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Generic Tableaux for Answer Set Programming

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Logic Programming (ICLP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4670))

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Abstract

We provide a general and modular framework for describing inferences in Answer Set Programming (ASP) that aims at an easy incorporation of additional language constructs. To this end, we generalize previous work characterizing computations in ASP by means of tableau methods. We start with a very basic core fragment in which rule heads and bodies consist of atomic literals. We then gradually extend this setting by focusing on the concept of an aggregate, understood as an operation on a collection of entities. We exemplify our framework by applying it to conjunctions in rule bodies, cardinality constraints as used in smodels, and finally to disjunctions in rule heads.

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References

  1. Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  2. Mitchell, D.: A SAT solver primer. Bulletin of the European Association for Theoretical Computer Science 85, 112–133 (2005)

    Google Scholar 

  3. Beame, P., Kautz, H., Sabharwal, A.: Towards understanding and harnessing the potential of clause learning. Journal of Artificial Intelligence Research 22, 319–351 (2004)

    MATH  Google Scholar 

  4. Gebser, M., Schaub, T.: Tableau calculi for answer set programming. In: Etalle, S., Truszczyński, M. (eds.) ICLP 2006. LNCS, vol. 4079, pp. 11–25. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. D’Agostino, M., Gabbay, D., Hähnle, R., Posegga, J.: Handbook of Tableau Methods. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  6. Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence 138(1-2), 181–234 (2002)

    Article  MATH  Google Scholar 

  7. Ferraris, P., Lifschitz, V.: Weight constraints as nested expressions. Theory and Practice of Logic Programming 5(1-2), 45–74 (2005)

    Article  MATH  Google Scholar 

  8. Liu, L., Truszczyński, M.: Properties of programs with monotone and convex constraints. In: Veloso, M., Kambhampati, S. (eds.) Proceedings of the National Conference on Artificial Intelligence (AAAI 2005), pp. 701–706. AAAI/MIT Press (2005)

    Google Scholar 

  9. Faber, W.: Unfounded sets for disjunctive logic programs with arbitrary aggregates. [19] 40–52

    Google Scholar 

  10. Ferraris, P.: Answer sets for propositional theories. [19] 119–131

    Google Scholar 

  11. Clark, K.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press, New York (1978)

    Google Scholar 

  12. van Gelder, A., Ross, K., Schlipf, J.: The well-founded semantics for general logic programs. Journal of the ACM 38(3), 620–650 (1991)

    Article  MATH  Google Scholar 

  13. Beame, P., Pitassi, T.: Propositional proof complexity: Past, present, and future. Bulletin of the European Association for Theoretical Computer Science 65, 66–89 (1998)

    MATH  Google Scholar 

  14. Järvisalo, M., Junttila, T., Niemelä, I.: Unrestricted vs restricted cut in a tableau method for Boolean circuits. Annals of Mathematics and Artificial Intelligence 44(4), 373–399 (2005)

    Article  MATH  Google Scholar 

  15. Syrjänen, T.: Lparse 1.0 user’s manual, http://www.tcs.hut.fi/Software/smodels/lparse.ps.gz

  16. Leone, N., Rullo, P., Scarcello, F.: Disjunctive stable models: Unfounded sets, fixpoint semantics, and computation. Information and Computation 135(2), 69–112 (1997)

    Article  MATH  Google Scholar 

  17. Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV system for knowledge representation and reasoning. ACM Transactions on Computational Logic 7(3), 499–562 (2006)

    Article  Google Scholar 

  18. Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: Conflict-driven answer set solving. In: Veloso, M. (ed.) Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 386–392. AAAI/MIT Press (2007)

    Google Scholar 

  19. Baral, C., Greco, G., Leone, N., Terracina, G. (eds.): LPNMR 2005. LNCS (LNAI), vol. 3662. Springer, Heidelberg (2005)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik, Universität Potsdam, August-Bebel-Str. 89, D-14482 Potsdam, Germany

    Martin Gebser & Torsten Schaub

Authors
  1. Martin Gebser
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  2. Torsten Schaub
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Véronica Dahl Ilkka Niemelä

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© 2007 Springer-Verlag Berlin Heidelberg

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Gebser, M., Schaub, T. (2007). Generic Tableaux for Answer Set Programming. In: Dahl, V., Niemelä, I. (eds) Logic Programming. ICLP 2007. Lecture Notes in Computer Science, vol 4670. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74610-2_9

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  • DOI: https://doi.org/10.1007/978-3-540-74610-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74608-9

  • Online ISBN: 978-3-540-74610-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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