  In this paper, we consider a method of computing minimal models in
circumscription using integer programming in propositional logic and
first-order logic with domain closure axioms and unique name axioms. This kind
of treatment is very important since this enable to apply various technique
developed in operations research to nonmonotonic reasoning.
  Nerode et al. (1995) are the first to propose a method of computing
circumscription using integer programming. They claimed their method was
correct for circumscription with fixed predicate, but we show that their method
does not correctly reflect their claim. We show a correct method of computing
all the minimal models not only with fixed predicates but also with varied
predicates and we extend our method to compute prioritized circumscription as
well.
