Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-25T00:53:46.494Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterizations of stable model semantics for logic programs with arbitrary constraint atoms

Published online by Cambridge University Press:  01 July 2009

YI-DONG SHEN ,
JIA-HUAI YOU  and
LI-YAN YUAN
YI-DONG SHEN
Affiliation:
State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China (e-mail: ydshen@ios.ac.cn)
JIA-HUAI YOU
Affiliation:
Department of Computing Science, University of Alberta, Edmonton, Alberta, T6G 2H1Canada (e-mail: you@cs.ualberta.ca, yuan@cs.ualberta.ca)
LI-YAN YUAN
Affiliation:
Department of Computing Science, University of Alberta, Edmonton, Alberta, T6G 2H1Canada (e-mail: you@cs.ualberta.ca, yuan@cs.ualberta.ca)
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented compactly. We show two applications. First, under this representation of constraint atoms, we generalize the Gelfond–Lifschitz transformation and apply it to define stable models (also called answer sets) for logic programs with arbitrary constraint atoms. The resulting semantics turns out to coincide with the one defined by Son et al. (2007), which is based on a fixpoint approach. One advantage of our approach is that it can be applied, in a natural way, to define stable models for disjunctive logic programs with constraint atoms, which may appear in the disjunctive head as well as in the body of a rule. As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches. Second, we show that our abstract representation of constraint atoms provides a means to characterize dependencies of atoms in a program with constraint atoms, so that some standard characterizations and properties relying on these dependencies in the past for logic programs with ordinary atoms can be extended to logic programs with constraint atoms.

Keywords

answer set programingabstract constraint atomsstable model semanticsGelfond–Lifschitz transformation
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 9 , Issue 4 , July 2009 , pp. 529 - 564
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baptiste, P. and Pape, C. 1996. Disjunctive constraints for manufacturing scheduling: Principles and extensions. International Journal of Computer Integrated Manufacturing 9 (4), 306–310.CrossRefGoogle Scholar
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving with Answer Sets. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Calimeri, F., Faber, W., Leone, N. and Perri, S. 2005. Declarative and computational properties of logic programs with aggregates. In Proc. IJCAI'05, Edinburgh, UK. Professional Book Center, 406–411.Google Scholar
Cohen, D., Jeavons, P. and Jonsson, P. 2000. Building tractable disjunctive constraints. Journal of the ACM 47 (5), 826–853.CrossRefGoogle Scholar
Dell'Armi, T., Faber, W., Ielpa, G., Leone, N., and Pfeifer, G. 2003. Aggregate functions in disjunctive logic programming: semantics, complexity and implementation in dlv. In Proc. IJCAI'03, Acapulco, Mexico. Morgan Kaufmann, 847–852.Google Scholar
Dell'Armi, T., Faber, W., Lelpa, G., and Leone, N. 2003. Aggregate functions in disjunctive logic programming: semantics, complexity, and implementation in DLV. In Proc. IJCAI'03, Utrecht, the Netherlands. Lecture Notes in Computer Science 1048, Springer, 847–852.Google Scholar
Denecker, M., Pelov, N. and Bruynooghe, M. 2001. Ultimate well-founded and stable semantics for logic programs with aggregates. In Proc. ICLP'01, Paphos, Cyprus. Lecture Notes in Computer Science 2237, Springer, 212–226.Google Scholar
Eiter, T. and Gottlob, G. 1993. Complexity results for disjunctive logic programming and application to nonmonotonic logics. In Proc. International Logic Programming Symposium, Vancouver, Canada. MIT Press, 266–278.Google Scholar
Elkabani, I., Pontelli, E. and Son, T. C. 2004. Smodels with clp and its applications: A simple and effective approach to aggregates in asp. In Proc. ICLP'04, Saint-Malo, France. Lecture Notes in Computer Science 3132, Springer, 73–89.Google Scholar
Elkabani, I., Pontelli, E. and Son, T. C. 2005. Smodelsa – A system for computing answer sets of logic programs with aggregates. In Proc. LPNMR'05, Diamante, Italy. Lecture Notes in Computer Science 3662, Springer, 427–431.Google Scholar
Faber, W., Leone, N. and Pfeifer, G. 2004. Recursive aggregates in disjunctive logic programs: Semantics and complexity. In Proc. JELIA'04, Lisbon, Portugal. Lecture Notes in Computer Science 33229, Springer, 200–212.Google Scholar
Fages, F. 1994. Consistency of Clark's completion and existence of stable models. Journal of Methods of Logic in Computer Science 1, 51–60.Google Scholar
Ferraris, P. 2005. Answer sets for propositional theories. In Proc. LPNMR'05, Diamante, Italy. Lecture Notes in Computer Science 3662, Springer, 119–131.Google Scholar
Gelfond, M. and Leone, N. 2002. Logic programming and knowledge representation – The a-prolog perspective. Artificial Intelligence 138 (1–2), 3–38.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. ICLP'88, Seattle, Washington. MIT Press, 1070–1080.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385.CrossRefGoogle Scholar
Lifschitz, V. 2002. Answer set programming and plan generation. Artificial Intelligence 138 (1–2), 39–54.CrossRefGoogle Scholar
Liu, L., Pontelli, E., Son, T. and Truszczynski, M. 2007. Logic programs with abstract constraint atoms: the role of computations. In Proc. ICLP'07, Porto, Portugal. Lecture Notes in Computer Science 4670, Springer, 286–301.Google Scholar
Liu, L. and Truszczynski, M. 2005. Properties of programs with monotone and convex constraints. In Proc. AAAI'05, Pittsburgh, USA. AAAI Press/The MIT Press, 701–706.Google Scholar
Liu, L. and Truszczynski, M. 2006. Properties and applications of programs with monotone and convex constraints. Journal of Artificial Intelligence Research 7, 299–334.CrossRefGoogle Scholar
Marek, V., Niemelä, I. and Truszczyński, M. 2008. Logic programs with monotone abstract constraint atoms. Theory and Practice of Logic Programming 8 (2), 167–199.CrossRefGoogle Scholar
Marek, V. W. and Remmel, J. B. 2004. Set constraints in logic programming. In Proc. LPNMR'04, Fort Lauderdale, USA. Lecture Notes in Computer Science 2923, Springer, 167–179.Google Scholar
Marek, V. W. and Truszczynski, M. 1999. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm: A 25-Year Perspective. Springer, 375–398.CrossRefGoogle Scholar
Marek, V. W. and Truszczynski, M. 2004. Logic programs with abstract constraint atoms. In Proc. AAAI'04, San Jose, USA. AAAI Press/The MIT Press, 86–91.Google Scholar
Marriott, K., Moulder, P. and Stuckey, P. 2001. Solving disjunctive constraints for interactive graphical applications. In Proc. CP'01, Paphos, Cyprus. Lecture Notes in Computer Science 2239, Springer, 361–376.Google Scholar
Mittal, S. and Falkenhainer, B. 1990. Dynamic constraint satisfaction problems. In Proc. AAAI'90, Boston, USA. AAAI Press/The MIT Press, 25–32.Google Scholar
Niemela, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 241–273.CrossRefGoogle Scholar
Pelov, N. 2004. Semantics of Logic Programs with Aggregates. Ph.D. thesis, Katholieke Universiteit Leuven, Leuven, http://www.cs.kuleuven.ac.be/publicaties/doctoraten/cw/cw2004_02.abs.html.Google Scholar
Pelov, W., Denecker, M. and Bruynooghe, M. 2003. Translation of aggregate programs to normal logic programs. In CEUR Workshop Proceedings, CEUR-WS.org, Messina, Italy, 29–42.Google Scholar
Pelov, W., Denecker, M. and Bruynooghe, M. 2007. Well-founded and stable semantics of logic programs with aggregates. Theory and Practice of Logic Programming 7 (3), 301–353.CrossRefGoogle Scholar
Pelov, W. and Truszczynski, M. 2004. Semantics of disjunctive programs with monotone aggregates – An operator-based approach. In Proc. NMR'04, Whistler, Canada, 327–334.Google Scholar
Przymusinski, T. C. 1991. Stable semantics for disjunctive programs. New Generation Computing 9, 401–424.CrossRefGoogle Scholar
Sato, T. 1990. Completed logic programs and their consistency. Journal of Logic Programming 9 (1), 33–44.CrossRefGoogle Scholar
Shen, Y. D. and You, J. H. 2007. A generalized Gelfond–Lifschitz transformation for logic programs with abstract constraints. In Proc. AAAI'07, Vancouver, Canada. AAAI Press, 483–488.Google Scholar
Simons, P., Niemela, I. and Soininen, T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138 (1–2), 181–234.CrossRefGoogle Scholar
Son, T. C. and Pontelli, E. 2007. A constructive semantic characterization of aggregates in answer set programming. Theory and Practice of Logic Programming 7 (3), 355–375.CrossRefGoogle Scholar
Son, T. C., Pontelli, E. and Tu, P. H. 2006. Answer sets for logic programs with arbitrary abstract constraint atoms. In Proc. AAAI'06, Boston, USA. AAAI Press, 129–134.Google Scholar
Son, T. C., Pontelli, E. and Tu, P. H. 2007. Answer sets for logic programs with arbitrary abstract constraint atoms. Journal of Artificial Intelligence Research 29, 353–389.CrossRefGoogle Scholar
You, J. and Yuan, L. 1994. A three-valued semantics for deductive databases and logic programs. Journal of Computer and System Sciences 49, 334–361.CrossRefGoogle Scholar
You, J. H., Yuan, L. Y., Liu, G. H. and Shen, Y. D. 2007. Logic programs with abstract constraints: representation, disjunction, and complexities. In Proc. LPNMR'07, Tempe, USA. Lecture Notes in Computer Science 4483, Springer, 228–240.Google Scholar