A type of Link used to describe intensional similarity between concepts.
IntensionalSimilarityLink <TV> A B
is equivalent to
ExtensionalSimilarityLink <TV> SatisfyingSetLink LambdaLink $Z EvaluationLink GroundedPredicateNode "pattern-of" ListLink $Z X SatisfyingSetLink LambdaLink $Z EvaluationLink GroundedPredicateNode "pattern-of" ListLink $Z Y
where the pattern-of predicate is a GroundedPredicateNode defined so that
where s(Z) is the prior of Z, reflecting it's simplicity, that is the simpler Z and the stronger it's discriminating power over X, the more it is a pattern of X. For the discriminating power of Z over X we also say that X is attracted to Z, that we can represent with the following link
AttractionLink X Z
where the strength of the TV of such attraction link is . Note that is the positive part of .
Although IntensionalSimilarity is different than ExtensionalSimilarity they have properties in common. For instance
IntensionalSimilarityLink <0, 1> A NotLink A
holds for any A (even fuzzy). That is because given any , if
that is Z is a pattern of A, then it entails that
that is is not a pattern of , thus and have no pattern in common.
Interestingly though it should be noted that
ExtensionalSimilarityLink <0, 1> A NotLink A
only holds if A is not a fuzzy set, so in that regard extensional similarity is actually more permissive than intensional similarity.