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The classes of an ontology may be extensional or intensional in nature. A class
is extensional if and only if it is characterized solely by its membership. More
precisely, a class C is extensional if and only if for any class C', if C' has exactly
the same members as C, then C and C' are identical. If a class does not satisfy
this condition, then it is intensional. While extensional classes are more well-behaved
and well-undefrstood mathematically, as well as less problematic philosophically,
they do not permit the fine grained distinctions that ontologies often need to make.
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