Definition of "Implication" :

noun: something that is inferred (deduced or entailed or implied)

"His resignation had political implications."

noun: a meaning that is not expressly stated but can be inferred

"The expectation was spread both by word and by implication."

noun: an accusation that brings into intimate and usually incriminating connection

noun: a relation implicated by virtue of involvement or close connection (especially an incriminating involvement)

"He was suspected of implication in several robberies."

noun: a logical relation between propositions p and q of the form if p then q'; if p is true then q cannot be false