Journal of Logic, Language and Information

, Volume 7, Issue 3, pp 369–388 | Cite as

An Interpretation of Default Logic in Minimal Temporal Epistemic Logic

  • Joeri Engelfriet
  • Jan Treur


When reasoning about complex domains, where information available is usually only partial, nonmonotonic reasoning can be an important tool. One of the formalisms introduced in this area is Reiter's Default Logic (1980). A characteristic of this formalism is that the applicability of default (inference) rules can only be verified in the future of the reasoning process. We describe an interpretation of default logic in temporal epistemic logic which makes this characteristic explicit. It is shown that this interpretation yields a semantics for default logic based on temporal epistemic models. A comparison between the various semantics for default logic will show the differences and similarities of these approaches and ours.

Nonmonotonic reasoning default logic temporal logic epistemic logic preferential entailment 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Amati, G., Aiello, L.C., Gabbay, D., and Pirri, F., 1996, “A structural property on modal frames characterizing default logic,” Journal of the IGPL 4, 7–22.Google Scholar
  2. Amati, G., Aiello, L.C., and Pirri, F., 1997, “Definability and commonsense reasoning,” Artificial Intelligence 93, 169–199.Google Scholar
  3. Benthem, J.F.A.K. van, 1983, The Logic of Time: A Model Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse, Dordrecht: Reidel.Google Scholar
  4. Besnard, P., 1989, An Introduction to Default Logic, Berlin: Springer-Verlag.Google Scholar
  5. Besnard, P. and Mercer, R.E., 1992, “Non-monotonic logics: A valuations-based approach,” pp. 77–84 in Artificial Intelligence V: Methodology, Systems, Applications, B. du Boulay and V. Sgurev, eds., Amsterdam: Elsevier Science Publishers.Google Scholar
  6. Besnard, P. and Schaub, T., 1994, “Possible worlds semantics for default logics,” Fundamenta Informaticae 21, 39–66.Google Scholar
  7. Etherington, D.W., 1987, “A semantics for default logic,” pp. 495–498 in Proceedings IJCAI87, J. McDermott, ed., San Mateo, CA: Morgan Kaufmann; see alsoGoogle Scholar
  8. Etherington, D.W., 1988, Reasoning with Incomplete Information, San Mateo, CA: Morgan Kaufmann.Google Scholar
  9. Engelfriet, J., 1996, “Minimal temporal epistemic logic,” Notre Dame Journal of Formal Logic, special issue on Combining Logics 37, 233–259.Google Scholar
  10. Engelfriet, J. and Treur, J., 1993, “A temporal model theory for default logic,” pp. 91–96 in Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Proceedings ECSQARU'93, M. Clarke, R. Kruse, and S. Moral, eds., Lecture Notes in Computer Science, Vol. 747, Berlin: Springer-Verlag.Google Scholar
  11. Engelfriet, J. and Treur, J., 1994, “Temporal theories of reasoning,” pp. 279–299 in Logics in Artificial Intelligence: Proceedings of the 4th European Workshop on Logics in Artificial Intelligence, JELIA '94, C. MacNish, D. Pearce, and L.M. Pereira, eds., Berlin: Springer-Verlag. Also in Journal of Applied Nonclassical Logics 5 (1995), 239–261.Google Scholar
  12. Engelfriet, J. and Treur, J., 1996, “Semantics for default logic based on specific branching time models,” pp. 60–64 in Proceedings of the 12th European Conference on Artificial Intelligence, W. Wahlster, ed., Chichester: John Wiley & Sons.Google Scholar
  13. Engelfriet, J., Herre, H., and Treur, J., 1995, “Nonmonotonic belief state frames and reasoning frames (extended abstract),” pp. 189–196 in Symbolic and Quantitative Approaches to Reasoning and Uncertainty: Proceedings ECSQARU'95, C. Froidevaux and J. Kohlas, eds., Lecture Notes in Artificial Intelligence, Vol. 946, Berlin: Springer-Verlag.Google Scholar
  14. Finger, M. and Gabbay, D., 1992, “Adding a temporal dimension to a logic system,” Journal of Logic, Language and Information 1, 203–233.Google Scholar
  15. Gabbay, D.M., 1982, “Intuitionistic basis for non-monotonic logic,” pp. 260–273 in 6th Conference on Automated Deduction, G. Goos and J. Hartmanis, eds., Lecture Notes in Computer Science, Vol. 138, Berlin: Springer-Verlag.Google Scholar
  16. Halpern, J.Y. and Moses, Y., 1984, “Towards a theory of knowledge and ignorance,” pp. 125–143 in Proceedings of the Workshop on Non-monotonic Reasoning, AAAI'84, Menlo Park: AAAI Press.Google Scholar
  17. Hoek, W. van der, Meyer, J.—J. Ch., and Treur J., 1995, “Temporalizing epistemic default logic,” pp. 173–190 in Information Systems — Correctness and Reusability, Selected papers from the ISCORE-95 Workshop, R.B. Feenstra and R. Wieringa, eds., London: World Scientific Publishers. Extended version in Journal of Logic, Language and Information, 1998, this issue.Google Scholar
  18. Kripke, S., 1965, “Semantical analysis of intuitionistic logic I,” pp. 92–130 in Formal Systems and Recursive Function Theory, J.N. Crossley and M. Dummett, eds., Amsterdam: North-Holland.Google Scholar
  19. Levesque, H.J., 1984, “A logic of implicit and explicit belief,” pp. 198–202 in Proceedings National Conference on Artificial Intelligence, AAAI84, San Mateo, CA: Morgan Kaufmann.Google Scholar
  20. Lin, F. and Reiter, R., 1996, “Rules as actions: A situation calculus semantics for logic programs,” Journal of Logic Programming, special issue on Reasoning about Action and Change (to appear).Google Scholar
  21. Lin, F. and Shoham, Y., 1992, “A logic of knowledge and justified assumptions,” Artificial Intelligence 57, 271–289.Google Scholar
  22. Lukaszewicz, W., 1990, Non-Monotonic Reasoning: Formalization of Commonsense Reasoning, New York: Ellis Horwood.Google Scholar
  23. Marek, V.W. and Truszczynski, M., 1989, “Relating autoepistemic and default logics,” pp. 276–288 in Proceedings of the First International Conference on the Principles of Knowledge Representation and Reasoning, R.J. Brachman, H.J. Levesque, and R. Reiter, eds., San Mateo, CA: Morgan Kaufmann.Google Scholar
  24. Marek, V.W. and Truszczynski, M., 1992, “More on modal aspects of default logic,” Fundamenta Informaticae 17, 99–116.Google Scholar
  25. Marek, V.W. and Truszczynski, M., 1993, Nonmonotonic Logics; Context-Dependent Reasoning, Berlin: Springer-Verlag.Google Scholar
  26. Marek, V.W., Schwarz, G.F., and Truszczynski, M., 1993, “Modal nonmonotonic logics: Ranges, characterization, computation,” Journal of the ACM 40, 963–990.Google Scholar
  27. McDermott, D. and Doyle, J., 1980, “Nonmonotonic logic I,” Artificial Intelligence 13, 41–72.Google Scholar
  28. Reiter, R., 1980, “A logic for default reasoning,” Artificial Intelligence 13, 81–132.Google Scholar
  29. Schaub, T., 1991, “Assertional default theories: A semantical view,” pp. 496–506 in Proceedings of the Second International Conference on the Principles of Knowledge Representation and Reasoning, J.A. Allen, R. Fikes, and E. Sandewall, eds., San Mateo, CA: Morgan Kaufmann.Google Scholar
  30. Schwarz, G., 1995, “In search of a “true” logic of knowledge: The nonmonotonic perspective,” Artificial Intelligence 79, 39–63.Google Scholar
  31. Schwarz, G. and Truszczynski, M., 1994, “Minimal knowledge problem: A new approach,” Artificial Intelligence 67, 113–141.Google Scholar
  32. Treur, J., 1994, “Temporal semantics of meta-level architectures for dynamic control of reasoning,” pp. 353–376 in Logic Program Synthesis and Transformation — Meta-Programming in Logic: Proceedings LOPSTR'94 and META'94, L. Fribourg and F. Turini, eds., Lecture Notes in Computer Science, Vol. 883, Berlin: Springer-Verlag.Google Scholar
  33. Voorbraak, F., 1993, “Preference-based semantics for nonmonotonic logics,” pp. 584–589 in Proceedings IJCAI93, R. Bajcsy, ed., San Mateo, CA: Morgan Kaufmann.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Joeri Engelfriet
    • 1
  • Jan Treur
    • 1
  1. 1.Department of Mathematics and Computer Science, Artificial Intelligence GroupVrije Universiteit AmsterdamAmsterdamThe Netherlands

Personalised recommendations