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implication has 6 distinct synonyms spread across 3 of its 5 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
something that is inferred (deduced or entailed or implied)
“his resignation had political implications”
a meaning that is not expressly stated but can be inferred
“the significance of his remark became clear only later”
an accusation that brings into intimate and usually incriminating connection
a logical relation between propositions p and q of the form `if p then q'; if p is true then q cannot be false
a relation implicated by virtue of involvement or close connection (especially an incriminating involvement)
“he was suspected of implication in several robberies”
Synonyms, antonyms and the broader and narrower relations for implication come from Princeton University’s WordNet. Full sources and licences.