Chapter

LATIN 2004: Theoretical Informatics

Volume 2976 of the series Lecture Notes in Computer Science pp 519-529

Procedural Semantics for Fuzzy Disjunctive Programs on Residuated Lattices

  • Dušan GullerAffiliated withInstitute of Informatics, Comenius University, Mlynská dolina

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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 h i , b j 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