Some time ago, McCarthy developed the domain circumscription formalism for closed‐world reasoning. Recently, attention has been directed towards other circumscriptive formalisms. The best known of these, predicate and formula circumscription, cannot be used to produce domain‐closure axioms; nor does it appear likely that the other forms can. Since these axioms are important in deductive database theory (and elsewhere), and since domain circumscription often can conjecture these axioms, there is reason to resurrect domain circumscription.

We focus on McCarthy's method of predicate circumscription in order to establish various results about its consistency, and about its ability to conjecture new information. A basic result is that predicate circumscription cannot account for the standard kinds of default reasoning. Another is that predicate circumscription yields no new information about the equality predicate. This has important consequences for the unique names and domain closure assumptions.