Symmetry Breaking for Distributed Multi-Context Systems

  • Christian Drescher
  • Thomas Eiter
  • Michael Fink
  • Thomas Krennwallner
  • Toby Walsh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6645)


Heterogeneous nonmonotonic multi-context systems (MCS) permit different logics to be used in different contexts, and link them via bridge rules. We investigate the role of symmetry detection and symmetry breaking in such systems to eliminate symmetric parts of the search space and, thereby, simplify the evaluation process. We propose a distributed algorithm that takes a local stance, i.e., computes independently the partial symmetries of a context and, in order to construct potential symmetries of the whole, combines them with those partial symmetries returned by neighbouring contexts. We prove the correctness of our methods. We instantiate such symmetry detection and symmetry breaking in a multi-context system with contexts that use answer set programs, and demonstrate computational benefit on some recently proposed benchmarks.


Symmetry Breaking Belief State Partial Symmetry Potential Symmetry Nonmonotonic Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aloul, F.A., Markov, I.L., Sakallah, K.A.: Shatter: efficient symmetry-breaking for Boolean satisfiability. In: DAC 2003, pp. 836–839. ACM, New York (2003)Google Scholar
  2. 2.
    Babai, L.: Automorphism groups, isomorphism, reconstruction. In: Graham, R.L., Grötschel, M., Lovász, L. (eds.) Handbook of Combinatorics, vol. 2, pp. 1447–1540. Elsevier, Amsterdam (1995)Google Scholar
  3. 3.
    Bairakdar, S., Dao-Tran, M., Eiter, T., Fink, M., Krennwallner, T.: Decomposition of distributed nonmonotonic multi-context systems. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS, vol. 6341, pp. 24–37. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)CrossRefzbMATHGoogle Scholar
  5. 5.
    Brewka, G., Eiter, T.: Equilibria in heterogeneous nonmonotonic multi-context systems. In: AAAI 2007, pp. 385–390. AAAI Press, Menlo Park (2007)Google Scholar
  6. 6.
    Crawford, J., Ginsberg, M., Luks, E., Roy, A.: Symmetry-breaking predicates for search problems. In: KR 1996, pp. 148–159. Morgan Kaufmann, San Francisco (1996)Google Scholar
  7. 7.
    Dao-Tran, M., Eiter, T., Fink, M., Krennwallner, T.: Distributed nonmonotonic multi-context systems. In: KR 2010, pp. 60–70. AAAI Press, Menlo Park (2010)Google Scholar
  8. 8.
    Drescher, C., Tifrea, O., Walsh, T.: Symmetry-breaking answer set solving (2011) (to appear)Google Scholar
  9. 9.
    Fox, M., Long, D.: The detection and exploitation of symmetry in planning problems. In: IJCAI 1999, pp. 956–961. Morgan Kaufmann, San Francisco (1999)Google Scholar
  10. 10.
    Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: clasp: A conflict-driven answer set solver. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 260–265. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Giunchiglia, F.: Contextual reasoning. Epistemologia, special issue on I Linguaggi e le Macchine 345, 345–364 (1992)Google Scholar
  12. 12.
    Giunchiglia, F., Serafini, L.: Multilanguage hierarchical logics or: How we can do without modal logics. Artif. Intell. 65(1), 29–70 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Katsirelos, G., Narodytska, N., Walsh, T.: Breaking generator symmetry. In: SymCon 2009 (2009)Google Scholar
  14. 14.
    McCarthy, J.: Generality in artificial intelligence. Commun. ACM 30, 1030–1035 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Puget, J.-F.: Automatic detection of variable and value symmetries. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 475–489. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christian Drescher
    • 1
    • 2
  • Thomas Eiter
    • 3
  • Michael Fink
    • 3
  • Thomas Krennwallner
    • 3
  • Toby Walsh
    • 1
    • 2
  1. 1.NICTAAustralia
  2. 2.University of New South WalesSydneyAustralia
  3. 3.Institut für InformationssystemeTechnische Universität WienViennaAustria

Personalised recommendations