A Complete Calculus for Possibilistic Logic Programming with Fuzzy
  Propositional Variables
  In this paper we present a propositional logic programming language for
reasoning under possibilistic uncertainty and representing vague knowledge.
Formulas are represented by pairs (A, c), where A is a many-valued proposition
and c is value in the unit interval [0,1] which denotes a lower bound on the
belief on A in terms of necessity measures. Belief states are modeled by
possibility distributions on the set of all many-valued 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.
