Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T07:41:34.515Z Has data issue: false hasContentIssue false
  • English
  • Français

Random logic programs: Linear model

Published online by Cambridge University Press:  05 September 2014

KEWEN WANG ,
LIAN WEN  and
KEDIAN MU
KEWEN WANG
Affiliation:
School of Information and Communication Technology, Griffith University, Australia (e-mail: k.wang@griffith.edu.au, l.wen@griffith.edu.au)
LIAN WEN
Affiliation:
School of Information and Communication Technology, Griffith University, Australia (e-mail: k.wang@griffith.edu.au, l.wen@griffith.edu.au)
KEDIAN MU
Affiliation:
School of Mathematical Sciences, Peking University, China (e-mail: mukedian@math.pku.edu.cn)
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of answer sets for a random program converges to a constant when the number of atoms approaches infinity. Several experimental results are also reported, which justify the suitability of the linear model. It is also experimentally shown that, under this model, the size distribution of answer sets for random programs tends to a normal distribution when the number of atoms is sufficiently large.

Keywords

answer set programmingrandom logic programs
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 15 , Issue 6 , November 2015 , pp. 818 - 853
Copyright
Copyright © Cambridge University Press 2014 

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

Achlioptas, D., Kirousis, L., Kranakis, E., Krizanc, D., Molloy, M. and Stamatiou, Y. 1997. Random constraint satisfaction: A more accurate picture. In Proceedings of the 3rd International Conference on Principles and Practice of Constraint Programming (CP-97), 107–120.Google Scholar
Achlioptas, D., Naor, A. and Peres, Y. 2005. Rigorous location of phase transitions in hard optimization problems. Nature 435, 7043, 759–764.CrossRefGoogle ScholarPubMed
Baral, C., Gelfond, M. and Rushton, N. 2009. Probabilistic reasoning with answer sets. Theory and Practice of Logic Programming 9, 1, 57–144.CrossRefGoogle Scholar
Blair, H., Dushin, F., Jakel, D., Rivera, D. and Sezgin, M. 1999. Continuous models of computation for logic programs: importing continuous mathematics into logic programming's algorithmic foundations. In The Logic Programming Paradigm, Springer, New York, 231–255.CrossRefGoogle Scholar
Brass, S. and Dix, J. 1999. Semantics of disjunctive logic programs based on partial evaluation. Journal of Logic Programming 38, 3, 167–312.Google Scholar
Cheeseman, P., Kanefsky, B. and Taylor, W. M. 1991. Where the really hard problems are. In Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI-91), 331–340.Google Scholar
Gebser, M., Kaufmann, B. and Schaub, T. 2009. The conflict-driven answer set solver clasp: Progress report. In Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-09), 509–514.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. Logic programs with classical negation. In Proceedings of the 7th International Conference on Logic Programming (ICLP-90), 579–597.Google Scholar
Gelfond, M. and Lifschitz, V. 1990. The stable model semantics for logic programming. In Proceedings of the 5th International Conference on Logic Programming (ICLP-88), 1070–1080.Google Scholar
Gent, I. and Walsh, T. 1994. The sat phase transition. In Proceedings of the Eleventh European Conference on Artificial Intelligence (ECAI-94), 105–109.Google Scholar
Huang, G., JiaX., C. X., C. and You, J. 2002. Two-literal logic programs and satisfiability representation of stable models: A comparison. In Proceedings 15th Canadian Conference on Artificial Intelligence, 119–131.Google Scholar
Huberman, B. and Hogg, T. 1987. Phase transitions in artificial intelligence systems. Artificial Intelligence 33, 2, 155–171.Google Scholar
Janhunen, T. 2006. Some (in)translatability results for normal logic programs and propositional theories. Journal of Applied Non-Classical Logics 1–2, 35–86.Google Scholar
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S. and Scarcello, F. 2006. The dlv system for knowledge representation and reasoning. ACM Transactions on Computational Logic 7, 3, 499–562.Google Scholar
Lonc, Z. and Truszczynski, M. 2004. Computing stable models: Worst-Case performance estimates. Theory and Practice of Logic Programming 4, 1–2, 193–231.CrossRefGoogle Scholar
Marek, V. and Truszczynski, M. 1991. Autoepistemic logic. Journal of the Association for Computing Machinery 38, 3, 588–619.CrossRefGoogle Scholar
Marek, V. and Truszczynski, M. 1993. Nonmonotonic Logic: Context-Dependent Reasonong. Springer, Berlin, Germany.Google Scholar
Mitchell, D., Selman, B. and Levesque, H. 1992. Hard and easy distributions of sat problems. In Proceedings of the 10th National Conference on Artificial Intelligence (AAAI-92), 459–465.Google Scholar
Monasson, R., Zecchina, R., Kirkpatrick, S., Selman, B. and Troyansky, L. 1999. 2+p-sat: Relation of typical-case complexity to the nature of the phase transition. Random Structures and Algorithms 15, 3–4, 414–435.3.0.CO;2-G>CrossRefGoogle Scholar
Namasivayam, G. 2009. Study of random logic programs. In Proceedings of the 25th International Conference on Logic Programming (ICLP-09), 555–556.Google Scholar
Namasivayam, G. and Truszczynski, M. 2009. Simple random logic programs. In Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR-09), 223–235.Google Scholar
Schlipf, J., Truszczynski, M. and Wong, D. 2005. On the distribution of programs with stable models. In Dagstuhl Seminar 05171 Abstracts Collection - Nonmonotonic Reasoning, Answer Set Prorgamming and Constraints.Google Scholar
Staab, S. and Studer, R. 2004. Handbook on Ontologies. Springer-Verlag, Berlin, Germany.CrossRefGoogle Scholar
Syrjänen, T. and Niemelä, I. 2001. The smodels system. In Proceedings of the 6th International ConferenceLogic Logic Programming and Nonmonotonic Reasoning (LPNMR-01), 434–438.Google Scholar
Wang, K. and Zhou, L. 2005. Comparisons and computation of well-founded semantics for disjunctive logic programs. ACM Transactions on Computational Logic 6, 2, 295–327.Google Scholar
Zhao, Y. and Lin, F. 2003. Answer set programming phase transition: A study on randomly generated programs. In Proceedings of the 19th International Conference on Logic Programming (ICLP-03), 239–253.Google Scholar