Contradiction Removal within Well Founded Semantics

Our purpose is to deene a semantics that extends Well Founded Semantics for programs with classical negation, and which avoids the absence of models caused by contradictions brought about by closed world assumptions. This extension relies on allowing to take back such closed world assumptions, through making their truth value become undeened, and thus permiting noncontradictory models to appear. We take back such assumptions in a minimal way for all alternative ways of removing contradictions, by means of simple transformations of the original program. The transformed programs have contradiction free Well Founded Models. Moreover, we identify a unique model that deenes the semantics of the original program, which is included in all the alternative contradiction free models. This unique model coincides with the Well Founded Model when the latter is noncontradictory. The notions of minimality and contradiction removal employed are useful for dealing with Belief Revision. These techniques for removing contradictions in the sense of classical logic, are also adequate for removing contradiction in the sense of integrity constraints violation. Another important result is that our removal semantics (the contradiction removal semantics) is deened as the Well Founded Model of a derived program obtained by a simple transformation from the original one. Thus no new model determining algorithms are needed. For noncontradictory programs the two programs coincide.