The \emph{non-interference (NI)} property defines a program
to be secure if changes to
high-security inputs cannot alter the values of low-security outputs.  NI
indirectly states the epistemic property
that no low-security principal acquires knowledge of high-security data.
We consider a directly epistemic account of \emph{information flow (IF)}
security focusing on the knowledge flows engendered by the program's
execution.  Storage effects are of primary interest,
since principals acquire knowledge from the execution only through these
effects.  The IF properties of the individual effectful actions
are characterized using a \emph{substructural epistemic logic} that
accounts for the knowledge transferred through their
execution.  We prove that a low-security principal never acquires knowledge of
a high-security input by executing a well-typed program.

The epistemic approach has several advantages over NI.  First, it directly
accounts for the knowledge flow engendered by a program.  Second, in contrast
to the bimodal NI property, the epistemic approach accounts for authorized
declassification.  We prove that a low-security principal acquires knowledge of
a high-security input \emph{only if} it is authorized by a proof in
authorization logic.  Third, the explicit formulation of IF properties as an
epistemic theory provides a crisp treatment of ``side channels.''  Rather than
prove that a principal \emph{does not know} a secret, we instead prove
that \emph{it is not provable} that the principal knows that secret.  The
latter statement characterizes the ``minimal model,'' for which a precise
statement may be made, whereas the former applies to ``any model,'' including
those with ``side channels'' that violate the model's basic premises.  Fourth,
the NI property is re-positioned as providing an \emph{adequacy} proof of the
epistemic theory of effects, ensuring that the logical theory corresponds to
the actual program behavior.  In this way we obtain a generalization of the
classical approach to IF security that extends to authorized declassification.