A Complete Calcultis for Possibilistic Logic Programming with Fuzzy Propositional Variables

Abstract

In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (ϕ, α), where ϕ is a many valued proposition and α ∈ [0, 1] is a lower bound on the belief on ϕ in terms of necessity measures. Belief states are modeled by possibility distributions on the set of all manyvalued interpretations. In this framework, (i) we define a syntax and a semantics of the general underlying uncertainty logic; (ii) we provide a modus ponens-style calculus for a sublanguage of Horn-rules and we prove that it is complete for determining the maximum degree of possibilistic belief with which a fuzzy propositional variable can be entailed from a set of formulas; and finally, (iii) we show how the computation of a partial matching between fuzzy propositional variables, in terms of necessity measures for fuzzy sets, can be included in our logic programming system.