From OpenCog

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.,

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

See FormulaPredicateLink for an example of specifying formulas in Atomese.