  We develop a logical framework for reasoning about knowledge and evidence in
which the agent may be uncertain about how to interpret their evidence. Rather
than representing an evidential state as a fixed subset of the state space, our
models allow the set of possible worlds that a piece of evidence corresponds to
to vary from one possible world to another, and therefore itself be the subject
of uncertainty. Such structures can be viewed as (epistemically motivated)
generalizations of topological spaces. In this context, there arises a natural
distinction between what is actually entailed by the evidence and what the
agent knows is entailed by the evidence -- with the latter, in general, being
much weaker. We provide a sound and complete axiomatization of the
corresponding bi-modal logic of knowledge and evidence entailment, and
investigate some natural extensions of this core system, including the addition
of a belief modality and its interaction with evidence interpretation and
entailment, and the addition of a "knowability" modality interpreted via a
(generalized) interior operator.
