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We propose a monotonic logic of internalised non-monotonic or instantinteractive proofs (LiiP) and reconstruct an existing monotonic logic ofinternalised monotonic or persistent interactive proofs (LiP) as a minimalconservative extension of LiiP. Instant interactive proofs effect a fragileepistemic impact in their intended communities of peer reviewers that consistsin the impermanent induction of the knowledge of their proof goal by means ofthe knowledge of the proof with the interpreting reviewer: If my peer reviewerknew my proof then she would at least then (in that instant) know that itsproof goal is true. Their impact is fragile and their induction of knowledgeimpermanent in the sense of being the case possibly only at the instant oflearning the proof. This accounts for the important possibility ofinternalising proofs of statements whose truth value can vary, which, asopposed to invariant statements, cannot have persistent proofs. So instantinteractive proofs effect a temporary transfer of certain propositionalknowledge (knowable ephemeral facts) via the transmission of certain individualknowledge (knowable non-monotonic proofs) in distributed systems of multipleinteracting agents.

Logic of Non-Monotonic Interactive Proofs (Formal Theory of Temporary Knowledge Transfer)