# IntensionalSimilarityLink

A type of Link used to describe intensional similarity between concepts.

## PLN Semantics

In PLN the IntensionalSimilarityLink between 2 concepts corresponds to the extensional similarity of their patterns (supersets, accounting for their simplicity). Formally

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 .

See FormulaPredicateLink for an example of specifying formulas in Atomese.

### Properties

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.