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Synonyms for Implication (same or very similar meaning)

WordNet sense 1 (a logical relation between propositions p and q of the form `if p then q'; if p is true then q cannot be false):
conditional relation, logical implication

WordNet sense 2 (a meaning that is not expressly stated but can be inferred):
import, significance, import

WordNet sense 3 (something that is inferred (deduced or entailed or implied)):
deduction, entailment

From the ODE community, based on WordNetadd/edit