General Domain Circumscription in its First-Order Reduction

We rst de ne general domain circumscription GDC and provide it with a semantics GDC subsumes existing domain circumscrip tion proposals in that it allows varying of arbitrary predicates functions or constants to maximize the minimization of the domain of a theory We then show that for the class of semi universal theories without func tion symbols that the domain circumscription of such theories can be constructively reduced to logically equivalent rst order theories by using an extension of the DLS algorithm previously proposed by the authors for reducing second order formulas We also isolate a class of domain cir cumscribed theories such that any arbitrary second order circumscrip tion policy applied to these theories is guaranteed to be reducible to a logically equivalent rst order theory In the case of semi universal the ories with functions and arbitrary theories which are not separated we provide additional results which although not guaranteed to provide re ductions in all cases do provide reductions in some cases These results are based on the use of xpoint reductions