Skeptical rational extensions
In this paper we propose a version of default logic with the following two properties: (1) defaults with mutually inconsistent justifications are never used together in constructing a set of default consequences of a theory; (2) the reasoning formalized by our logic is related to the traditional skeptical mode of default reasoning. Our logic is based on the concept of a skeptical rational extension. We give characterization results for skeptical rational extensions and an algorithm to compute them. We present some complexity results. Our main goal is to characterize cases when the class of skeptical rational extensions is closed under intersection. In the case of normal default theories our logic coincides with the standard skeptical reasoning with extensions. In the case of seminormal default theories our formalism provides a description of the standard skeptical reasoning with rational extensions.
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- 1.P. Besnard. An introduction to default logic. Springer-Verlag, Berlin, 1989.Google Scholar
- 2.G. Brewka. Cumulative default logic: in defense of nonmonotonic inference rules. Artificial Intelligence, 50:183–205, 1991.Google Scholar
- 3.G. Brewka. Nonmonotonic reasoning: logical foundations of commonsense. Cambridge University Press, Cambridge, UK, 1991.Google Scholar
- 4.M. Gelfond, V. Lifschitz, H. Przymusinska, and M. Truszczyński. Disjunctive defaults. In Second international conference on principles of knowledge representation and reasoning, KR '91, Cambridge, MA, 1991.Google Scholar
- 5.G. Gottlob. Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2:397–425, 1992.Google Scholar
- 6.W. Marek and M. Truszczyński. Nonmonotonic logics; context-dependent reasoning. Berlin: Springer-Verlag, 1993.Google Scholar
- 7.A. Mikitiuk and M. Truszczyński. Rational default logic and disjunctive logic programming. In A. Nerode and L. Pereira, editors, Logic programming and non-monotonic reasoning, pages 283–299. MIT Press, 1993.Google Scholar
- 8.A. Mikitiuk and M. Truszczyński. Constrained and rational default logic. In preparation, 1995.Google Scholar
- 9.D. Poole. What the lottery paradox tells us about default reasoning. In Proceedings of the 2nd conference on principles of knowledge representation and reasoning, KR '89, pages 333–340, San Mateo, CA., 1989. Morgan Kaufmann.Google Scholar
- 10.R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.Google Scholar
- 11.T. Schaub. Considerations on Default Logics. PhD thesis, Technischen Hochschule Darmstadt, 1992.Google Scholar