A declarative semantics for depth-first logic programs

Abstract

Depth-first evaluation causes a gap between the result of the computation and the classical declarative semantics for logic programs. The paper presents a new semantics for logic programs closing that gap. Although not classical, this semantics, called biquantale semantics, is declarative, since it is based on a notion of validity in a certain class of models. Depth-first evaluation is sound and complete with respect to biquantale semantics. Thus, the computational result is exactly reflected. Complementing the model theoretic semantics by a proof theoretic one, a substructural calculus is presented which is sound and complete with respect to biquantale semantics. Although the main interest is in definite programs, we consider adding a form of negation. Both the model theoretic and the proof theoretic semantics can be generalised to programs with negation.