Skip to main content
Log in

FO(ID) as an extension of DL with rules

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

There are many interesting Knowledge Representation questions surrounding rule languages for the Semantic Web. The most basic one is of course: which kind of rules should be used and how do they integrate with existing Description Logics? Similar questions have already been addressed in the field of Logic Programming, where one particular answer has been provided by the language of FO(ID). FO(ID) is an extension of first-order logic with a rule-based representation for inductive definitions. By offering a general integration of first-order logic and Logic Programs, it also induces a particular way of extending Description Logics with rules. The goal of this paper is to investigate this integration and discover whether there are interesting extensions of DL with rules that can be arrived at by imposing appropriate restrictions on the highly expressive FO(ID).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook. Theory, Implementation and Applications. Cambridge University Press (2002)

  2. Bruijn, J.D., Pearce, D., Polleres, A., Valverde, A.: Quantified equilibrium logic and hybrid rules. In: International Conference on Web Reasoning and Rule Systems (RR) (2007)

  3. Büchi, J.R.: Weak second order arithmetic and finite automata. Z. Math. Log. Grundl. Math. 6, 66–92 (1960)

    Article  MATH  Google Scholar 

  4. Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Perspectives in Mathematical Logic. Springer (1997)

  5. Denecker, M., Vennekens, J.: Well-founded semantics and the algebraic theory of non-monotone inductive definitions. In: Baral, C., Brewka, G., Schlipf, J. (eds.) Ninth International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR. Lecture Notes in Artificial Intelligence, vol. LNAI 4483, pp. 84–96. Springer (2007)

  6. Drabent, W., Henriksson, J., Maluszynski, J.: HD-rules: a hybrid system interfacing prolog with DL-reasoners. In: 2nd International Workshop on Applications of Logic Programming to the Web, Semantic Web and Semantic Web Services (2007)

  7. Ebbinghaus, H.D., Flum, J.: Finite Model Theory. Perspectives in Mathematical Logic. Springer (1995)

  8. Eiter, T., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with description logics for the semantic web. In: Proceedings of the International Conference of Knowledge Representation and Reasoning (KR) (2004)

  9. Grädel, E., Walukiewicz, I.: Guarded fixed point logic. In: LICS (Logic in Computer Science), pp. 45–55 (1999)

  10. Grosof, B., Horrocks, I., Volz, R., Decker, S.: Description logic programs: combining logic programs with description logic. In: Proceedings of the 12th International Conference on World Wide Web (2003)

  11. Heymans, S., de Bruijn, J., Predoiu, L., Feier, C., Van Nieuwenborgh, D.: Guarded hybrid knowledge bases. Theory and Practice of Logic Programming (TPLP) 8(3), 411–429 (2008)

    MATH  Google Scholar 

  12. Heymans, S., Van Nieuwenborgh, D., Vermeir, D.: Open answer set programming with guarded programs. ACM Trans. Comput. Log. 9(4), 1–53 (2008)

    Article  MathSciNet  Google Scholar 

  13. Horrocks, I., Patel-Schneider, P.F., Boley, H., Tabet, S., Grosof, B., Dean, M.: SWRL: a semantics web rule language combining OWL and RuleML (2004). W3C submission. http://www.w3.org/Submission/2004/SUBM-SWRL-20040521/. Accessed January 2010

  14. Kreutzer, S.: Expressive equivalence of least and inflationary fixed-point logic. In: Proceedings of the 17th IEEE Symposium on Logic in Computer Science (LICS) (2002)

  15. Lenzerini, M.: Tbox and Abox reasoning in expressive description logics. In: Proc. of KR-96, pp. 316–327. Morgan Kaufmann (1996)

  16. Mitchell, D., Ternovska, E.: A framework for representing and solving NP search problems. In: AAAI’05, pp. 430–435. AAAI Press/MIT Press (2005)

  17. Moschovakis, Y.N.: Elementary Induction on Abstract Structures. North-Holland Publishing Company, Amsterdam- New York (1974)

    MATH  Google Scholar 

  18. Motik, B., Rosati, R.: Reconciling description logics and rules. J. ACM (JACM) 57(5), 165–228 (2010)

    Google Scholar 

  19. Motik, B., Sattler, U., Studer, R.: Query answering for OWL-DL with rules. In: Proc. of the 3rd International Semantic Web Conference (ISWC) (2004)

  20. Rosati, R.: On the decidability and complexity of integrating ontologies and rules. J. Web Semant. 3, 61–73 (2005)

    MathSciNet  Google Scholar 

  21. Rosati, R.: DL+log: tight integration of description logics and disjunctive datalog. In: Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning (KR 2006), pp. 68–78 (2006)

  22. Van Gelder, A.: The alternating fixpoint of logic programs with negation. J. Comput. Syst. Sci. 47(1), 185–221 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  23. Vennekens, J., Denecker, M.: FO(ID) as an extension of DL with rules. In: European Semantic Web Conference. Lecture Notes in Computer Science, vol. 5554, pp. 384–398 (2009)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Joost Vennekens.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vennekens, J., Denecker, M. & Bruynooghe, M. FO(ID) as an extension of DL with rules. Ann Math Artif Intell 58, 85–115 (2010). https://doi.org/10.1007/s10472-010-9207-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-010-9207-9

Keywords

Mathematics Subject Classifications (2010)

Navigation