Be based on; of theories and claims, for example.

synonyms: build on, repose on, rest on.

Roget 484: believe, credit; give faith to, give credit to, credence to; see, realize; assume, receive; set down for, take for; have it, take it; consider, esteem, presume.    count upon, depend upon, calculate upon, pin one's faith upon, reckon upon, lean upon, build upon, rely upon, rest upon; lay one's account for; make sure of.    make oneself easy about, on that score; take on trust, take on credit; take for granted, take for gospel; allow some weight to, attach some weight to.    know, know for certain; have know, make no doubt; doubt not; be, rest assured etc. adj.; persuade oneself, assure oneself, satisfy oneself; make up one's mind.    give one credit for; confide in, believe in, put one's trust in; place in, repose in, implicit confidence in; take one's word for, at one's word; place reliance on, rely upon, swear by, regard to.    think, hold; take, take it; opine, be of opinion, conceive, trow^†, ween^†, fancy, apprehend; have it, hold a belief, possess, entertain a belief, adopt a belief, imbibe a belief, embrace a belief, get hold of a belief, hazard, foster, nurture a belief, cherish a belief, have an opinion, hold an opinion, possess, entertain an opinion, adopt an opinion, imbibe an opinion, embrace an opinion, get hold of an opinion, hazard an opinion, foster an opinion, nurture an opinion, cherish an opinion etc. n.. view as, consider as, take as, hold as, conceive as, regard as, esteem as, deem as, look upon as, account as, set down as; surmise etc. 514.    get it into one's head, take it into one's head; come round to an opinion; swallow etc. (credulity) 486.    cause to be believed etc. v.; satisfy, persuade, have the ear of, gain the confidence of, assure; convince, convict^†, convert; wean, bring round; bring over, win over; indoctrinate etc. (teach) 537; cram down the throat; produce conviction, carry conviction; bring home to, drive home to.    go down, find credence, pass current; be received etc. v., be current etc. adj.; possess, take hold of, take possession of the mind.    ... show more