WordNet sense 1 (express a supposition):

say

WordNet sense 2 (take for granted or as a given; suppose beforehand):

presuppose

WordNet sense 3 (to believe especially on uncertain or tentative grounds):

conjecture, hypothesize, speculate, theorize, hypothecate, hypothesise, theorise

WordNet sense 4 (expect, believe, or suppose):

guess, imagine, opine, reckon, think