Knowledge, Truth, and Belief probably don’t have the kind of direct relation that we might think of at first.
First we have to understand that Plato’s divided line is the core of the Western worldview and it distinguishes between Ratio and Doxa. Doxa is both belief and appearances Ratio is divided into non-representable and representable intelligibles and Doxa is divided into grounded and ungrounded belief. The limits of the divided line is the paradoxical on the side of belief and the super-rational on the side of the rational. Contradiction, Paradox and Absurdity are forms of mixture and the Supra-Rational is when two things are so at the same time without mixture.
Now Aristotle defines the types of knowledge and there is a kind of knowledge for each part of the divided line which are nous, sophia, epsiteme, on the ratio side and techne, phroneses, and metis on the doxa side.
So knowledge is not just epistemic, i.e. scientific and theoretical knowledge but there is a kind of knowledge for each type of experience within the interval of the divided line.
Associated with Doxa there are the aspects of Being where identity and presence is associated with ungrounded belief while reality and truth is identified with grounded belief. What is associated with the ratio is the nonduals where order and right is associated with representatble intelligibles and good and fate is associated with the non-representable intelligibles.
So there is a structure there which is quite clear. There are types of knowledge that cover all the types of experience identified in the divided line. What we call knowledge Episteme related to science is just one kind of knowledge, and so were have severely limited the extent of knowledge and forgotten many ancient forms of knowledge. So our worldview is more limited than the ancient Greek worldview in this respect. Belief is related to doxa, but doxa also means appearances. Belief is explicitly a reliance on and an interpretation of experiences that may or may not be reliable.
With regard to ungrounded belief we need to exercise judgment (phronesis) and we need to concentrate on identity and presence as the basis of our belief, and so in this sense judgment is phenomenological at this level. Husserl famously brackets anything beyond appearance. His slogan is “to the phenomena itself” as it appears. With respect to grounded belief our concern should be with reality and truth, i.e. validation and verification, and there are techniques and methods we use to attempt to ascertain the truth and reality of things beyond their mere appearance. This is what was bracketed by Husserl. Part of the relation to technique is also the poesis of the phenomena, i.e. its unfolding and production out of itself, i.e. its internal dynamic. If the phenomena has its own inner dynamic independent of use we tend to think it has a reality outside and independent of us, and then we can check our statements about this dynamic’s outcomes to verify their truth. If we can predict outcomes then we think we have causal understanding of the phenomena.
Truth is a ground in Logos and Reality is a ground in physus. There is also the nondual ground in Nomos, i.e. Order, and that is what takes us into the representable arena across the central line between doxa and ratio. With regard representations we distinguish between Law and the Spirit of the Law (Right). As we scale the divided line different criteria come into play. But the arena of representations is the realm of what we normally call knowledge in our society. But for Plato and Aristotle this is only one kind of knowledge among many the others of which have become downplayed in our tradition as it has strayed away from its Greek roots.