Abstract minimality and circumscription

摘要

In this paper, we present an alternative approach to the generalization of circumscription. Traditionally, the generalization of circumscription involves the change of ordering among models, while in the present study we only try to generalize the minimality criteria of models. We define the notion of abstractly minimal (or (P,Z)-minimal) models by isomorphism. Under this generalization we come up with the fact that some theories which are unsatisfiable in the original circumscription will be satisfiable now. Moreover, we prove that this generalization is completely coincident with the original circumscription in the case of well-founded theories.