The examples in this paper all circumscribe the predicate ab. However, they differ in what they take as variable in the circumscription. The declarative expression of common sense requires that we be definite about what is circumscribed and what is variable in the circumscription. We have the following objectives.
1. The general facts of common sense are described by a collection of sentences that are not oriented in advance to particular problems.
2. It is prescribed how to express the facts of particular situations including the goals to be achieved.
3. The general system prescribes what is to be circumscribed and what is variable.
4. Once the facts to be taken into account are chosen, the circumscription process proceeds in a definite way resulting in a definite theory -- in general second order.
5. The conclusions reached taking a given set of facts into account are intuitively reasonable.
These objectives are the same as those of (McCarthy 1959) except that that paper used only monotonic reasoning.
The examples of this paper suggest defining a simple abnormality formalism used as follows.
1. The general facts include ab and a variety of aspects.
2. The specific facts do not involve ab.
3. The circumscription of ab is done with all predicates variable. This means that the axioms must be sufficient to tie them down.
I had hoped that the simple abnormality formalism would be adequate to express common sense knowledge. Unfortunately, this seems not to be the case. Consider the following axioms.
We ask whether Tweety flies. Simply circumscribing ab leaves this undecided, because Tweety can either be abnormal in aspect1 or in aspect3. Common sense tells us that we should conclude that Tweety flies. This can be achieved by preferring to have Tweety abnormal in aspect1 to having Tweety abnormal in aspect3. It is not yet clear whether this can be done using the simple circumscriptive formalism. Our approach to solving this problem is discussed in the following section on prioritized circumscription. However, simple abnormality theories may be adequate for an interesting set of common sense axiomatizations.