Abstract
Current literature offers a number of different approaches to what could generally be called “probabilistic logic programming”. These are usually based on Horn clauses. Here, we introduce a new formalism, Logic Programs with Annotated Disjunctions, based on disjunctive logic programs. In this formalism, each of the disjuncts in the head of a clause is annotated with a probability. Viewing such a set of probabilistic disjunctive clauses as a probabilistic disjunction of normal logic programs allows us to derive a possible world semantics, more precisely, a probability distribution on the set of all Herbrand interpretations. We demonstrate the strength of this formalism by some examples and compare it to related work.
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
Apt, K.R., Bezem, M.: Acyclic programs. New Generation Computing 9, 335–363 (1991)
Bacchus, F.: Using first-order probability logic for the construction of bayesian networks. In: Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence, pp. 219–226 (1993)
Baral, C., Gelfond, M., Rushton, N.: Probabilistic reasoning with answer sets. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 21–33. Springer, Heidelberg (2003)
Breese, J.S., Goldman, R.P., Wellman, M.P.: Introduction to the special section on knowledge-based construction of probabilistic and decision models. IEEE Transactions on Systems, Man, and Cybernetics 24(11), 1577–1579 (1994)
Brewka, G.: Logic programming with ordered disjunction. In: Proceedings of the 18th National Conference on Artificial Intelligence, AAAI 2002, pp. 100–105. Morgan Kaufmann, San Francisco (2002)
Cussens, J.: Stochastic logic programs: Sampling, inference and applications. In: Proceedings of the Sixteenth Annual Conference on Uncertainty in Artificial Intelligence, pp. 115–122. MK (2000)
Dekhtyar, A., Subrahmanian, V.S.: Hybrid probabilistic programs. Journal of Logic Programming 43(3), 187–250 (2000)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New generation computing 9, 365–385 (1991)
Getoor, L., Friedman, N., Koller, D., Pfeffer, A.: Learning Probabilistic Relational Models. In: Dzeroski, S., Lavrac, N. (eds.) Relational Data Mining, pp. 7–34. Springer, Heidelberg (2001) (to appear)
Halpern, J.Y.: Reasoning about uncertainty. MIT Press, Cambridge (2003)
Halpern, J.Y.: An analysis of first-order logics of probability. Artificial Intelligence 46, 311–350 (1989)
Kersting, K., De Raedt, L.: Bayesian logic programs. In: Cussens, J., Frisch, A. (eds.) Work-in-Progress Reports of the Tenth International Conference on Inductive Logic Programming, ILP 2000 (2000)
Lakshmanan, L.V.S., Sadri, F.: Probabilistic deductive databases. In: Bruynooghe, M. (ed.) Proceedings of the International Symposium on Logic Programming, pp. 254–268. MIT Press, Cambridge (1994)
Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1987)
Lobo, J., Minker, J., Rajasekar, A.: Foundations of Disjunctive Logic Programming. MIT Press, Cambridge (1992)
Lukasiewicz, T.: Fixpoint characterizations for many-valued disjunctive logic programs. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 336–350. Springer, Heidelberg (2001)
Muggleton, S.: Learning stochastic logic programs. Electronic Transactions in Artificial Intelligence 5(041) (2000)
Ng, R.T., Subrahmanian, V.S.: Probabilistic logic programming. Information and Computation 101(2), 150–201 (1992)
Ngo, L., Haddawy, P.: Answering queries from context-sensitive probabilistic knowledge bases. Theoretical Computer Science 171(1-2), 147–177 (1997)
Poole, D.: The Independent Choice Logic for modelling multiple agents under uncertainty. Artificial Intelligence 94(1-2), 7–56 (1997)
Sakama, C.: Possible model semantics for disjunctive databases II (extended abstract). In: Logic Programming and Non-monotonic Reasoning, pp. 107–114 (1990)
Sakama, C., Inoue, K.: On the equivalence between disjunctive and abductive logic programs. In: International Conference on Logic Programming, pp. 489–503 (1994)
Sato, T., Kameya, Y.: PRISM: A language for symbolic-statistical modeling. In: Proceedings of IJCAI 1997, pp. 1330–1335 (1997)
Van Gelder, A., Ross, K.A., Schlipf, J.S.: The Well-Founded Semantics for General Logic Programs. Journal of the ACM 38(3), 620–650 (1991)
Vennekens, J., Verbaeten, S.: A general view on probabilistic logic programming. In: Proceedings of the 15th Belgian-Dutch Conference on Artificial Intelligence, pp. 299–306 (2003), http://www.cs.kuleuven.ac.be/~joost/bnaic.ps
Vennekens, J., Verbaeten, S.: Logic programs with annotated disjunctions. Technical Report CW386, K.U. Leuven (2003), http://www.cs.kuleuven.ac.be/~joost/techrep.ps
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
Vennekens, J., Verbaeten, S., Bruynooghe, M. (2004). Logic Programs with Annotated Disjunctions. In: Demoen, B., Lifschitz, V. (eds) Logic Programming. ICLP 2004. Lecture Notes in Computer Science, vol 3132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27775-0_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-27775-0_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22671-0
Online ISBN: 978-3-540-27775-0
eBook Packages: Springer Book Archive