On semantics of logic programs with uncertainties

We will first attempt to give semantics for logic programs with uncertainties. Our basic definitions of logic programs with uncertainties follow. We will define a proof procedure for logic programs with uncertainties which corresponds to an interpreter and present a sufficient condition for certainty functions of clauses to achieve the completeness of the proof procedure. We study the finite-failure set with certainty threshold which is actually the implementation used to infer the negation as failure in logic programs with uncertainties. Then we will give an interesting characterization. This is the first attempt to consider the negation as failure in logic programs with uncertainties from the semantical point of view.