The phrase "predicated on" is often used to indicate the underlying assumption or basis upon which something is built or operates. There are a variety of synonyms that convey a similar meaning, such as "founded on", "based on", "relying on", "built on", "resting upon" or "hinging on". Each of these phrases can be used to describe the fundamental principle that determines the success or failure of a particular concept, idea, or belief. These synonyms emphasize the importance of having a strong foundation upon which to build something, and highlight the critical role that assumptions and beliefs play in shaping our understanding of the world around us.