zbMATH — the first resource for mathematics

Twelve definitions of a stable model. (English) Zbl 1185.68166
Garcia de la Banda, Maria (ed.) et al., Logic programming. 24th international conference, ICLP 2008, Udine, Italy, December 9–13 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-89981-5/pbk). Lecture Notes in Computer Science 5366, 37-51 (2008).
Summary: This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prolog-style programs, but there are reasons why each of them is valuable and interesting. A new characterization of stable models can suggest an alternative picture of the intuitive meaning of logic programs; or it can lead to new algorithms for generating stable models; or it can work better than others when we turn to generalizations of the traditional syntax that are important from the perspective of answer set programming; or it can be more convenient for use in proofs; or it can be interesting simply because it demonstrates a relationship between seemingly unrelated ideas.
For the entire collection see [Zbl 1154.68013].

68N17 Logic programming
68Q55 Semantics in the theory of computing
Smodels; ASSAT
PDF BibTeX Cite
Full Text: DOI
[1] 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 Mateo (1988)
[2] Balduccini, M., Gelfond, M.: Logic programs with consistency-restoring rules. In: Working Notes of the AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning (2003), http://www.krlab.cs.ttu.edu/papers/download/bg03.pdf
[3] Bidoit, N., Froidevaux, C.: Minimalism subsumes default logic and circumscription in stratified logic programming. In: Proc. LICS 1987, pp. 89–97 (1987)
[4] Clark, K.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press, New York (1978)
[5] Faber, W., Leone, N., Pfeifer, G.: Recursive aggregates in disjunctive logic programs: Semantics and complexity. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS, vol. 3229. Springer, Heidelberg (2004) · Zbl 1111.68380
[6] Fages, F.: A fixpoint semantics for general logic programs compared with the well–supported and stable model semantics. New Generation Computing 9, 425–443 (1991) · Zbl 0737.68014
[7] Ferraris, P., Lifschitz, V.: Weight constraints as nested expressions. Theory and Practice of Logic Programming 5, 45–74 (2005) · Zbl 1093.68017
[8] Ferraris, P., Lee, J., Lifschitz, V.: A new perspective on stable models. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 372–379 (2007)
[9] Ferraris, P.: Answer sets for propositional theories. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS, vol. 3662, pp. 119–131. Springer, Heidelberg (2005) · Zbl 1152.68408
[10] Fine, K.: The justification of negation as failure. In: Proceedings of the Eighth International Congress of Logic, Methodology and Philosophy of Science, pp. 263–301. North Holland, Amsterdam (1989) · Zbl 0689.03003
[11] Gebser, M., Liu, L., Namasivayam, G., Neumann, A., Schaub, T., Truszczyński, M.: The first answer set programming system competition. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS, vol. 4483, pp. 3–17. Springer, Heidelberg (2007) · Zbl 05211322
[12] Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) Proceedings of International Logic Programming Conference and Symposium, pp. 1070–1080. MIT Press, Cambridge (1988)
[13] Gelfond, M., Lifschitz, V.: Logic programs with classical negation. In: Warren, D., Szeredi, P. (eds.) Proceedings of International Conference on Logic Programming (ICLP), pp. 579–597 (1990)
[14] Gelfond, M.: On stratified autoepistemic theories. In: Proceedings of National Conference on Artificial Intelligence (AAAI), pp. 207–211 (1987)
[15] Heyting, A.: Die formalen Regeln der intuitionistischen Logik. In: Sitzungsberichte der Preussischen Akademie der Wissenschaften. Physikalisch-mathematische Klasse, pp. 42–56 (1930) · JFM 56.0823.01
[16] Lee, J., Lifschitz, V., Palla, R.: A reductive semantics for counting and choice in answer set programming. In: Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), pp. 472–479 (2008)
[17] Lee, J.: A model-theoretic counterpart of loop formulas. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 503–508 (2005)
[18] Lifschitz, V., Tang, L.R., Turner, H.: Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25, 369–389 (1999) · Zbl 0940.68075
[19] Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 526–541 (2001) · Zbl 1365.68149
[20] Lifschitz, V.: On the declarative semantics of logic programs with negation. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 177–192. Morgan Kaufmann, San Mateo (1988) · Zbl 0718.68019
[21] Lin, F., Reiter, R.: Rules as actions: A situation calculus semantics for logic programs. Journal of Logic Programming 31, 299–330 (1997) · Zbl 0882.68031
[22] Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. In: Proceedings of National Conference on Artificial Intelligence (AAAI), pp. 112–117 (2002)
[23] Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. Artificial Intelligence 157, 115–137 (2004), http://www.cs.ust.hk/faculty/flin/papers/assat-aij-revised.pdf · Zbl 1085.68544
[24] Lin, F., Zhou, Y.: From answer set logic programming to circumscription via logic of GK. In: Proceedings of International Joint Conference on Artificial Intelligence, IJCAI (2007) · Zbl 1216.68270
[25] Lin, F.: A Study of Nonmonotonic Reasoning. PhD thesis, Stanford University (1991)
[26] Marek, V., Truszczyński, M.: Stable semantics for logic programs and default theories. In: Proc. North American Conf. on Logic Programming, pp. 243–256 (1989)
[27] McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of artificial intelligence. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 4, pp. 463–502. Edinburgh University Press, Edinburgh (1969) · Zbl 0226.68044
[28] McCarthy, J.: Circumscription–a form of non-monotonic reasoning. Artificial Intelligence 13, 27–39, 171–172 (1980) · Zbl 0435.68073
[29] McCarthy, J.: Applications of circumscription to formalizing common sense knowledge. Artificial Intelligence 26(3), 89–116 (1986)
[30] McDermott, D., Doyle, J.: Nonmonotonic logic I. Artificial Intelligence 13, 41–72 (1980) · Zbl 0435.68074
[31] McDermott, D.: Nonmonotonic logic II: Nonmonotonic modal theories. Journal of ACM 29(1), 33–57 (1982) · Zbl 0477.68099
[32] Moore, R.: Semantical considerations on nonmonotonic logic. Artificial Intelligence 25(1), 75–94 (1985) · Zbl 0569.68079
[33] Niemelä, I., Simons, P.: Extending the Smodels system with cardinality and weight constraints. In: Minker, J. (ed.) Logic-Based Artificial Intelligence, pp. 491–521. Kluwer, Dordrecht (2000) · Zbl 0979.68015
[34] Pearce, D., Tompits, H., Woltran, S.: Encodings for equilibrium logic and logic programs with nested expressions. In: Brazdil, P.B., Jorge, A.M. (eds.) EPIA 2001. LNCS, vol. 2258, pp. 306–320. Springer, Heidelberg (2001) · Zbl 1053.68695
[35] Pearce, D.: A new logical characterization of stable models and answer sets. In: Dix, J., Pereira, L., Przymusinski, T. (eds.) NMELP 1996. LNCS (LNAI), vol. 1216, pp. 57–70. Springer, Heidelberg (1997)
[36] Reiter, R.: A logic for default reasoning. Artificial Intelligence 13, 81–132 (1980) · Zbl 0435.68069
[37] Reiter, R.: Circumscription implies predicate completion (sometimes). In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 418–420 (1982)
[38] Reiter, R.: Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems. MIT Press, Cambridge (2001) · Zbl 1018.03022
[39] Saccá, D., Zaniolo, C.: Stable models and non-determinism in logic programs with negation. In: Proceedings of ACM Symposium on Principles of Database Systems (PODS), pp. 205–217 (1990)
[40] van Emden, M., Clark, K.: The logic of two-person games. In: Micro-PROLOG: Programming in Logic, pp. 320–340. Prentice-Hall, Englewood Cliffs (1984)
[41] van Emden, M., Kowalski, R.: The semantics of predicate logic as a programming language. Journal of ACM 23(4), 733–742 (1976) · Zbl 0339.68004
[42] Van Gelder, A., Ross, K.A., Schlipf, J.S.: Unfounded sets and well-founded semantics for general logic programs. In: Proceedings of the Seventh ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Austin, Texas, March 21-23, 1988, pp. 221–230. ACM Press, New York (1988)
[43] Van Gelder, A., Ross, K., Schlipf, J.: The well-founded semantics for general logic programs. Journal of ACM 38(3), 620–650 (1991) · Zbl 0799.68045
[44] Van Gelder, A.: Negation as failure using tight derivations for general logic programs. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 149–176. Morgan Kaufmann, San Mateo (1988) · Zbl 0726.68065
[45] Wallace, M.: Tight, consistent and computable completions for unrestricted logic programs. Journal of Logic Programming 15, 243–273 (1993) · Zbl 0787.68021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.