With new experiences/new information come new beliefs. We let go the old beliefs when the context in which they were true (the old information) has changed. Nothing can be true but that it is true in its (proper) context. Take away its context, and a thing cannot remain true; restore its context and it is true again. I see no "wrong" beliefs.
Think of a claim as a speech act. The context is the time, place, and circumstances of the act. Presupposition is that which must be true in order for the speech act to carry off. If you are unfamiliar with the philosopher John Austin, I recommend his seminal work on Speech Act Theory
How to Do Things with Words. He described what I call "presupposition" as the
felicity conditions or "happiness conditions" that must be true for a speech act to carry off. There has been an enormous amount of philosophical and linguistic work built on the foundation of that short monograph. (Apologies if you are considerably more knowledgeable about the philosophy of language than I am guessing.)
As an example of the context I mean: "I went to the store," was true yesterday. Today it is no longer true unless I restore the context in which it was true: "I went to the store yesterday." The belief that "the world is flat" was based on a set of information (including philosophy), a set that has since changed for most of us. Even the scope of "the world" has changed, and so very little about it can remain true for us.
I am assuming a non-solipsist philosophy--that something exists independently of myself and can be communicated to me (and filtered) through sensory experiences. Our minds impose models on our experiences. Different beliefs are competing models, none of which can be fully isomorphic with reality in the sense that it makes accurate predictions of events in the external world. The best model is that which predicts future sensory experiences the most accurately. Hence, we can only get closer to empirical truth but never fully attain it. That is agnosticism in the sense that Aldous Huxley originally defined it--a denial of knowledge of the absolute. Knowledge is experiential and cannot be quantified in any conventional sense (i.e. omniscience is impossible) since it is based on ephemeral experiences.
"Accurate reality" at any given moment is what we each know it to be based on the information we have. Knowing, understanding and believing are interpresent. We understand reality to the extent that what we know is sublimated to a wholly imagined greater truth that we each believe in. (Not that that's inherently a good or bad thing.)
I would define knowledge as truth that is presupposed by the maker of the speech act to be true. So, if John says "Jack believes that Mary is pregnant", you cannot infer that John believes in her pregnancy. If he says "Jack knows that Mary is pregnant", you can infer that he is convinced of it. If I say "John believes Mary is pregnant", you cannot infer that I believe her pregnant. If I say "John knows Mary is pregnant", you can infer my belief in her pregnancy. Presuppositions remain constant under negation. So, if I say "John does not know that Mary is pregnant", you can still infer I believe in her pregnancy. This may all be a bit pedantic and tedious, but I am trying to show you how I construe presuppositions and that I am working with a clear concept of them and a set of linguistic tests for examining them.
I'm confused by your intermingled terms, the distinctions of which mean little to me, but will just ask to clarify one: What distinguishes the "presupposed truth" of knowledge from the synthetic truth that we know for certain (provided knowing is the act that gives us "knowledge" and certainty is a measure of "belief")?
The distinction is that presupposition is grounded in the speech act. It bears on the beliefs and intentions of the speaker of an utterance. Synthetic truth refers to truth that can only be understood as an accurate model of reality. Analytic truth is self-evident from the meanings of the words. It is an interesting fact about logic that it conventionally consists only of assertions. It pays no attention to presuppositions or speech act theory, nor do logicians have a clear method for talking about presuppositions. It comes with no formal way of translating natural language expressions into logic, just the logician's intuitive grasp of how that translation process ought to work.