Page 100 - DCAP506_ARTIFICIAL_INTELLIGENCE

Artificial Intelligence

Notes 7.5 Circumscription

Circumscription is a rule of speculation that permits you to come to the conclusion that the objects
you can demonstrate that posses some property, p, are actually all the objects that posses that
property.
Circumscription can also deal with default reasoning.
Assume we know: bird(tweety)

 x: penguin(x) bird(x)
 x: penguin(x) flies(x)
and we desire to insert the truth that naturally, birds fly.

In circumscription this phrase would be specified as:
A bird will fly if it is not abnormal
and can therefore be represented by:
 x: bird(x)  abnormal(x)  flies(x).
Though, this is not enough, we cannot conclude

flies(tweety)
as we cannot prove
abnormal(tweety).

This is where we pertain circumscription and, in this case, we will suppose that those things that are
exposed to be abnormal are the only things to be abnormal
So we can rewrite our default rule as:

 x: bird(x)  flies(x)  abnormal(x)
and add the following
 x: abnormal(x)
as there is nothing that cannot be exposed to be abnormal.
If we now insert the truth:

penguin(tweety)
Evidently we can prove
abnormal(tweety).

If we circumscribe abnormal now we would adjoin the sentence,
a penguin (tweety) is the abnormal thing:
 x: abnormal(x)  penguin(x).

Did u know? The difference between Default logic and circumscription:
Defaults are sentences in language itself, not supplementary inference rules.

94 LOVELY PROFESSIONAL UNIVERSITY