Analysing and Extending Well-Founded and Partial Stable Semantics Using Partial Equilibrium Logic

Abstract

In [4] a nonmonotonic formalism called partial equilibrium logic (PEL) was proposed as a logical foundation for the well-founded semantics (WFS) of logic programs. PEL consists in defining a class of minimal models, called partial equilibrium (p-equilibrium), inside a non-classical logic called HT 2. In [4] it was shown that, on normal logic programs, p-equilibrium models coincide with Przymusinki’s partial stable (p-stable) models. This paper begins showing that this coincidence still holds for the more general class of disjunctive programs, so that PEL can be seen as a way to extend WFS and p-stable semantics to arbitrary propositional theories. We also study here the problem of strong equivalence for various subclasses of p-equilibrium models, investigate transformation rules and nonmonotonic inference, and consider a reduction of PEL to equilibrium logic. In addition we examine the behaviour of PEL on nested logic programs and its complexity in the general case.