Abstract
Statistical Default Logic (SDL) is an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, e.g., hypothesis testing and the estimation of a population‘s mean, variance and proportions. This paper presents an embedding of an important subset of SDL theories, called literal statistical default theories, into stable model semantics. The embedding is designed to compute the signature set of literals that uniquely distinguishes each extension on a statistical default theory at a pre-assigned error-bound probability.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bacchus, F., Grove, A., Halpern, J., Koller, D.: Statistical Foundations for Default Reasoning. In: Proceedings of The International Joint Conference on Artificial Intelligence 1993 (IJCAI 1993), pp. 563–569 (1993)
Cramér, H.: Mathematical Methods of Statistics. Princeton University Press, Princeton (1946)
Dekhtyar, A., Subrahmanian, V.S.: Hybrid Probabilistic Programs. Journal of Logic Programming 43(3), 187–250 (2000)
Eiter, T., Leone, N., Mateis, C., Pfeifer, G., Scarcello, F.: The KR system: Progress Report, Comparisons and Benchmarks. In: Cohen, A., Schubert, L., Shaprio, S. (eds.) KR 1998: Principles of Knowledge Representation and Reasoning, Morgan Kaufmann, San Francisco (1998)
Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programming. In: Kowalski, R., Bowen, K. (eds.) Proceedings of the 5th International Conference on Logic Programming, pp. 1070–1080. MIT Press, Cambridge (1988)
Gelfond, M., Lifschitz, V.: Logic Programs with Classical Negation. In: Warren, D., Szeredi, P. (eds.) Proceedings of the 7th International Conference on Logic Programming, pp. 579–597. MIT Press, Cambridge (1990)
Kyburg Jr., H.E., Teng, C.M.: Statistical Inference as Default Logic. International Journal of Pattern Recognition and Artificial Intelligence 13(2), 267–283 (1999)
Larsen, R.J., Marx, M.L.: An Introduction to Mathematical Statistics. Prentice Hall, Upper Saddle River (2001)
Lukasiewicz, T.: Fixpoint Characterizations for Many-Valued Disjunctive Logic Programs with Probabilistic Semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 336–350. Springer, Heidelberg (2001)
Lukasiewicz, T.: Probabilistic Default Reasoning with Conditional Constraints. Annals of Mathematics and Artificial Intelligence 34(1-3), 35–88 (2002)
Marek, Truszczyński: Nonmonotonic Logic. Springer, Berlin (1993)
Moore: Statistics. W. H. Freeman Press, San Francisco (1979)
Ng, R., Subrahmanian, V.S.: Stable semantics for probabilistic deductive databases. Information and Computation 110(1), 42–83 (1994)
Niemelä, I., Simons, P.: Efficient Implementation of the Well-founded and Stable Model Semantics. In: Maher, M. (ed.) Proceedings of the Joint International Conference and Symposium on Logic Programming, MIT Press, Cambridge (1996)
Reiter, R.: A Logic for Default Reasoning. Artificial Intelligence 13, 81–132 (1980)
Wheeler, G.R.: A Resource Bounded Default Logic. In: Delgrande, J., Schuaub, T. (eds.) Proceedings of the 10th International Workshop on Non-monotonic Reasoning (NMR 2004), Whistler, British Columbia, pp. 416–422 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wheeler, G.R., Damásio, C. (2004). An Implementation of Statistical Default Logic. In: Alferes, J.J., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2004. Lecture Notes in Computer Science(), vol 3229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30227-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-30227-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23242-1
Online ISBN: 978-3-540-30227-8
eBook Packages: Springer Book Archive