Weak and Strong Disjunction in Possibilistic ASP

  • Kim Bauters
  • Steven Schockaert
  • Martine De Cock
  • Dirk Vermeir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6929)


Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating certainty values with rules. The resulting framework allows to combine both non-monotonic reasoning and reasoning under uncertainty in a single framework. While PASP has been well-studied for possibilistic definite and possibilistic normal programs, we argue that the current semantics of possibilistic disjunctive programs are not entirely satisfactory. The problem is twofold. First, the treatment of negation-as-failure in existing approaches follows an all-or-nothing scheme that is hard to match with the graded notion of proof underlying PASP. Second, we advocate that the notion of disjunction can be interpreted in several ways. In particular, in addition to the view of ordinary ASP where disjunctions are used to induce a non-deterministic choice, the possibilistic setting naturally leads to a more epistemic view of disjunction. In this paper, we propose a semantics for possibilistic disjunctive programs, discussing both views on disjunction. Extending our earlier work, we interpret such programs as sets of constraints on possibility distributions, whose least specific solutions correspond to answer sets.


Possibility Distribution Possibilistic Logic Disjunctive Program Stable Model Semantic Extend Logic Program 
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.
    Baral, C.: Knowledge, Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)CrossRefzbMATHGoogle Scholar
  2. 2.
    Baral, C., Gelfond, M., Rushton, N.: Probabilistic reasoning with answer sets. Theory and Practice of Logic Programming 9(1), 57–144 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bauters, K., Schockaert, S., De Cock, M., Vermeir, D.: Possibilistic answer set programming revisited. In: Proc. of UAI 2010 (2010)Google Scholar
  4. 4.
    Confalonieri, R., Nieves, J.C., Vázquez-Salceda, J.: Pstable semantics for logic programs with possibilistic ordered disjunction. In: Proc. of AI*IA 2009, pp. 52–61 (2009)Google Scholar
  5. 5.
    Damásio, C.V., Pereira, L.M.: Monotonic and residuated logic programs. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 748–759. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Dubois, D., Lang, J., Prade, H.: Towards possibilistic logic programming. In: Proc. of ICLP 1991, pp. 581–595 (1991)Google Scholar
  7. 7.
    Dubois, D., Lang, J., Prade, H.: Possibilistic logic. Handbook of Logic for Artificial Intelligence and Logic Programming 3(1), 439–513 (1994)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Dubois, D., Prade, H.: Can we enforce full compositionality in uncertainty calculi? In: Proc. of AAAI 1994, pp. 149–154 (1994)Google Scholar
  9. 9.
    Dubois, D., Prade, H., Schockaert, S.: Rules and meta-rules in the framework of possibility theory and possibilistic logic. Scientia Iranica (to appear, 2011)Google Scholar
  10. 10.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385 (1991)CrossRefzbMATHGoogle Scholar
  11. 11.
    Gelfond, M., Lifzchitz, V.: The stable model semantics for logic programming. In: Proc. of ICLP 1988, pp. 1081–1086 (1988)Google Scholar
  12. 12.
    Lifschitz, V., Schwarz, G.: Extended logic programs as autoepistemic theories. In: Proc. of LPNMR 1993, pp. 101–114 (1993)Google Scholar
  13. 13.
    Nicolas, P., Garcia, L., Stéphan, I., Lefèvre, C.: Possibilistic uncertainty handling for answer set programming. Annals of Mathematics and Artificial Intelligence 47(1–2), 139–181 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Nieves, J.C., Osorio, M., Cortés, U.: Semantics for possibilistic disjunctive programs. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 315–320. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Osorio, M., Pérez, J.A.N., Ramírez, J.R.A., Macías, V.B.: Logics with common weak completions. Journal of Logic and Computation 16(6), 867–890 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5(2), 285–309 (1955)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 3–28 (1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kim Bauters
    • 1
  • Steven Schockaert
    • 1
  • Martine De Cock
    • 1
  • Dirk Vermeir
    • 2
  1. 1.Department of Applied Mathematics and Computer ScienceUniversiteit GentGentBelgium
  2. 2.Department of Computer ScienceVrije Universiteit BrusselBrusselBelgium

Personalised recommendations