Compiling Fuzzy Answer Set Programs to Fuzzy Propositional Theories

  • Jeroen Janssen
  • Stijn Heymans
  • Dirk Vermeir
  • Martine De Cock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5366)

Abstract

We show how a fuzzy answer set program can be compiled to an equivalent fuzzy propositional theory whose models correspond to the answer sets of the program. This creates a basis for constructing fuzzy answer set solvers, such as solvers based on fuzzy SAT-solvers or on linear programming.

Keywords

answer set programming fuzzy logic Clark’s completion fuzzy ASSAT 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lukasiewicz, T.: Fuzzy description logic programs under the answer set semantics for the semantic web. In: Proceedings of the Second International Conference on Rules and Rule Markup Languages for the Semantic Web (RuleML 2006), pp. 89–96. IEEE Computer Society, Los Alamitos (2006)CrossRefGoogle Scholar
  2. 2.
    Lukasiewicz, T., Straccia, U.: Tightly integrated fuzzy description logic programs under the answer set semantics for the semantic web. In: Marchiori, M., Pan, J.Z., de Sainte Marie, C. (eds.) RR 2007. LNCS, vol. 4524, pp. 289–298. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Van Nieuwenborgh, D., De Cock, M., Vermeir, D.: An introduction to fuzzy answer set programming. Annals of Mathematics and Artificial Intelligence 50(3-4), 363–388 (2007)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Damásio, C., Medina, J., Ojeda-Aciego, M.: Sorted multi-adjoint logic programs: termination results and applications. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS, vol. 3229, pp. 260–273. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Kifer, M., Subrahmanian, V.S.: Theory of generalized annotated logic programming and its applications. Journal of Logic Programming 12(3-4), 335–367 (1992)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Straccia, U.: Annotated answer set programming. In: Proceedings of the 11th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2006 (2006)Google Scholar
  7. 7.
    Hähnle, R.: Many-valued logic and mixed integer programming. Annals of Mathematics and Artificial Intelligence 12(3-4), 231–263 (1994)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Lepock, C., Pelletier, F.J.: Fregean algebraic tableaux: Automating inferences in fuzzy propositional logic. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS, vol. 3835, pp. 43–48. Springer, Heidelberg (2005)Google Scholar
  9. 9.
    Straccia, U.: Reasoning and experimenting within Zadeh’s fuzzy propositional logic. Technical report, Paris, France (2000)Google Scholar
  10. 10.
    Clark, K.L.: Negation as failure. In: Logic and Databases, pp. 293–322. Plenum Press, New York (1978)Google Scholar
  11. 11.
    Bell, C., Nerode, A., Ng, R.T., Subrahmanian, V.S.: Mixed integer programming methods for computing nonmonotonic deductive databases. Journal of the ACM 41(6), 1178–1215 (1994)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Lin, F., Zhao, Y.: ASSAT: computing answer sets of a logic program by sat solvers. Artificial Intelligence 157(1-2), 115–137 (2004)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1999)CrossRefMATHGoogle Scholar
  14. 14.
    Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)CrossRefMATHGoogle Scholar
  15. 15.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proceedings of the Fifth International Conference and Symposium on Logic Programming (ICLP/SLP 1988), ALP, IEEE, pp. 1081–1086. The MIT Press, Cambridge (1988)Google Scholar
  16. 16.
    van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. Journal of the Association for Computing Machinery 38(3), 620–650 (1991)MathSciNetMATHGoogle Scholar
  17. 17.
    Tarski, A.: A lattice theoretical fixpoint theorem and its application. Pacific Journal of Mathematics 5, 285–309 (1955)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jeroen Janssen
    • 1
  • Stijn Heymans
    • 2
  • Dirk Vermeir
    • 1
  • Martine De Cock
    • 2
  1. 1.Dept. of Computer ScienceVrije Universiteit BrusselBelgium
  2. 2.Dept. of Applied Mathematics and Computer ScienceUniversiteit GentBelgium

Personalised recommendations