# ExtensionalImplicationLink

From OpenCog

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

For more information, see this page

## PLN Semantics

In PLN ExtensionalImplicationLink between 2 predicates is equivalent to the ExtensionalInheritanceLink between their satisfying sets, that is

ExtensionalImplicationLink <TV> P Q

is equivalent to

ExtensionalInheritanceLink <TV> SatisfyingSetLink P SatisfyingSetLink Q

Thus the TV strength is calculated as follows (according to the formula in Section 2.4.1.1 of the PLN book)

TV.s = Sum_X f(P(X), Q(X)) / Sum_X P(X)

assuming all x are uniformly distributed, else

TV.s = Sum_X f(P(X), Q(X)) * X.s / Sum_X P(X) * X.s

if we want to consider a non uniform mass function. f as currently implemented is the min function.

See PredicateFormulaLink for an example of specifying formulas in Atomese.