Definitions of 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)

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

  Example: "His resignation had political implications"

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

  Example: "The expectation was spread both by word and by implication"