Circumscription is one of the major formalizations of nonmonotonic
reasoning. It however has several drawbacks. The first of thesee is
that the circumscription of a satisfiable theory can sometimes be
unsatisfiable. The second is that cirumscription does not deal well
with equality. These problems can be overcome by redefining
circumscription, and modifying the minimality criterion. Various different
possibilities are considered, and some are shown to be equivalent.