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Multi-lattices as a Basis for Generalized Fuzzy Logic Programming

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3849))

Abstract

A prospective study of the use of ordered multi-lattices as underlying sets of truth-values for a generalised framework of logic programming is presented. Specifically, we investigate the possibility of using multi-lattice-valued interpretations of logic programs and the theoretical problems that this generates with regard to its fixed point semantics.

Partially supported by Spanish DGI project TIC2003-09001-C02-01.

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References

  1. Benado, M.: Les ensembles partiellement ordonnés et le théorème de raffinement de Schreier, II. Théorie des multistructures. Czech. Math. J. 5(80), 308–344 (1955)

    MathSciNet  Google Scholar 

  2. Cordero, P., Gutiérrez, G., Martínez, J., de Guzmán, I.P.: A new algebraic tool for automatic theorem provers. Ann. Math. and Artif. Intelligence 42(4), 369–398 (2004)

    Article  MATH  Google Scholar 

  3. 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 (LNAI), vol. 3229, pp. 260–273. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Damásio, C., Pereira, L.: 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 

  5. Hansen, D.: An axiomatic characterization of multi-lattices. Discrete Mathematics 1, 99–101 (1981)

    Article  Google Scholar 

  6. Khamsi, M.A., Misane, D.: Fixed point theorems in logic programming. Ann. Math. and Artif. Intelligence 21, 231–243 (1997)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. Martínez, J., Gutiérrez, G., de Guzmán, I.P., Cordero, P.: Generalizations of lattices looking at computation. Discrete Mathematics 295, 107–141 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Medina, J., Ojeda-Aciego, M., Vojtáš, P.: 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 

  10. Ran, A., Reurings, M.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. of the AMS 132(5), 1435–1443 (2003)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. Stouti, A.: A fuzzy version of Tarski’s fixpoint theorem. Archivum mathematicum 40, 273–279 (2004)

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J. (2006). Multi-lattices as a Basis for Generalized Fuzzy Logic Programming. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds) Fuzzy Logic and Applications. WILF 2005. Lecture Notes in Computer Science(), vol 3849. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11676935_8

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  • DOI: https://doi.org/10.1007/11676935_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32529-1

  • Online ISBN: 978-3-540-32530-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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