A Logic for Reasoning about Well-Founded Semantics: Preliminary Report

The paper presents a preliminary solution to a long-standing problem in the foundations of well-founded semantics for logic programs. The problem addressed is this: which logic can be considered adequate for well-founded semantics (WFS) in the sense that its minimal models (appropriately defined) coincide with the partial stable models of a logic program? We approach this problem by identifying the HT 2 frames previously proposed by Cabalar [4] to capture WFS as structures of a kind used by Dosen [5] to characterise a family of logics weaker than intuitionistic and minimal logic. We identify partial stable models as minimal models in this semantics and we axiomatise the resulting logic.