Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Priorities on defaults with prerequisites, and their application in treating specificity in terminological default logic


In a recent paper we have proposed terminological default logic as a formalism that combines means both for structured representation of classes and objects and for default inheritance of properties. The major drawback that terminological default logic inherits from general default logic is that it does not take precedence of more specific defaults over more general ones into account. This behavior has already been criticized in the general context of default logic, but it is all the more problematic in the terminological case where the emphasis lies on the hierarchical organization of concepts.

The present paper addresses the problem of modifying terminological default logic such that more specific defaults are preferred. We assume that the specificity ordering is induced by the hierarchical organization of concepts, which means that default information is not taken into account when computing priorities. It turns out that the existing approaches for expressing priorities between defaults do not seem to be appropriate for defaults with prerequisites. Therefore we shall consider an alternative approach for dealing with prioritization in the framework of Reiter's default logic. The formalism is presented in the general setting of default logic where priorities are given by an arbitrary partial ordering on the defaults. We shall exhibit some interesting properties of the new formalism, compare it with existing approaches, and describe an algorithm for computing extensions. In the terminological case, we thus obtain an automated default reasoning procedure that takes specificity into account.

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


  1. 1.

    Baader, F. and Hollunder, B.: Embedding defaults into terminological knowledge representation formalisms, inProc. 3rd Int. Conf. on Knowledge Representation and Reasoning, Cambridge, MA, 1992.

  2. 2.

    Baader, F. and Hollunder, B.: How to prefer more specific defaults in terminological default logic, inProc. 13th Int. Joint Conf. on Artificial Intelligence, Chambery, France, 1993.

  3. 3.

    Besnard, P.:An Introduction to Default Logic, Symbolic Computation Series, Springer, 1989.

  4. 4.

    Brachman, R. J., McGuinness, D. L., Patel-Schneider, P. F., Resnick, L. A., and Borgida, A.: Living with CLASSIC: When and how to use a KL-ONE-like languages, in J. Sowa (ed.),Principles of Semantic Networks, Morgan Kaufmann, San Mateo, CA, 1991, pp. 401–456.

  5. 5.

    Brass, S.: Deduction with Supernormal Defaults, in G. Brewka, K. P. Jantke and P. H. Schmitt (eds),Nonmonotonic and Induction Logics, 2nd Int. Workshop, Springer LNCS 659, 1992.

  6. 6.

    Brewka, G.: Adding priorities and specificity to default logic, in C. MacNish, D. Pearce and L. M. Pereira (eds),Logics in Artificial Intelligence, European Workshop, JELIA'94, York, UK, Springer LNAI 838, 1994, pp. 247–260.

  7. 7.

    Brewka, G.: Preferred subtheories: An extended logical framework for default reasoning, inProc. 11th Int. Joint Conf. on Artificial Intelligence, Detroit, MI, 1989.

  8. 8.

    Brewka, G.:Nonmonotonic Reasoning: Logical Foundations of Commonsense, Cambridge University Press, Cambridge, 1991.

  9. 9.

    Delgrande, J. P. and Jackson, W. K.: Default logic revisited, inProc. 2nd Int. Conf. on Knowledge Representation and Reasoning, Cambridge, MA, 1991.

  10. 10.

    Junker, U. and Brewka, G.: Handling partially ordered defaults in TMS, inProc. 1st European Conf. on Symbolic and Quantitative Approaches for Uncertainty, Marseille, France, 1991.

  11. 11.

    Kobsa, A.: The SB-ONE knowledge representation workbench, inPreprint of the Workshop on Formal Aspects of Semantic Networks, Two Harbours, CA, 1989.

  12. 12.

    Lifschitz, V.: Computing circumscription, inProc. 9th Int. Joint Conf. on Artificial Intelligence, Los Angeles, CA, 1985.

  13. 13.

    Mays, E. and Dionne, B: Making KR systems useful, inTerminological Logic Users Workshop, Proc., KIT-Report 95, TU, Berlin, 1991, pp. 11–12.

  14. 14.

    MacGregor, R.: Statement of interest, in K. von Luck, B. Nebel and C. Peltason (eds),Statement of Interest 2nd Int. Workshop on Terminological Logics, Document D-91-13, DFKI Kaiserslautern, 1991.

  15. 15.

    Ginsberg, M. L. (ed.),Readings in Nonmonotonic Reasoning, Morgan Kaufmann, Los Altos, CA, 1987.

  16. 16.

    μBACK, System presentation, inTerminological Logic Users Workshop, Proc., KIT-Report 95, TU, Berlin, 1991, p. 186.

  17. 17.

    Padgham, L. and Nebel, B.: Combining classification and nonmonotonic inheritance reasoning: A first step, in Z. W. Ras and J. Komorowski (eds),Methodologies for Intelligent Systems (ISMIS'93), North-Holland, Amsterdam, 1993.

  18. 18.

    Peltason, C., v. Luck, K. and Kindermann, C. (Org.):Terminological Logic Users Workshop, Proc., KIT Report 95, TU, Berlin, 1991.

  19. 19.

    Reiter, R.: A logic for default reasoning,Artificial Intelligence 13(1–2) (1980), 81–132.

  20. 20.

    Reiter, R. and Criscuolo, G.: On interacting defaults, inProc. 7th Int. Joint Conf. on Artificial Intelligence, 1981.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Baader, F., Hollunder, B. Priorities on defaults with prerequisites, and their application in treating specificity in terminological default logic. J Autom Reasoning 15, 41–68 (1995).

Download citation

Key words

  • terminological default logic
  • default theories with priorities
  • knowledge representation

AMS Subject Classification

  • 68T30