Logic of Non-Monotonic Interactive Proofs (Formal Theory of Temporary Knowledge Transfer)
This addresses the problem of formalizing temporary knowledge transfer in distributed systems for researchers in logic and multi-agent systems, but it is incremental as it builds on prior monotonic logic.
The paper introduces a non-monotonic logic (LiiP) for modeling temporary knowledge transfer in interactive proofs, where proofs induce ephemeral knowledge in peer reviewers, and reconstructs an existing monotonic logic (LiP) as an extension of it.
We propose a monotonic logic of internalised non-monotonic or instant interactive proofs (LiiP) and reconstruct an existing monotonic logic of internalised monotonic or persistent interactive proofs (LiP) as a minimal conservative extension of LiiP. Instant interactive proofs effect a fragile epistemic impact in their intended communities of peer reviewers that consists in the impermanent induction of the knowledge of their proof goal by means of the knowledge of the proof with the interpreting reviewer: If my peer reviewer knew my proof then she would at least then (in that instant) know that its proof goal is true. Their impact is fragile and their induction of knowledge impermanent in the sense of being the case possibly only at the instant of learning the proof. This accounts for the important possibility of internalising proofs of statements whose truth value can vary, which, as opposed to invariant statements, cannot have persistent proofs. So instant interactive proofs effect a temporary transfer of certain propositional knowledge (knowable ephemeral facts) via the transmission of certain individual knowledge (knowable non-monotonic proofs) in distributed systems of multiple interacting agents.