(McCarthy 1980) introduces the circumscription method of nonmonotonic reasoning and gives motivation, some mathematical properties and some examples of its application. The present paper is logically self-contained, but motivation may be enhanced by reading the earlier paper. We don't repeat its arguments about the importance of nonmonotonic reasoning in AI, and its examples are instructive.
Here we give a more symmetric definition of circumscription and applications to the formal expression of common sense facts. Our long term goal (far from realized in the present paper) is to express these facts in a way that would be suitable for inclusion in a general purpose database of common sense knowledge. We imagine this database to be used by AI programs written after the initial preparation of the database. It would be best if the writers of these programs didn't have to be familiar with how the common sense facts about particular phenomena are expressed. Thus common sense knowledge must be represented in a way that is not specific to a particular application.
It turns out that many such common sense facts can be formalized in a uniform way. A single predicate ab, standing for ``abnormal'' is circumscribed with certain other predicates and functions considered as variables that can be constrained to achieve the circumscription subject to the axioms. This also seems to cover the use of circumscription to represent default rules.