Procedural semantics for fuzzy disjunctive programs on residuated lattices

Abstract

In the paper, we present a procedural semantics for fuzzy disjunctive programs - sets of graded implications of the form: (h1V ⋯Vhn ← b1 & ⋯ & bm, c) (n > 0, m ≥ 0) where hi, bj are atoms and c a truth degree from a complete residuated lattice L = (L,≤,∨,∧,*, ⇒,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. © Springer-Verlag 2004.