Completeness results for circumscription

We investigate the model theory of the notion of circumscription, and find completeness theorems that provide a partial converse to a result of McCarthy. We show that the circumscriptive theorems are precisely the truths of the minimal models, in the case of various classes of theories, and for various versions of circumscription. We also present an example of commonsense reasoning in which first-order circumscription does not achieve the intuitive and desired minimization.