The importance of open and recursive circumscription (Q1117210)

The problems of inconsistency, incompleteness etc. of circumscription are considered. \textit{P. L. Mott} [Artif. Intell. 31, 87-98 (1987; Zbl 0624.68082)] proposed two restrictions of standad circumscription, called closed and non-recursive circumscription. Mott's propositions are criticized here. In particular, closed circumscription used very unnaturally binding of free variables in substitutional frameworks. According to the authors, Mott's restrictions are too hard. The arguments for open and recursive circumscription \((=\) standard) are given.