We propose a logic of interactive proofs as the first and main step towards
an intuitionistic foundation for interactive computation to be obtained via an
interactive analog of the G\"odel-Kolmogorov-Art\"emov definition of
intuitionistic logic as embedded into a classical modal logic of proofs, and of
the Curry-Howard isomorphism between intuitionistic proofs and typed programs.
Our interactive proofs effectuate a persistent epistemic impact in their
intended communities of peer reviewers that consists in the induction of the
(propositional) knowledge of their proof goal by means of the (individual)
knowledge of the proof with the interpreting reviewer. That is, interactive
proofs effectuate a transfer of propositional knowledge---(to-be-)known
facts---via the transfer of certain individual knowledge---(to-be-)known
proofs---in distributed and multi-agent systems. In other words, we as a
community can have the formal common knowledge that a proof is that which if
known to one of our peer members would induce the knowledge of its proof goal
with that member.