postulate vs presuppose

postulate is a noun but presuppose is not a noun.

Word	Noun	Adjective	Verb	Adverb
postulate	Yes	No	Yes	No
presuppose	No	No	Yes	No

As verbs, presuppose is a hypernym of postulate; that is, presuppose is a word with a broader meaning than postulate:

Other hypernyms of postulate include suppose.

postulate (noun)	presuppose (noun)
(logic) a proposition that is accepted as true in order to provide a basis for logical reasoning

postulate (verb)	presuppose (verb)
take as a given; assume as a postulate or axiom	require as a necessary antecedent or precondition
maintain or assert	take for granted or as a given; suppose beforehand
require as useful, just, or proper