  We propose parametric constructive Kripke-semantics for multi-agent
KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions
of two basic functional building blocks, namely bias (or viewpoint) and
visibility, functioning also as the parameters of the doxastic and epistemic
accessibility relation. The doxastic accessibility relates two possible worlds
whenever the application of the composition of bias with visibility to the
first world is equal to the application of visibility to the second world. The
epistemic accessibility is the transitive closure of the union of our doxastic
accessibility and its converse. Therefrom, accessibility relations for common
and distributed belief and knowledge can be constructed in a standard way. As a
result, we obtain a general definition of knowledge in terms of belief that
enables us to view S5-knowledge as accurate (unbiased and thus true)
KD45-belief, negation-complete belief and knowledge as exact KD45-belief and
S5-knowledge, respectively, and perfect S5-knowledge as precise (exact and
accurate) KD45-belief, and all this generically for arbitrary functions of bias
and visibility. Our results can be seen as a semantic complement to previous
foundational results by Halpern et al. about the (un)definability and
(non-)reducibility of knowledge in terms of and to belief, respectively.
