Circumscribing Abnormality

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Circumscribing Abnormality

Extending a set of sentences by the closed world assumption for some relation constant , expressed by a default rule as shown above, has the same effect as circumscribing (with all object, function and relation constants varied). In particular, circumscribing abnormality can be expressed by the default rule

(<<= (not (ab ?aspect ?x)) (consis (not (ab ?aspect ?x))))

Consider, for instance, the nonmonotonic database that contains, in addition to this standard default, two facts.

(bird tweety)

(<= (flies ?x) (bird ?x) (not (ab aspect1 ?x)))

Birds fly unless they are abnormal in aspect1). This database nonmonotonically entails the conclusion that everything is not abnormal, including tweety:

(not (ab ?x))

From this, we can conclude that tweety flies.

Suppose, on the other hand, that our database includes also the fact that tweety is abnormal in aspect1:

(ab aspect1 Tweety)

In this case, we can no longer infer that tweety is not abnormal, and, therefore, we cannot conclude that tweety is a flier. Note, however, that we have not asserted that tweety cannot fly; we have only prevented the default rule from taking effect in this case.

Vishal I. Sikka
Wed Dec 7 13:23:42 PST 1994