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logical implication has 2 distinct synonyms spread across 1 of its 1 sense. 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.
a logical relation between propositions p and q of the form `if p then q'; if p is true then q cannot be false
Synonyms, antonyms and the broader and narrower relations for logical implication come from Princeton University’s WordNet. Full sources and licences.