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>
$Z EvaluationLink GroundedPredicateNode "pattern-of" ListLink$Z
X
$Z EvaluationLink GroundedPredicateNode "pattern-of" ListLink$Z
Y


where the pattern-of predicate is a GroundedPredicateNode defined so that

${\displaystyle \operatorname {pattern-of} (Z,X)=s(Z)\times (P(Z|X)-P(Z|\neg X))^{+}}$

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 ${\displaystyle (P(Z|X)-P(Z|\neg X))^{+}}$. Note that ${\displaystyle (x)^{+}}$ is the positive part of ${\displaystyle x}$.

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
A


holds for any A (even fuzzy). That is because given any ${\displaystyle Z}$, if

${\displaystyle (P(Z|\neg A)

that is Z is a pattern of A, then it entails that

${\displaystyle (P(Z|\neg \neg A)>P(Z|\neg A)}$

that is ${\displaystyle Z}$ is not a pattern of ${\displaystyle \neg A}$, thus ${\displaystyle A}$ and ${\displaystyle \neg A}$ have no pattern in common.

Interestingly though it should be noted that

ExtensionalSimilarityLink <0, 1>
A