# ExtensionalSimilarityLink

A type of Link used in OpenCog to define extensional implication.

For more information, see this page

## PLN Semantics

In PLN the ExtensionalSimilarityLink between 2 concepts is defined as
ratio between the common properties (or elements) of two nodes and the total properties (or elements) of these nodes, *i.e.*,

**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{sim}(A, B) = \frac{P(A \wedge B)}{P(A \vee B)}}**

where **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 \wedge}**
denotes the fuzzy intersection. The TV of the similarity of A and B can also be seen as the TV of concept **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 A \wedge B}**
in the context **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 A \vee B}**
as explained in this thread [1]

See PredicateFormulaLink for an example of specifying formulas in Atomese.