presuppose vs premise

presuppose is not a noun while premise is a noun.

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

As verbs, premise is a hyponym of presuppose; that is, premise is a word with a more specific, narrower meaning than presuppose:

Other hyponyms of presuppose include posit, postulate, premiss.

presuppose (noun)	premise (noun)
	a statement that is assumed to be true and from which a conclusion can be drawn

presuppose (verb)	premise (verb)
require as a necessary antecedent or precondition	take something as preexisting and given
take for granted or as a given; suppose beforehand	set forth beforehand, often as an explanation
	furnish with a preface or introduction