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An introduction to fuzzy answer set programming

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Abstract

In this paper we show how the concepts of answer set programming and fuzzy logic can be successfully combined into the single framework of fuzzy answer set programming (FASP). The framework offers the best of both worlds: from the answer set semantics, it inherits the truly declarative non-monotonic reasoning capabilities while, on the other hand, the notions from fuzzy logic in the framework allow it to step away from the sharp principles used in classical logic, e.g., that something is either completely true or completely false. As fuzzy logic gives the user great flexibility regarding the choice for the interpretation of the notions of negation, conjunction, disjunction and implication, the FASP framework is highly configurable and can, e.g., be tailored to any specific area of application. Finally, the presented framework turns out to be a proper extension of classical answer set programming, as we show, in contrast to other proposals in the literature, that there are only minor restrictions one has to demand on the fuzzy operations used, in order to be able to retrieve the classical semantics using FASP.

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References

  1. Alsinet, T., Godo, L., Sandri, S.: Two formalisms of extended possibilistic logic programming with context-dependent fuzzy unification: a comparative description. Electr. Notes Theor. Comput. Sci. 66(5), 1–21 (2002)

    Article  Google Scholar 

  2. Balduccini, M., Gelfond, M.: Logic programs with consistency-restoring rules. In: Proceedings of the International Symposium on Logical Formalization of Commonsense Reasoning, AAAI 2003 Spring Symposium Series (2003)

  3. Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge Press (2003)

  4. Birkhoff, G.: Lattice Theory, vol. 25, 3rd edn. American Mathematical Society Colloquium Publications (1967)

  5. Brewka, G.: Logic programming with ordered disjunction. In: Proceedings of the 18th National Conference on Artificial Intelligence and Fourteenth Conference on Innovative Applications of Artificial Intelligence, July 2002, pp. 100–105. AAAI Press (2002)

  6. Brewka, G., Eiter, T.: Preferred answer sets for extended logic programs. Artif. Intell. 109(1–2), 297–356 (April 1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Buccafurri, F., Leone, N., Rullo, P.: Strong and weak constraints in disjunctive datalog. In: Proceedings of the 4th International Conference on Logic Programming (LPNMR ’97), pp. 2–17 (1997)

  8. Damasio, C.V., Pereira, L.M.: Sorted monotonic logic programs and their embedding. In: Proceedings of the 10th Intl. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU-04), pp. 807–814 (2004)

  9. Damasio, C.V., Medina, J., Ojeda-Aciego, M.: Sorted multi-adjoint logic programs: termination results and applications. Lect. Notes Comput. Sci. 3229, 252–265 (2007)

    Article  MathSciNet  Google Scholar 

  10. De Vos, M., Vermeir, D.: On the role of negation in choice logic programs. In: Logic Programming and Non-Monotonic Reasoning Conference (LPNMR’99). LNAI, vol. 1730, pp. 236–246. Springer (1999)

  11. Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets Syst. 144(1), 3–23 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Eiter, T., Faber, W., Leone, N., Pfeifer, G.: The diagnosis frontend of the dlv system. AI Commun. 12(1–2), 99–111 (1999)

    MathSciNet  Google Scholar 

  13. Gabbay, D., Laenens, E., Vermeir, D.: Credulous vs. sceptical semantics for ordered logic programs. In: Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning, pp. 208–217. Morgan Kaufmann (1991)

  14. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Logic Programming, Proceedings of the Fifth International Conference and Symposium, August 1988, pp. 1070–1080. Seattle, Washington, The MIT Press. (1988)

    Google Scholar 

  15. Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9(3–4), 365–386 (1991)

    Article  Google Scholar 

  16. Dix, D.N.J., Kuter, U.: Planning in answer set programming using ordered task decomposition. In: Proceedings of the 27th German Annual Conference on Artificial Intelligence (KI ’03). LNAI, vol. 2821, pp. 490–504. Springer (2003)

  17. Mateis, C.: Extending disjunctive logic programming by t-norms. In: Proceedings of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR99), LNAI, vol. 1730, pp. 290–304. Springer (1999)

  18. Nicolas, P., Garcia, L., Stéphan, I.: Possibilistic stable models. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence, pp. 248–253 (2005)

  19. Nicolas, P., Garcia, L., Stéphan, I., Lefèvre, C.: Possibilistic uncertainty handling for answer set programming. Ann. Math. Artif. Intell. 47(1–2), 139–181 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  20. Nogueira, M., Balduccini, M., Gelfond, M., Watson, R., Barry, M.: An a-prolog decision support system for the space shuttle. In: Third International Symposium on Practical Aspects of Declarative Languages. LNCS, vol. 1990, pp. 169–183. Springer (2001)

  21. Novák, V., Perfilieva, I., Moc̆kor̆, J.: Mathematical Principles of Fuzzy Logic. Kluwer (1999)

  22. Sacca, D., Zaniolo, C.: Stable models and non-determinism in logic programs with negation. In: PODS ’90: Proceedings of the Ninth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 205–217. ACM Press (1990)

  23. Soininen, T., Niemelä, I.: Developing a declarative rule language for applications in product configuration. In: Proceedings of the 1st International Workshop on Practical Aspects of Declarative Languages (PADL ’99). LNCS, vol. 1551, pp. 305–319. Springer (1999)

  24. 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-06) (2006)

  25. Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pac. J. Math. 5, 285–309 (1955)

    MATH  MathSciNet  Google Scholar 

  26. van Gelder, A., Ross, K.A., Schlipf, J.S.: Unfounded sets and well-founded semantics for general logic programs. In: Proceedings of the 7th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, March 1988, pp. 221–230. ACM Press, Austin, Texas, (1988)

    Chapter  Google Scholar 

  27. van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. Assoc. Comput. Mach. 38(3), 620–650 (1991)

    MATH  MathSciNet  Google Scholar 

  28. Van Nieuwenborgh, D., Vermeir, D.: Preferred answer sets for ordered logic programs. Theory Pract. Log. Program. 6(1–2), 107–167 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  29. Wagner, G.: A logical reconstruction of fuzzy inference in databases and logic programs. In: Proceedings of the International Fuzzy Set Association World Congress (IFSA’97) (1997)

  30. Yager, R.: Including importances in owa aggregations using fuzzy systems modeling. IEEE Trans. Fuzzy Syst. 6(2), 286–291 (1998)

    Article  Google Scholar 

  31. Zadeh, L.: Fuzzy logic and approximate reasoning. Synthese 30, 407–428 (1975)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Vrije Universiteit Brussel, VUB, Pleinlaan 2, 1050, Brussels, Belgium

    Davy Van Nieuwenborgh & Dirk Vermeir

  2. Department of Applied Mathematics and Computer Science, Universiteit Gent, UGent, Krijgslaan 281 (S9), 9000, Ghent, Belgium

    Martine De Cock

Authors
  1. Davy Van Nieuwenborgh
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  2. Martine De Cock
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  3. Dirk Vermeir
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Correspondence to Davy Van Nieuwenborgh.

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Van Nieuwenborgh, D., De Cock, M. & Vermeir, D. An introduction to fuzzy answer set programming. Ann Math Artif Intell 50, 363–388 (2007). https://doi.org/10.1007/s10472-007-9080-3

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