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When an approximate concept becomes precise


Suppose an approximate concept represented by a predicate p(x) has a sufficient condition suff(x) and a necessary condition nec(x). Thus we have


In general the sufficient and the necessary conditions will not coincide, i.e. we will not have


However, they made coincide with some restriction on x, i.e. we may have


Another way an approximate concept may become definite is by a mapping from the space in which it is first formalized into more restricted space. We'll combine specialization with mapping in


where the function f maps a subset of the original domain into a specialized domain in which the concept p(x) becomes definite.

John McCarthy
Wed Feb 2 15:59:04 PST 2000