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Synonyms for Postulate (same or very similar meaning)

WordNet sense 1 ((logic) a proposition that is accepted as true in order to provide a basis for logical reasoning):
posit

WordNet sense 2 (require as useful, just, or proper):
ask, demand, involve, necessitate, need, take, require, call for

WordNet sense 3 (maintain or assert):
contend


From the ODE community, based on WordNetadd/edit