Procedural Semantics for Fuzzy Disjunctive Programs on Residuated Lattices

  • Dušan Guller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


In the paper, we present a procedural semantics for fuzzy disjunctive programs – sets of graded implications of the form:

\((h_1 \vee ... \vee h_n \longleftarrow b_1 \& ... \& b_m, c)~~~~~~~(n > 0, m \geq 0)\)

where hi, bj are atoms and c a truth degree from a complete residuated lattice

\(L = (L, \leq, \vee, \wedge, *, \Longrightarrow, 0, 1).\)

A graded implication can be understood as a means of the representation of incomplete and uncertain information; the incompleteness is formalised by the consequent disjunction of the implication, while the uncertainty by its truth degree. We generalise the results for Boolean lattices in [3] to the case of residuated ones. We take into consideration the non-idempotent triangular norm ⋆, instead of the idempotent ∧, as a truth function for the strong conjunction &. In the end, the coincidence of the proposed procedural semantics and the generalised declarative, fixpoint semantics from [4] will be reached.


Disjunctive logic programming multivalued logic programming fuzzy logic knowledge representation and reasoning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brass, S., Dix, J., Przymusinski, T.: Computation of the Semantics for Autoepistemic Beliefs. Artificial Intelligence 112(1-2), 104–123 (1999)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Brewka, G., Dix, J.: Knowledge Representation with Logic Programs. In: Handbook of Phil. Logic, ch. 6, 2nd edn., vol. 6. Oxford University Press, Oxford (2001)Google Scholar
  3. 3.
    Guller, D.: Procedural semantics for fuzzy disjunctive programs. In: Baaz, M., Voronkov, A. (eds.) LPAR 2002. LNCS (LNAI), vol. 2514, pp. 247–261. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Guller, D.: Model and fixpoint semantics for fuzzy disjunctive programs with weak similarity. In: Abraham, A., Jain, L.C., Zwaag, B.J. v.d. (eds.) Innovations in Intelligent Systems. Studies in Fuzziness and Soft Computing, vol. 140. Springer, Heidelberg (to appear, 2004)Google Scholar
  5. 5.
    Kifer, M., Lozinskii, E.L.: A logic for reasoning with inconsistency. Journal of Automated Reasoning 9(2), 179–215 (1992)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Kifer, M., Subrahmanian, V.S.: Theory of the generalized annotated logic programming and its applications. Journal of Logic Programming 12, 335–367 (1992)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Lukasiewicz, T.: Many-valued disjunctive logic programs with probabilistic semantics. In: Gelfond, M., Leone, N., Pfeifer, G. (eds.) LPNMR 1999. LNCS (LNAI), vol. 1730, pp. 277–289. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Lukasiewicz, T.: Fixpoint characterizations for many-valued disjunctive logic programs with probabilistic semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 336–350. Springer, Heidelberg (2001)Google Scholar
  9. 9.
    Mateis, C.: Extending disjunctive logic programming by t-norms. In: Gelfond, M., Leone, N., Pfeifer, G. (eds.) LPNMR 1999. LNCS (LNAI), vol. 1730, pp. 290–304. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    Mateis, C.: Quantitative disjunctive logic programming: semantics and computation. AI Communications 13(4), 225–248 (2000)MATHMathSciNetGoogle Scholar
  11. 11.
    Minker, J., Seipel, D.: Disjunctive Logic Programming: A Survey and Assessment. In: Kakas, A.C., Sadri, F. (eds.) Computational Logic: Logic Programming and Beyond. LNCS (LNAI), vol. 2407, pp. 472–511. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Subrahmanian, V.S.: On the semantics of quantitative logic programs. In: Proc. of the 4th IEEE Symposium on Logic Programming, Washington DC, pp. 173–182. Computer Society Press (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Dušan Guller
    • 1
  1. 1.Institute of InformaticsComenius University, Mlynská dolinaBratislavaSlovakia

Personalised recommendations