A Note on Some Explicit Modal Logics
Eric Pacuit

Abstract:
Artemov introduced the Logic of Proofs ($\LP$) as a logic of explicit
proofs.  We can also offer an epistemic reading of this formula: "$t$
is a possible justification of $\phi$".  Motivated, in part, by this
epistemic reading, Fitting introduced a Kripke style semantics for
$\LP$ in [Fitting].  In this note, we prove soundness and completeness
of some axiom systems which are not covered in [Fitting].

Keywords: Explicit Modal Logic;  Logic of Proofs