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

$\operatorname {pattern-of} (Z,X)=s(Z)\times (P(Z|X)-P(Z|\neg X))^{+}$ 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 $(P(Z|X)-P(Z|\neg X))^{+}$ . Note that $(x)^{+}$ is the positive part of $x$ .

See PredicateFormulaLink 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 $Z$ , if

$(P(Z|\neg A) that is Z is a pattern of A, then it entails that

$(P(Z|\neg \neg A)>P(Z|\neg A)$ that is $Z$ is not a pattern of $\neg A$ , thus $A$ and $\neg A$ have no pattern in common.

Interestingly though it should be noted that

ExtensionalSimilarityLink <0, 1>
A