Abstract
In this paper, we present a new query answering algorithm for Lukaszewicz' general open default theory. This algorithm, instead of computing all the extensions of the theory, computes only a set of defaults which proves the query. The advantages of our approach in comparison with other existent methods is that it is oriented by the query, it deals with open defaults and it can be easily adapted both for credulous and skeptical reasoning.
The strong point of our algorithm is that we do not perform the initial step of the instanciation of open defaults. The free variables of open defaults will be instanciated during our algorithm by the unification mechanism.
Firstly, we translate a default logic into a new variant of Poole's formalism. In this translation, we associate to every default of the theory, a default's name which is a simple literal parameterized by the free variables of the default. Thus, the defaults can be easily manipulated. In this context, answering a query requires the computation of a sequence of defaults which proves the formula and satisfies some properties (groundness and regularity). Concerning the provability of the query and the groundness property, we propose a modification of Inoue's production algorithm. Concerning the regularity property, we show how Poole's method can be adapted to check it.
Chapter PDF
Similar content being viewed by others
References
Baader F. & Hollunder B., Embedding defaults into terminological knowledge representation formalism, Proceedings of KR 92, p. 306–317, 1992.
Besnard Ph., Quiniou R., Quinton P., A theorem prover for a decidable subset of default logic, Proceedings of AAAI, 1983, p. 27–30.
Bibel W., Automated Theorem Proving, Vieweg, 1987.
Boï J.M., Innocente E., Rauzy A., Siegel P., Production Fields: a new approach to deduction problems and two algorithms for propositional calculus, Revue d'Intelligence Artificielle, vol. 6, nr. 3, 1992, p. 235–253.
Brewka G., Cumulative default logics: in defense of non-monotonic inference rules, Artificial Intelligence, vol. 50 (1–2), 1991, p. 183–205.
Chang C. & Lee R., Symbolic logic and mechanical theorem proving, Academic Press, 1973.
Ciorba V., Une méthode de preuve pour la logique des défauts de Lukaszewicz, Technical report LRI, 1996, to appear.
K. Inoue, Linear resolution for consequence finding, Artificial Intelligence, nr. 56, p. 301–353, 1992.
Junker U. et Konolige K., Computing the extensions of autoepistemic and default logics with a Truth Maintenance System, Proceedings of AAAI, 1990, p. 278–283.
Lévy F., Weak extensions for default theories, Proceedings of ECSQARU, 1993, Lecture Notes in Computer Science, nr. 747, p. 233–240.
Lukaszewicz W., Considerations on default logic — an alternative approach, Computational Intelligence, vol 4, 1988, p. 1–16.
Mengin J., Prioritized conflict resolution for default reasoning, Proceedings of ECAI, 1994, p.376–380.
Nicolas P. & Duval B., A theorem prover for Lukaszewicz' Open Default Theory, Proceedings of ECSQARU, 1995, Lecture Notes in Computer Science, nr. 946, p. 311–319.
Poole D., Variables in hypotheses, Proceedings of IJCAI, 1987, p. 905–908.
Poole D., A logical framework for default reasoning, Artificial Intelligence, vol. 36, 1988, p. 27–46.
Reiter R., A logic for default reasoning. Artificial Intelligence, vol 13, 1980, p. 81–132.
Risch V., Analytic tableaux for default logics, Journal of Applied Non-Classical Logics, vol. 6, nr. 1., 1996, p. 71–88.
Rychlik P., Some variations on default logic, Proceedings of AAAI, 1991, p. 373–378.
Schaub T., On constrained default theories, Proceedings of ECAI, 1992, p. 304–308.
Schaub T. A new methodology for query-answering in default logics via structure oriented theorem prover, Journal of Automated Reasoning, vol. 15, nr.1, 1995, p. 95–165.
Siegel P., Représentation et utilisation de la connaissance en calcul propositionnel, Thèse de doctorat d'état en informatique, Université d'Aix-Marseille II, juillet 1987.
Thielscher M, On prediction in Theorist, Artificial Intelligence, vol. 60, 1993, p. 283–292.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ciorba, V. (1996). A query answering algorithm for Lukaszewicz' general open default theory. In: Alferes, J.J., Pereira, L.M., Orlowska, E. (eds) Logics in Artificial Intelligence. JELIA 1996. Lecture Notes in Computer Science, vol 1126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61630-6_14
Download citation
DOI: https://doi.org/10.1007/3-540-61630-6_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61630-6
Online ISBN: 978-3-540-70643-4
eBook Packages: Springer Book Archive