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Logic Programs with Abstract Constraint Atoms: The Role of Computations

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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 new perspectives on the semantics of logic programs with constraints. To this end we introduce several notions of computation and propose to use the results of computations as answer sets of programs with constraints. We discuss the rationale behind different classes of computations and study the relationships among them and among the corresponding concepts of answer sets. The proposed semantics generalize the answer set semantics for programs with monotone, convex and/or arbitrary constraints described in the literature.

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References

  1. Balduccini, M., Gelfond, M., Nogueira, M.: Answer Set Based Design of Knowledge Systems. Annals of Mathematics and Artificial Intelligence (2006)

    Google Scholar 

  2. Dell’Armi, T., et al.: Aggregate Functions in Disjunctive Logic Programming: Semantics, Complexity, and Implementation in DLV. In: IJCAI, pp. 847–852 (2003)

    Google Scholar 

  3. Denecker, M., Pelov, N., Bruynooghe, M.: Ultimate well-founded and stable semantics for logic programs with aggregates. In: Codognet, P. (ed.) ICLP 2001. LNCS, vol. 2237, pp. 212–226. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. Elkabani, I., Pontelli, E., Son, T.C.: Smodels with CLP and its applications. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 73–89. Springer, Heidelberg (2004)

    Google Scholar 

  5. Erdem, E., Lifschitz, V., Ringe, D.: Temporal phylogenetic networks and logic programming. TPLP 6(5), 539–558 (2006)

    MATH  Google Scholar 

  6. Faber, W., Leone, N., Pfeifer, G.: Recursive aggregates in disjunctive logic programs: Semantics and complexity. In: Alferes, J.J., Leite, J.A. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 200–212. Springer, Heidelberg (2004)

    Google Scholar 

  7. Ferraris, P.: Answer sets for propositional theories. In: Logic Programming and Nonmonotonic Reasoning, pp. 119–131. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Joint Int. Conf. and Symp. on Logic Programming, pp. 1070–1080. MIT Press, Cambridge (1988)

    Google Scholar 

  9. Gelfond, M.: Representing Knowledge in A-Prolog. In: Computational Logic: Logic Programming and Beyond, pp. 413–451. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Heljanko, K., Niemelä, I.: Bounded LTL model checking with stable models. Theory and Practice of Logic Programming 3(4,5), 519–550 (2003)

    Article  MATH  Google Scholar 

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

    Google Scholar 

  12. Marek, V.W., Nerode, A., Remmel, J.: Logic Programs, Well-orderings, and Forward Chaining. Annals of Pure and Applied Logic 96, 231–276 (1999)

    Article  MATH  Google Scholar 

  13. Marek, V.W., Truszczyński, M.: Nonmonotonic Logic: Context-Dependent Reasoning. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  14. Marek, V.W., Truszczyński, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm, pp. 375–398. Springer, Heidelberg (1999)

    Google Scholar 

  15. Marek, V.W., Remmel, J.B.: Set constraints in logic programming. In: Logic Programming and Nonmonotonic Reasoning, pp. 167–179. Springer, Heidelberg (2004)

    Google Scholar 

  16. Marek, V.W., Truszczyński, M.: Logic programs with abstract constraint atoms. In: National Conference on Artificial Intelligence (AAAI) AAAI Press / The MIT Press (2004)

    Google Scholar 

  17. Niemelä, I.: Logic programming with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25(3,4), 241–273 (1999)

    Article  MATH  Google Scholar 

  18. Pelov, N.: Semantic of Logic Programs with Aggregates. PhD thesis, K.U. Leuven (2004)

    Google Scholar 

  19. Son, T.C., Pontelli, E.: A Constructive Semantic Characterization of Aggregates in Answer Set Programming. Theory and Practice of Logic Programming (2007)

    Google Scholar 

  20. Son, T.C., Pontelli, E., Elkabani, I.: An Unfolding-Based Semantics for Logic Programming with Aggregates. Computing Research Repository (2006) (cs.SE/0605038)

    Google Scholar 

  21. Son, T.C., Pontelli, E., Tu, P.H.: Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms. Journal of Artificial Intelligence Research (accepted 2007)

    Google Scholar 

  22. van Emden, M.H., Kowalski, R.A.: The Semantics of Predicate Logic as a Programming Language. Journal of the ACM 23(4), 733–742 (1976)

    Article  MATH  Google Scholar 

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Véronica Dahl Ilkka Niemelä

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Liu, L., Pontelli, E., Son, T.C., Truszczyński, M. (2007). Logic Programs with Abstract Constraint Atoms: The Role of Computations. 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_20

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  • DOI: https://doi.org/10.1007/978-3-540-74610-2_20

  • 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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