Qualified Logic Programming with Bivalued Predicates

Research on the field of uncertainty in logic programming has evolved during the last 25 years. In a recent paper [M. Rodríguez-Artalejo and C.A. Romero-Díaz. Quantitative logic programming revisited. In J. Garrigue and M. Hermenegildo, editors, Functional and Logic Programming (FLOPS'08), volume 4989 of LNCS, pages 272–288. Springer Verlag, 2008] we have revised a classical approach by van Emden's to Quantitative Logic Programming [M.H. van Emden. Quantitative deduction and its fixpoint theory. Journal of Logic Programming, 3(1):37–53, 1986], generalizing it to a generic scheme QLP(D) for so-called Qualified Logic Programming over a parametrically given domain D, whose elements play the role of generalized truth values and can be used to qualify logical assertions. In this paper we present an extension of QLP(D) yielding a more expressive scheme BQLP(D), which supports a simple kind of negation based on bivalued predicates and allows threshold constraints in clause bodies in order to impose lower bounds to the qualifications computed by program clauses. The new scheme has a rigorous declarative semantics and a sound and strongly complete goal resolution procedure which can be efficiently implemented using constraint logic programming technology.