Symbolic Execution and Thresholding for Efficiently Tuning Fuzzy Logic Programs

  • Ginés MorenoEmail author
  • Jaime Penabad
  • José A. Riaza
  • Germán Vidal
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10184)


Fuzzy logic programming is a growing declarative paradigm aiming to integrate fuzzy logic into logic programming. One of the most difficult tasks when specifying a fuzzy logic program is determining the right weights for each rule, as well as the most appropriate fuzzy connectives and operators. In this paper, we introduce a symbolic extension of fuzzy logic programs in which some of these parameters can be left unknown, so that the user can easily see the impact of their possible values. Furthermore, given a number of test cases, the most appropriate values for these parameters can be automatically computed. Finally, we show some benchmarks that illustrate the usefulness of our approach.


Fuzzy logic programming Symbolic execution Tuning 


  1. 1.
    Almendros-Jiménez, J.M., Bofill, M., Luna-Tedesqui, A., Moreno, G., Vázquez, C., Villaret, M.: Fuzzy XPath for the automatic search of fuzzy formulae models. In: Beierle, C., Dekhtyar, A. (eds.) SUM 2015. LNCS (LNAI), vol. 9310, pp. 385–398. Springer, Cham (2015). doi: 10.1007/978-3-319-23540-0_26 CrossRefGoogle Scholar
  2. 2.
    Almendros-Jiménez, J.M., Luna, A., Moreno, G.: Fuzzy XPath through fuzzy logic programming. New Gener. Comput. 33(2), 173–209 (2015)CrossRefGoogle Scholar
  3. 3.
    Ansótegui, C., Bofill, M., Manyà, F., Villaret, M.: Building automated theorem provers for infinitely-valued logics with satisfiability modulo theory solvers. In: Proceeding of ISMVL 2012, pp. 25–30 (2012)Google Scholar
  4. 4.
    Baldwin, J.F., Martin, T.P., Pilsworth, B.W.: Fril- Fuzzy and Evidential Reasoning in Artificial Intelligence. Wiley, New York (1995)Google Scholar
  5. 5.
    Barrett, C.W., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, 185, pp. 825–885. IOS Press (2009)Google Scholar
  6. 6.
    Bofill, M., Moreno, G., Vázquez, C., Villaret, M.: Automatic proving of fuzzy formulae with fuzzy logic programming and SMT. In: Fredlund, L.A. (ed.) Programming and Computer Languages 2013, vol. 64, p. 19. ECEASST (2013)Google Scholar
  7. 7.
    Ishizuka, M., Kanai, N.: Prolog-ELF incorporating fuzzy logic. In: Proceeding of the IJCAI 1985, pp. 701–703. Morgan Kaufmann (1985)Google Scholar
  8. 8.
    Julián, P., Medina, J., Moreno, G., Ojeda-Aciego, M.: Efficient thresholded tabulation for fuzzy query answering. In: Bouchon-Meunier, B., Magdalena, L., Ojeda-Aciego, M., Verdegay, J.L., Yager, R.R. (eds.) Foundations of Reasoning under Uncertainty. STUDFUZZ, vol. 249, pp. 125–149. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Julián, P., Moreno, G., Penabad, J.: Operational/interpretive unfolding of multi-adjoint logic programs. J. Univ. Comput. Sci. 12(11), 1679–1699 (2006)Google Scholar
  10. 10.
    Julián, P., Moreno, G., Penabad, J.: An improved reductant calculus using fuzzy partial evaluation techniques. Fuzzy Sets Syst. 160, 162–181 (2009). MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Julián-Iranzo, P., Moreno, G., Penabad, J., Vázquez, C.: A fuzzy logic programming environment for managing similarity and truth degrees. In: EPTCS, vol. 173, pp. 71–86 (2015).
  12. 12.
    Julián-Iranzo, P., Moreno, G., Penabad, J., Vázquez, C.: A declarative semantics for a fuzzy logic language managing similarities and truth degrees. In: Alferes, J.J.J., Bertossi, L., Governatori, G., Fodor, P., Roman, D. (eds.) RuleML 2016. LNCS, vol. 9718, pp. 68–82. Springer, Cham (2016). doi: 10.1007/978-3-319-42019-6_5 CrossRefGoogle Scholar
  13. 13.
    Kifer, M., Subrahmanian, V.S.: Theory of generalized annotated logic programming and its applications. J. Logic Program. 12, 335–367 (1992)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Lassez, J.L., Maher, M.J., Marriott, K.: Unification revisited. In: Foundations of Deductive Databases and Logic Programming, pp. 587–625. Morgan Kaufmann, Los Altos, CA (1988)Google Scholar
  15. 15.
    Lee, R.: Fuzzy logic and the resolution principle. J. ACM 19(1), 119–129 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Li, D., Liu, D.: A Fuzzy Prolog Database System. Wiley, New York (1990)Google Scholar
  17. 17.
    Lloyd, J.W.: Foundations of Logic Programming. Springer-Verlag, Berlin (1987)CrossRefzbMATHGoogle Scholar
  18. 18.
    Medina, J., Ojeda-Aciego, M., Vojtáš, P.: Similarity-based Unification: a multi-adjoint approach. Fuzzy Sets Syst. 146, 43–62 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Morcillo, P.J., Moreno, G., Penabad, J., Vázquez, C.: A practical management of fuzzy truth-degrees using FLOPER. In: Dean, M., Hall, J., Rotolo, A., Tabet, S. (eds.) RuleML 2010. LNCS, vol. 6403, pp. 20–34. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-16289-3_4 CrossRefGoogle Scholar
  20. 20.
    Moreno, G., Vázquez, C.: Fuzzy logic programming in action with FLOPER. J. Softw. Eng. Appl. 7, 237–298 (2014)CrossRefGoogle Scholar
  21. 21.
    Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic. Chapman & Hall, Boca Ratón (2006)zbMATHGoogle Scholar
  22. 22.
    Rodríguez-Artalejo, M., Romero-Díaz, C.A.: Quantitative logic programming revisited. In: Garrigue, J., Hermenegildo, M.V. (eds.) FLOPS 2008. LNCS, vol. 4989, pp. 272–288. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-78969-7_20 CrossRefGoogle Scholar
  23. 23.
    Straccia, U.: Managing uncertainty and vagueness in description logics, logic programs and description logic programs. In: Baroglio, C., Bonatti, P.A., Małuszyński, J., Marchiori, M., Polleres, A., Schaffert, S. (eds.) Reasoning Web. LNCS, vol. 5224, pp. 54–103. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-85658-0_2 CrossRefGoogle Scholar
  24. 24.
    Vidal, A., Bou, F., Godo, L.: An SMT-based solver for continuous t-norm based logics. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds.) SUM 2012. LNCS (LNAI), vol. 7520, pp. 633–640. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-33362-0_53 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ginés Moreno
    • 1
    Email author
  • Jaime Penabad
    • 2
  • José A. Riaza
    • 1
  • Germán Vidal
    • 3
  1. 1.Department of Computing SystemsUCLMAlbaceteSpain
  2. 2.Department of MathematicsUCLMAlbaceteSpain
  3. 3.MiST, DSICUniversitat Politècnica de ValènciaValenciaSpain

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