Procedural Semantics for Fuzzy Disjunctive Programs on Residuated Lattices

  • Dušan Guller
Conference paper

DOI: 10.1007/978-3-540-24698-5_55

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)
Cite this paper as:
Guller D. (2004) Procedural Semantics for Fuzzy Disjunctive Programs on Residuated Lattices. In: Farach-Colton M. (eds) LATIN 2004: Theoretical Informatics. LATIN 2004. Lecture Notes in Computer Science, vol 2976. Springer, Berlin, Heidelberg

Abstract

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.

Keywords

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

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

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