Title: Attainable Knowledge,
Abstract: The article investigates an evidence-based semantics for epistemic logics in
which pieces of evidence are interpreted as equivalence relations on the
epistemic worlds. It is shown that the properties of knowledge obtained from
potentially infinitely many pieces of evidence are described by modal logic S5.
At the same time, the properties of knowledge obtained from only a finite
number of pieces of evidence are described by modal logic S4. The main
technical result is a sound and complete bi-modal logical system that describes
properties of these two modalities and their interplay.