Strong Negation in Well-Founded and Partial Stable Semantics for Logic Programs

A formalism called partial equilibrium logic (PEL) has recently been proposed as a logical foundation for the well-founded semantics (WFS) of logic programs. In PEL one defines a class of minimal models, called partial equilibrium models, in a non-classical logic, HT . On logic programs partial equilibrium models coincide with Przymusinski’s partial stable (p-stable) models, so that PEL can be seen as a way to extend WFS and p-stable semantics to arbitrary propositional theories. We study several extensions of PEL with strong negation and compare these with previous systems extending WFS with explicit negation, notably WSFX [10] and p-stable models with “classical” negation [11].