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International Colloquium on Theoretical Aspects of Computing

ICTAC 2013: Theoretical Aspects of Computing – ICTAC 2013 pp 355–372Cite as

Embedding Functions into Disjunctive Logic Programs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8049))

Abstract

We extend the notions of completion and loop formulas of normal logic programs with functions to a class of nested expressions that properly include disjunctive logic programs. We show that answer sets for such a logic program can be characterized as the models of its completion and loop formulas. These results provide a basis for computing answer sets of disjunctive programs with functions, by solvers for the Constraint Satisfaction Problem. The potential benefit in answer set computations for this approach has been demonstrated previously in the implementation called fasp. We also present a formulation of completion and loop formulas for disjunctive logic programs with variables. This paper focuses on the theoretical development of these extensions.

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References

  1. Bartholomew, M., Lee, J.: Stable models of formulas with intensional functions. In: KR 2012, Rome, Italy, pp. 2–12. AAAI Press (2012)

    Google Scholar 

  2. Baselice, S., Bonatti, P.A., Criscuolo, G.: On finitely recursive programs. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 89–103. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Brewka, G., Eiter, T., Truszczynski, M.: Answer set programming at a glance. Communications of the ACM 54(12), 92–103 (2011)

    Article  Google Scholar 

  4. Bria, A., Faber, W., Leone, N.: Normal Form Nested Programs. In: Hölldobler, S., Lutz, C., Wansing, H. (eds.) JELIA 2008. LNCS (LNAI), vol. 5293, pp. 76–88. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Cabalar, P.: A functional action language front-end. In: ASPOCP 2005 (July 2005), http://www.dc.fi.udc.es/~cabalar/asp05_C.pdf

  6. Calimeri, F., Cozza, S., Ianni, G., Leone, N.: Computable Functions in ASP: Theory and Implementation. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 407–424. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Chen, Y., Lin, F., Wang, Y., Zhang, M.: First-order loop formulas for normal logic programs. In: KR 2006, UK, pp. 298–307. AAAI Press (2006)

    Google Scholar 

  8. Erdem, E., Lifschitz, V.: Tight logic programs. Theory and Practice of Logic Programming 3(4-5), 499–518 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Erdoğan, S.T., Lifschitz, V.: Definitions in answer set programming. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 483–484. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Ferraris, P., Lee, J., Lifschitz, V.: Stable models and circumscription. Artificial Intelligence 175(1), 236–263 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: ICLP 1988, Seattle, Washington, pp. 1070–1080. MIT Press (1988)

    Google Scholar 

  12. Giunchiglia, E., Lierler, Y., Maratea, M.: Answer set programming based on propositional satisfiability. Journal of Automated Reasoning 36(4), 345–377 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lee, J.: A model-theoretic counterpart of loop formulas. In: IJCAI 2005, Edinburgh, Scotland, UK, pp. 503–508. Professional Book Center (2005)

    Google Scholar 

  14. Lee, J., Meng, Y.: First-order stable model semantics and first-order loop formulas. J. Artif. Intell. Res. (JAIR) 42, 125–180 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Lee, J., Lifschitz, V.: Loop formulas for disjunctive logic programs. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 451–465. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  16. 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  MathSciNet  Google Scholar 

  17. Lifschitz, V.: Foundations of logic programming. In: Principles of Knowledge Representation, pp. 69–127. CSLI Publications (1996)

    Google Scholar 

  18. Lifschitz, V.: Logic programs with intensional functions. In: KR 2012, Rome, Italy, pp. 24–31. AAAI Press (2012)

    Google Scholar 

  19. Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Transactions on Computational Logic 2(4), 526–541 (2001)

    Article  MathSciNet  Google Scholar 

  20. Lifschitz, V., Razborov, A.A.: Why are there so many loop formulas? ACM Transactions on Computational Logic 7(2), 261–268 (2006)

    Article  MathSciNet  Google Scholar 

  21. Lifschitz, V., Tang, L.R., Turner, H.: Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25(3-4), 369–389 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lin, F., Wang, Y.: Answer set programming with functions. In: KR 2008, Sydney, Australia, pp. 454–464. AAAI Press (2008)

    Google Scholar 

  23. Lin, F., Zhao, Y.: ASSAT: computing answer sets of a logic program by SAT solvers. Artificial Intelligence 157(1-2), 115–137 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  24. Liu, L., Truszczynski, M.: Properties and applications of programs with monotone and convex constraints. JAIR 27, 299–334 (2006)

    MathSciNet  MATH  Google Scholar 

  25. Wiktor Marek, V., Truszczynski, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: A 25-Year Perspective, pp. 375–398. Springer, Berlin (1999)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  27. Pearce, D., Valverde, A.: Towards a First Order Equilibrium Logic for Nonmonotonic Reasoning. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 147–160. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  28. Šimkus, M., Eiter, T.: \(\mathbb{FDNC}\): Decidable non-monotonic disjunctive logic programs with function symbols. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 514–530. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  29. Wang, Y., You, J.-H., Lin, F., Yuan, L.-Y., Zhang, M.: Weight constraint programs with evaluable functions. AMAI 60(3-4), 341–380 (2010)

    MathSciNet  MATH  Google Scholar 

  30. Yang, B., Zhang, M., Zhang, Y.: Applying answer set programming to points-to analysis of object-oriented language. In: Huang, D.-S., Gan, Y., Bevilacqua, V., Figueroa, J.C. (eds.) ICIC 2011. LNCS, vol. 6838, pp. 676–685. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  31. You, J.-H., Yuan, L.-Y., Mingyi, Z.: On the equivalence between answer sets and models of completion for nested logic programs. In: IJCAI 2003, Acapulco, Mexico, pp. 859–866. Morgan Kaufmann (2003)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Guizhou University, Guiyang, China

    Yisong Wang

  2. Department of Computing Science, University of Alberta, Canada

    Jia-Huai You

  3. Chongqing University of Arts and Sciences, China

    Mingyi Zhang

  4. Guizhou Academy of Sciences, Guiyang, China

    Mingyi Zhang

Authors
  1. Yisong Wang
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  2. Jia-Huai You
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  3. Mingyi Zhang
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Editor information

Editors and Affiliations

  1. International Institute for Software Technology, United Nations University, P.O. Box 3058, Macau, China

    Zhiming Liu

  2. Department of Computer Science, University of York, Deramore Lane, YO10 5GH, York, UK

    Jim Woodcock

  3. Software Engineering Institute, East China Normal University, 3663 Zhongshan Road (North), 200062, Shanghai, China

    Huibiao Zhu

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Wang, Y., You, JH., Zhang, M. (2013). Embedding Functions into Disjunctive Logic Programs. In: Liu, Z., Woodcock, J., Zhu, H. (eds) Theoretical Aspects of Computing – ICTAC 2013. ICTAC 2013. Lecture Notes in Computer Science, vol 8049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39718-9_21

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  • DOI: https://doi.org/10.1007/978-3-642-39718-9_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39717-2

  • Online ISBN: 978-3-642-39718-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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