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On Reachability of Minimal Models of Multilattice-Based Logic Programs

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MICAI 2007: Advances in Artificial Intelligence (MICAI 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4827))

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Abstract

In this paper some results are obtained regarding the existence and reachability of minimal fixed points for multiple-valued functions on a multilattice. The concept of inf-preserving multi-valued function is introduced, and shown to be a sufficient condition for the existence of minimal fixed point; then, we identify a sufficient condition granting that the immediate consequence operator for multilattice-based fuzzy logic programs is sup-preserving and, hence, computes minimal models in at most ω iterations.

Partially supported by Andalusian project P06-FQM-02049 and Spanish project TIN2006-15455-C03-01.

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References

  1. Damásio, C., 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)

    Chapter  Google Scholar 

  2. Vojtáš, P.: Fuzzy logic programming. Fuzzy sets and systems 124(3), 361–370 (2001)

    Article  MathSciNet  Google Scholar 

  3. Medina, J., Ojeda-Aciego, M.: Multi-adjoint logic programming with continuous semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 351–364. Springer, Heidelberg (2001)

    Google Scholar 

  4. Fitting, M.: Bilattices and the semantics of logic programming. Journal of Logic Programming 11, 91–116 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  5. Loyer, Y., Straccia, U.: Epistemic foundation of the well-founded semantics over bilattices. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 513–524. Springer, Heidelberg (2004)

    Google Scholar 

  6. Lakshmanan, L.V.S., Sadri, F.: On a theory of probabilistic deductive databases. Theory and Practice of Logic Programming 1(1), 5–42 (2001)

    Article  MathSciNet  Google Scholar 

  7. Rounds, W., Zhang, G.-Q.: Clausal logic and logic programming in algebraic domains. Information and Computation 171, 183–200 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Benado, M.: Les ensembles partiellement ordonnés et le théorème de raffinement de Schreier, II. Théorie des multistructures. Czechoslovak Mathematical Journal 5(80), 308–344 (1955)

    MathSciNet  Google Scholar 

  9. Hansen, D.: An axiomatic characterization of multilattices. Discrete Mathematics 1, 99–101 (1981)

    Article  Google Scholar 

  10. Martínez, J., Gutiérrez, G., de Guzmán, I., Cordero, P.: Generalizations of lattices via non-deterministic operators. Discrete Mathematics 295, 107–141 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Multi-lattices as a basis for generalized fuzzy logic programming. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds.) WILF 2005. LNCS (LNAI), vol. 3849, pp. 61–70. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: A fixed-point theorem for multi-valued functions with application to multilattice-based logic programming. Lect. Notes in Computer Science, vol. 4578, pp. 37–44 (2007)

    Google Scholar 

  13. Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Fuzzy logic programming via multilattices. Fuzzy Sets and Systems 158(6), 674–688 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. d’Orey, V.: Fixed point theorems for correspondences with values in a partially ordered set and extended supermodular games. Journal of Mathematical Economics 25, 345–354 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  15. Echenique, F.: A short and constructive proof of Tarski’s fixed-point theorem. International Journal of Game Theory 33, 215–218 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. Stouti, A.: A generalized Amman’s fixed point theorem and its application to Nash equilibrium. Acta Mathematica Academiae Paedagogicae Nyíregyháziensis 21, 107–112 (2005)

    MATH  MathSciNet  Google Scholar 

  17. Zhou, L.: The set of Nash equilibria of a supermodular game is a complete lattice. Games and economic behavior 7, 295–300 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  18. Khamsi, M.A., Misane, D.: Fixed point theorems in logic programming. Annals of Mathematics and Artificial Intelligence 21, 231–243 (1997)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dept. Matemática Aplicada. Universidad de Málaga,  

    Jesús Medina, Manuel Ojeda-Aciego & Jorge Ruiz-Calviño

Authors
  1. Jesús Medina
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  2. Manuel Ojeda-Aciego
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  3. Jorge Ruiz-Calviño
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Alexander Gelbukh Ángel Fernando Kuri Morales

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Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J. (2007). On Reachability of Minimal Models of Multilattice-Based Logic Programs. In: Gelbukh, A., Kuri Morales, Á.F. (eds) MICAI 2007: Advances in Artificial Intelligence. MICAI 2007. Lecture Notes in Computer Science(), vol 4827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76631-5_26

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  • DOI: https://doi.org/10.1007/978-3-540-76631-5_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76630-8

  • Online ISBN: 978-3-540-76631-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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