Abstract
An approach to skeptical query-answering in Constrained Default Logic based on the Connection Method is presented. We adapt a recently proposed general method to skeptical reasoning in Default Logics—a method which does neither strictly require the inspection of all extensions nor the computation of entire extensions to decide whether a formula is skeptically entailed. We combine this method with a credulous reasoner which uses the Connection Method as the underlying calculus for classical logic. Furthermore, we develop the notion of a skeptical default proof and show how such a proof can be extracted whenever our calculus proves skeptical entailment of a particular query.
On leave from FG Intellektik, TH Darmstadt
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
W. Bibel. Automated Theorem Proving. Vieweg, Braunschweig, second edition, 1987.
G. Brewka. Cumulative default logic: In defense of nonmonotonic inference rules. Artificial Intelligence, 50(2):183–205, 1991.
J. Delgrande, T. Schaub, and W. Jackson. Alternative approaches to default logic. Artificial Intelligence, 70(1–2):167–237, 1994.
D. Etherington. Reasoning with Incomplete Information. Research Notes in Artificial Intelligence. Pitman, London, 1988.
M. Ginsberg. A circumscriprive theorem prover. In M. Reinfrank et al., editors, Proceedings of the Second International Workshop on Non-Monotonic Reasoning, pages 100–114. Springer, 1989.
G. Gottlob. Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2(3):397–425, June 1992.
U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logic with a TMS. In Proceedings of the National Conference on Artificial Intelligence, 1990.
W. Marek and M. Truszczyński. Computing intersection of autoepistemic expansions. In W. Marek et al., editors, Proceedings of the First International Workshop on Logic Programming and Nonmonotonic Reasoning, pages 37–50. MIT Press, 1991.
A. Mikitiuk and M. Truszczyński. Rational versus constrained default logic. In C. Mellish, editor, Proceedings of the International Joint Conference on Artificial Intelligence, pages 1509–1515. Morgan Kaufmann, 1995.
R. Moore. Semantical considerations on nonmonotonic logics. Artificial Intelligence, 25:75–94, 1985.
I. Niemelä. A decision method for nonmonotonic reasoning based on autoepistemic reasoning. In J. Doyle et al., editors, Proceedings of the 4th International Conference on the Principles of Knowledge Representation and Reasoning, pages 473–484. Morgan Kaufmann, 1994.
D. Poole. A logical framework for default reasoning. Artificial Intelligence, 36:27–47, 1988.
D. Poole. Compiling a default reasoning system into prolog. New Generation Computing, 9(1):3–38, 1991.
R. Reiter. A logic for default reasoning. Artificial Intelligence, 13(1–2):81–132, 1980.
A. Rothschild. Algorithmische Untersuchungen zu Defaultlogiken. Diplomarbeit, FG Intellektik, FB Informatik, TH Darmstadt, Germany, 1993.
T. Schaub. On commitment and cumulativity in default logics. In R. Kruse and P. Siegel, editors, Proceedings of European Conference on Symbolic and Quantitative Approaches to Uncertainty, pages 304–309. Springer, 1991.
T. Schaub. Variations of constrained default logic. In M. Clarke, R. Kruse, and S. Moral, editors, Proceedings of European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, pages 312–317. Springer, 1993.
T. Schaub. A new methodology for query-answering in default logics via structure-oriented theorem proving. Journal of Automated Reasoning, 15(1):95–165, 1995.
C. Schwind. A tableaux-based theorem prover for a decidable subset of default logic. In M. Stickel, editor, Proceedings of the Conference on Automated Deduction. Springer, 1990.
M. Thielscher. On prediction in Theorist. Artificial Intelligence, 60(2):283–292, 1993.
M. Thielscher and T. Schaub. Default reasoning by deductive planning. Journal of Automated Reasoning, 15(1):1–40, 1995.
A. Zhang and W. Marek. On the classification and existence of structures in default logic. Fundamenta Informaticae, 8(4):485–499, 1990.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schaub, T., Thielscher, M. (1996). Skeptical query-answering in Constrained Default Logic. In: Gabbay, D.M., Ohlbach, H.J. (eds) Practical Reasoning. FAPR 1996. Lecture Notes in Computer Science, vol 1085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61313-7_101
Download citation
DOI: https://doi.org/10.1007/3-540-61313-7_101
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61313-8
Online ISBN: 978-3-540-68454-1
eBook Packages: Springer Book Archive