On the relationship between well-founded and stable partial models

Abstract

The central issue of this paper is the definition of a new unifying semantics for ordered logic programs, called assumption-free semantics, capable of capturing different interesting semantics such as the well-founded and stable (partial model) semantics. It turns out that every ordered program possesses exactly one minimal assumption-free partial model which we call the well-founded partial model and one or more maximal assumption-free partial models called stable partial models. Moreover, this stable model semantics can be viewed as taking the best of the previous approaches for ordered programs while keeping their (common) underlying intuition. It is shown that the new concepts for ordered programs are proper generalizations of the corresponding concepts for classical logic programs, thus giving a new unifying definition for the traditional notions of well-founded and stable (partial) models. Furthermore, we discuss the relationship between stable and well-founded partial models, the main result being that the intersection of all stable partial models is exactly the well-founded partial model in all cases but a very special type of ordered programs, and map the results to the more restricted class of traditional logic programs.