Abstract
We present an epistemic default logic, based on the metaphore of a meta-level architecture. Upward reflection is formalized by a nonmonotonic entailment relation, based on the objective facts that are either known or unknown at the object level. Then, the meta (monotonic) reasoning process generates a number of “default-beliefs” of object-level formulas. We extend this framework by proposing a mechanism to reflect these defaults down. Such a reflection is seen as essentially having a temporal flavour: defaults derived at the meta-level are projected as facts in a “next” object level state. In this way, we obtain temporal models for default reasoning in meta-level formalisms which can be conceived as labeled branching trees. Thus, descending the tree corresponds to shifts in time that model downward reflection, whereas the branching of the tree corresponds to ways of combining possible defaults. All together, this yields an operational or procedural semantics of reasoning by default, which admits one to reason about it by means of branching-time temporal logic. Finally, we define sceptical and credulous entailment relations based on these temporal models and we characterize Reiter extensions in our semantics.
Similar content being viewed by others
References
Doherty, P., 1991, “NM3 — A three-valued cumulative non-monotonic formalism,” pp. 196–211 in Logics in AI, J. van Eijck, ed., LNCS 478, Berlin: Springer-Verlag.
Engelfriet, J. and Treur, J., 1993, “A temporal model theory for default logic,” pp. 91–96 in Proc. 2nd European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, ECSQARU '93, M. Clarke, R. Kruse, and S. Moral, eds., Berlin: Springer-Verlag.
Finger, M. and Gabbay, D., 1992, “Adding a temporal dimension to a logic system,” Journal of Logic, Language and Information 1, 203–233.
Giunchiglia, E., Traverso, P., and Giunchiglia, F., 1993, “Multicontext systems as a specification framework for complex reasoning systems,” pp. 45–72 in Formal Specification of Complex Reasoning Systems, J. Treur and Th. Wetter, eds., Chichester: Ellis Horwood.
Hughes, G.E. and Cresswell, M.J., 1968, An Introduction to Modal Logic, London: Methuen & Co. Ltd.
Halpern, J.Y. and Moses, Y.O., 1984, “Towards a theory of knowledge and ignorance,” pp. 125–143 in Proc. Workshop on Non-Monotonic Reasoning, AAAI.
Meyer, J.—J. Ch. and van der Hoek, W., 1991, “Non-monotonic reasoning by monotonic means,” pp. 399–411 in Logics in AI (Proc. JELIA '90), J. van Eijck, ed., LNCS 478, Berlin: Springer-Verlag.
Meyer, J.—J. Ch. and van der Hoek, W., 1995, “A default logic based on epistemic states,” Fundamentae Informatica 23(1), 33–65.
Meyer, J.—J. Ch. and van der Hoek, W., 1995, Epistemic Logic for AI and Computer Science, Cambridge Tracts in Theoretical Computer Science, Vol. 41, Cambridge: Cambridge University Press.
Moore, R.C., 1985, “Semantical considerations on nonmonotonic logic,” Artificial Intelligence 25, 75–94.
Reiter, R., 1980, “A logic for default reasoning,” Artificial Intelligence 13, 81–132.
Reiter, R., 1987, “Nonmonotonic reasoning,” Annual Reviews of Computer Science 2, 147–187.
Shoham, Y., 1987, “A semantical approach to nonmonotonic logics,” pp. 388–392 in Proceedings 10th IJCAI, J. McDermott (ed.), San Mateo, CA: Morgan Kaufmann.
Shoham, Y., 1988, Reasoning about Change, Cambridge, Massachusetts: MIT Press.
Tan, Y.—H. and Treur, J., 1991, “A bimodular approach to nonmonotonic reasoning,” pp. 461–475 in Proc. WOCFAI'91, M. DeGlas and D. Gabbay, eds., Paris: Angkor.
Tan, Y.—H. and Treur, J., 1992, “Constructive default logic and the control of defeasible reasoning,” pp. 299–303 in Proc. of the European Conference on Artificial Intelligence, ECAI'92, B. Neumann, ed., Chichester: Wiley & Sons.
Treur, J., 1994, “Temporal semantics of metalevel architectures for dynamic control of reasoning,” pp. 353–377 in Proc. META'94, Pisa, LNCS 883, Berlin: Springer-Verlag.
van der Hoek, W., Meyer J.—J. Ch., and Treur, J., 1994, “Formal semantics of temporal epistemic reflection,” pp. 332–352 in Proc. META'94, Pisa, LNCS 883, Berlin: Springer-Verlag.
Weyhrauch, R.W., 1980, “Prolegomena to a theory of mechanized formal reasoning,” Artificial Intelligence J. 13, 133–170.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van der Hoek, W., Meyer, JJ. & Treur, J. Temporalizing Epistemic Default Logic. Journal of Logic, Language and Information 7, 341–367 (1998). https://doi.org/10.1023/A:1008264012385
Issue Date:
DOI: https://doi.org/10.1023/A:1008264012385