, M.-C.: Combining Horn Rules and Description Logics in CARIN. Artifician Intelligence 104(1-2), 165–209 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Lloyd, J.W.: Foundations of Logic Programming (second, extended edition). Springer, Heidelberg (1987)zbMATHGoogle Scholar
  18. 18.
    Motik, B., Horrocks, I., Rosati, R., Sattler, U.: Can OWL and Logic Programming Live Together Happily Ever After? In: Cruz, I., Decker, S., Allemang, D., Preist, C., Schwabe, D., Mika, P., Uschold, M., Aroyo, L. (eds.) ISWC 2006. LNCS, vol. 4273, pp. 501–514. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Motik, B., Sattler, U., Studer, R.: Query Answering for OWL-DL with rules. Journal of Web Semantics 3(1), 41–60 (2005)Google Scholar
  20. 20.
    Ortiz, M., Calvanese, D., Eiter, T.: Data complexity of Answering Unions of Conjunctive Queries in shiq. Technical report, Faculty of Computer Science, Free University of Bozen-Bolzano (2006)Google Scholar
  21. 21.
    Rosati, R.: On the Decidability and Complexity of Integrating Ontologies and Rules. Journal of Web Semantics 3(1), 61–73 (2005)Google Scholar
  22. 22.
    Rosati, R.: DL+log: Tight Integration of Description Logics and Disjunctive Datalog. In: Proceedings of the 10th KR, pp. 68–78. AAAI Press, Stanford (2006)Google Scholar
  23. 23.
    W3C. OWL: Web Ontology Language Semantics and Abstract Syntax.
  24. 24.
    W3C. Rule Interchange Format Working Group.
  25. 25.
    W3C. SWRL: A Semantic Web Rule Language Combining OWL and RuleML.

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Jing Mei
    • 1
  • Zuoquan Lin
    • 1
  • Harold Boley
    • 2
  1. 1.Department of Information Science, Peking University, Beijing 100871China
  2. 2.Institute for Information Technology - e-Business, National Research Council of Canada, Fredericton, NB, E3B 9W4Canada

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