# 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

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\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 **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle (P(Z|X) - P(Z|\neg X))^+}**
. Note that **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle (x)^+}**
is the positive part of **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x}**
.

See PredicateFormulaLink for an example of specifying formulas in Atomese.