Advertisement

Argumentation-Based Semantics for Logic Programs with First-Order Formulae

  • Phan Minh DungEmail author
  • Tran Cao Son
  • Phan Minh Thang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9862)

Abstract

This paper studies different semantics of logic programs with first order formulae under the lens of argumentation framework. It defines the notion of an argumentation-based answer set and the notion of an argumentation-based well-founded model for programs with first order formulae. The main ideas underlying the new approach lie in the notion of a proof tree supporting a conclusion given a program and the observation that proof trees can be naturally employed as arguments in an argumentation framework whose stable extensions capture the program’s well-justified answer semantics recently introduced in [23]. The paper shows that the proposed approach to dealing with programs with first order formulae can be easily extended to a generalized class of logic programs, called programs with FOL-representable atoms, that covers various types of extensions of logic programming proposed in the literature such as weight constraint atoms, aggregates, and abstract constraint atoms. For example, it shows that argumentation-based well-founded model is equivalent to the well-founded model in [27] for programs with abstract constraint atoms. Finally, the paper relates the proposed approach to others and discusses possible extensions.

Keywords

Logic Program Logic Programming Argumentation Framework Proof Tree Order Formula 
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.

References

  1. 1.
    Balduccini, M., Gelfond, M., Watson, R., Nogueira, M.: The USA-Advisor: a case study in answer set planning. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 439–442. Springer, Heidelberg (2001)Google Scholar
  2. 2.
    Baral, C.: Knowledge Representation, Reasoning, and Declarative Problem Solving with Answer Sets. Cambridge University Press, Cambridge (2003)CrossRefzbMATHGoogle Scholar
  3. 3.
    Baral, C., Provetti, A., Son, T.C. (eds.): Theory and Practice of Logic Programming Special Issue on Answer Set Programming, vol. 3. Cambridge Univeristy Press, Cambridge (2003)Google Scholar
  4. 4.
    Bartholomew, M., Lee, J., Meng, Y.: First-order extension of the FLP stable model semantics via modified circumscription. In: IJCAI 2011, pp. 724–730. IJCAI/AAAI (2011)Google Scholar
  5. 5.
    Bondarenko, A., Dung, P.M., Kowalski, R.A., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artif. Intell. 93, 63–101 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chisham, B., Pontelli, E., Son, T.C., Wright, B.: Cdaostore: a phylogenetic repository using logic programming and web services. In: Gallagher, J.P., Gelfond, M. (eds.) Technical Communications, ICLp 2011, pp. 209–219 (2011)Google Scholar
  7. 7.
    Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  8. 8.
    Dung, P.M.: An argumentation-theoretic foundations for logic programming. J. Log. Program. 22(2), 151–171 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77, 321–357 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Faber, W., Leone, N., Pfeifer, G.: Recursive aggregates in disjunctive logic programs: semantics and complexity. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 200–212. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Gebser, M., Guziolowski, C., Ivanchev, M., Schaub, T., Siegel, A., Thiele, S., Veber, P.: Repair and prediction (under inconsistency) in large biological networks with answer set programming. In: KR 2010, pp. 497–507. AAAI Press (2010)Google Scholar
  12. 12.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: LPICS, pp. 1070–1080 (1988)Google Scholar
  13. 13.
    Kakas, A., Mancarella, P.: Generalized stable models: a semantics for abduction. In: Proceedings of ECAI-90, pp. 385–391 (1990)Google Scholar
  14. 14.
    Lifschitz, V.: Answer set programming and plan generation. Artif. Intell. 138(1–2), 39–54 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lloyd, J.: Foundations of Logic Programming. Springer, Berlin (1987). Second, extended editionCrossRefzbMATHGoogle Scholar
  16. 16.
    Marek, V., Truszczyński, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: A 25-Year Perspective, pp. 375–398 (1999)Google Scholar
  17. 17.
    Marek, V.W., Niemelä, I., Truszczynski, M.: Logic programs with monotone abstract constraint atoms. TPLP 8(2), 167–199 (2008)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Niemelä, I.: Logic programming with stable model semantics as a constraint programming paradigm. Ann. Math. Artif. Intell. 25(3,4), 241–273 (1999)CrossRefzbMATHGoogle Scholar
  19. 19.
    Niemelä, I., Simons, P., Soininen, T.: Stable model semantics for weight constraint rules. In: LPNMR, pp. 315–332 (1999)Google Scholar
  20. 20.
    Pelov, N., Denecker, M., Bruynooghe, M.: Partial stable models for logic programs with aggregates. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 207–219. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  21. 21.
    Przymusinski, T.: Stable semantics for disjunctive programs. New Gener. Comput. 9(3,4), 401–425 (1991)CrossRefzbMATHGoogle Scholar
  22. 22.
    Schulz, C., Toni, F.: Logic programming in assumption-based argumentation revisited - semantics and graphical representation. In: AAAI 2015, pp. 1569–1575. AAAI Press (2015)Google Scholar
  23. 23.
    Shen, Y., Wang, K., Eiter, T., Fink, M., Redl, C., Krennwallner, T., Deng, J.: FLP answer set semantics without circular justifications for general logic programs. Artif. Intell. 213, 1–41 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Son, T.C., Pontelli, E.: A constructive semantic characterization of aggregates in answer set programming. Theory Pract. Logic Program. 7(03), 355–375 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Son, T.C., Pontelli, E., Tu, P.H.: Answer sets for logic programs with arbitrary abstract constraint atoms. In: AAAI (2006)Google Scholar
  26. 26.
    Van Gelder, A., Ross, K., Schlipf, J.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)MathSciNetzbMATHGoogle Scholar
  27. 27.
    Wang, Y., Lin, F., Zhang, M., You, J.: A well-founded semantics for basic logic programs with arbitrary abstract constraint atoms. In: AAAI (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Phan Minh Dung
    • 1
    Email author
  • Tran Cao Son
    • 2
  • Phan Minh Thang
    • 3
  1. 1.Department of Computer ScienceAsian Institute of TechnologyKlong LuangThailand
  2. 2.Department of Computer ScienceNew Mexico State UniversityLas CrucesUSA
  3. 3.Department of Computer ScienceBurapha University International CollegeBangsaenThailand

Personalised recommendations