Abstract
We investigate rule dependency graphs and their colorings for characterizing the computation of answer sets of logic programs. We start from a characterization of answer sets in terms of totally colored dependency graphs. To a turn, we develop a series of operational characterizations of answer sets in terms of operators on partial colorings. In analogy to the notion of a derivation in proof theory, our operational characterizations are expressed as (non-deterministically formed) sequences of colorings, turning an uncolored graph into a totally colored one. This results in an operational framework in which different combinations of operators result in different formal properties. Among others, we identify the basic strategy employed by the noMoRe system and justify its algorithmic approach. Also, we distinguish Fitting’s and well-founded semantics.
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.
Similar content being viewed by others
References
Anger, C., Konczak, K., Linke, T.: noMoRe: Non-monotonic reasoning with logic programs. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 521–524. Springer, Heidelberg (2002)
Apt, K., Blair, H., Walker, A.: Towards a theory of declarative knowledge. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 89–148. Morgan Kaufmann, San Francisco (1987)
Brignoli, G., Costantini, S., D’Antona, O., Provetti, A.: Characterizing and computing stable models of logic programs: the non-stratified case. In: Baral, C., Mohanty, H. (eds.) Proceedings of the Conference on Information Technology, Bhubaneswar, India, pp. 197–201. AAAI Press, Menlo Park (1999)
Dimopoulos, Y., Torres, A.: Graph theoretical structures in logic programs and default theories. Theoretical Computer Science 170, 209–244 (1996)
Eiter, T., Leone, N., Mateis, C., Pfeifer, G., Scarcello, F.: A deductive system for nonmonotonic reasoning. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 363–374. Springer, Heidelberg (1997)
Fages, F.: Consistency of clark’s completion and the existence of stable models. Journal of Methods of Logic in Computer Science 1, 51–60 (1994)
Fitting, M.: Fixpoint semantics for logic programming a survey. Theoretical Computer Science 278(1-2), 25–51 (2002)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and deductive databases. New Generation Computing 9, 365–385 (1991)
Linke, T.: Graph theoretical characterization and computation of answer sets. In: Nebel, B. (ed.) Proceedings of the International Joint Conference on Artificial Intelligence, pp. 641–645. Morgan Kaufmann Publishers, San Francisco (2001)
Linke, T.: Using nested logic programs for answer set programming. In: De Voss, M., Provetti, A. (eds.) Proceedings of the Workshop on Answer Set Programming: Advances in Theory and Implementation (ASP 2003), pp. 181–194, CEUR (2003)
Linke, T., Anger, C., Konczak, K.: More on noMoRe. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 468–480. Springer, Heidelberg (2002)
Linke, T., Schaub, T.: An approach to query-answering in Reiter’s default logic and the underlying existence of extensions problem. In: Dix, J., et al. (eds.) Proceedings of the Sixth European Workshop on Logics in Artificial Intelligence, pp. 233–247. Springer, Heidelberg (1998)
Linke, T., Schaub, T.: Alternative foundations for Reiter’s default logic. Artificial Intelligence 124(1), 31–86 (2000)
Lloyd, J.: Foundations of Logic Programming. Springer, Heidelberg (1987)
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, pp. 289–303. The MIT Press, Cambridge (1996)
Papadimitriou, C., Sideri, M.: Default theories that always have extensions. Artificial Intelligence 69, 347–357 (1994)
van Gelder, K.: Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM 38(3), 620–650 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Konczak, K., Linke, T., Schaub, T. (2003). Graphs and Colorings for Answer Set Programming: Abridged Report. In: Lifschitz, V., Niemelä, I. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2004. Lecture Notes in Computer Science(), vol 2923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24609-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-24609-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20721-4
Online ISBN: 978-3-540-24609-1
eBook Packages: Springer Book Archive