Abstract
A number of generalizations of answer set programming have been proposed in the literature to deal with vagueness, uncertainty, and partial rule satisfaction. We introduce a unifying framework that entails most of the existing approaches to fuzzy answer set programming. In this framework, rule bodies are defined using arbitrary fuzzy connectives with monotone partial mappings. As an approximation of full answer sets, k–answer sets are introduced to deal with conflicting information, yielding a flexible framework that encompasses, among others, existing work on valued constraint satisfaction and answer set optimization.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proceedings of the Fifth International Conference and Symposium on Logic Programming (ICLP/SLP 1988), pp. 1081–1086. ALP, IEEE, The MIT Press (1988)
Van Nieuwenborgh, D., De Cock, M., Vermeir, D.: An introduction to fuzzy answer set programming. Annals of Mathematics and Artificial Intelligence 50(3-4), 363–388 (2007)
Lukasiewicz, T., Straccia, U.: Tightly integrated fuzzy description logic programs under the answer set semantics for the semantic web. In: Marchiori, M., Pan, J.Z., de Sainte Marie, C. (eds.) RR 2007. LNCS, vol. 4524, pp. 289–298. Springer, Heidelberg (2007)
Straccia, U.: Annotated answer set programming. In: Proceedings of the 11th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2006) (2006)
Damásio, C.V., Pereira, L.M.: Antitonic logic programs. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS, vol. 2173, pp. 379–392. Springer, Heidelberg (2001)
Damásio, C.V., Medina, J., Ojeda-Aciego, M.: Sorted multi-adjoint logic programs: termination results and applications. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS, vol. 3229, pp. 260–273. Springer, Heidelberg (2004)
Schiex, T., Fargier, H., Verfaillie, G.: Valued constraint satisfaction problems: hard and easy problems. In: Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI 1995), pp. 631–637 (1995)
Dubois, D., Fortemps, P.: Computing improved optimal solutions to max–min flexible constraint satisfaction problems. European Journal of Operational Research 118, 95–126 (1999)
Tarski, A.: A lattice theoretical fixpoint theorem and its application. Pacific Journal of Mathematics 5, 285–309 (1955)
Damasio, C.V., Pereira, L.M.: An encompassing framework for paraconsistent logic programs. Journal of Applied Logic 3, 67–95 (2003)
Damásio, C.V., Pereira, L.M.: Hybrid probabilistic logic programs as residuated logic programs. In: Brewka, G., Moniz Pereira, L., Ojeda-Aciego, M., de Guzmán, I.P. (eds.) JELIA 2000. LNCS, vol. 1919, pp. 57–72. Springer, Heidelberg (2000)
Brewka, G., Niemelä, I., Truszczyński, M.: Answer set optimization. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence, pp. 867–872. Morgan Kaufmann Publishers, San Francisco (2003)
Janssen, J., Heymans, S., Vermeir, D., De Cock, M.: Compiling fuzzy answer set programs to fuzzy propositional theories. In: Proceedings of the 24th International Conference on Logic Programming (ICLP 2008). Springer, Heidelberg (2008) (to appear)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Janssen, J., Schockaert, S., Vermeir, D., De Cock, M. (2009). General Fuzzy Answer Set Programs. In: Di Gesù, V., Pal, S.K., Petrosino, A. (eds) Fuzzy Logic and Applications. WILF 2009. Lecture Notes in Computer Science(), vol 5571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02282-1_44
Download citation
DOI: https://doi.org/10.1007/978-3-642-02282-1_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02281-4
Online ISBN: 978-3-642-02282-1
eBook Packages: Computer ScienceComputer Science (R0)