Adding closed world assumptions to well-founded semantics

Abstract

Given a program P we specify an enlargement of its well-founded model which gives meaning to the adding of closed world assumptions. We do so by proposing the desirable principles of a closed world assumption (CWA), and proceed to formally define and apply them to well-founded semantics (WFS), in order to obtain a WFS added with CWA, the O-semantics. After an introduction and motivating examples, there follow the presentation of the concepts required to formalize the model structure, the properties it enjoys, and the criteria and procedures which follow the precise characterization of the preferred unique maximal model that gives the intended meaning to the O-semantics of a program, the O-model. Some properties are also exhibited that permit a more expedite obtention of the models. Several detailed examples are introduced throughout to illustrate the concepts and their application. Comparison is made with other work, and in the conclusions the novelty of the approach is brought out.