Journal of Logic, Language and Information

, Volume 7, Issue 3, pp 341–367

Temporalizing Epistemic Default Logic


  • Wiebe van der Hoek
    • Department of Computer ScienceUtrecht University
  • John-Jules Meyer
    • Department of Computer ScienceUtrecht University
  • Jan Treur
    • Department of Mathematics and Computer ScienceFree University of Amsterdam

DOI: 10.1023/A:1008264012385

Cite this article as:
van der Hoek, W., Meyer, J. & Treur, J. Journal of Logic, Language and Information (1998) 7: 341. doi:10.1023/A:1008264012385


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.

Epistemic statesdefault reasoningmeta-level architecturestemporal models

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© Kluwer Academic Publishers 1998