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Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)

Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer) Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer) SIMON KRAMER, SK-R&D LLC (Switzerland) We produce a decidable super-intuitionistic normal modal logic of internalised intuitionistic (and thus disjunctive and monotonic) interactive proofs (LIiP) from an existing classical counterpart of classical monotonic non-disjunctive interactive proofs (LiP). Intuitionistic interactive proofs effect a durable epistemic impact in the possibly adversarial communication medium CM (which is imagined as a distinguished agent) and only in that, that consists in the permanent induction of the perfect and thus disjunctive knowledge of their proof goal by means of CM's knowledge of the proof: If CM knew my proof then CM would persistently and also disjunctively know that my proof goal is true. So intuitionistic interactive proofs effect a lasting transfer of disjunctive propositional knowledge (disjunctively knowable facts) in the communication medium of multiagent distributed systems via the transmission of certain individual knowledge (knowable intuitionistic proofs). Our (necessarily) CM-centred notion of proof is also a disjunctive explicit refinement of KD45-belief, and yields also such a refinement of standard S5-knowledge. Monotonicity but not communality is a commonality of LiP, LIiP, and their internalised notions of proof. As a side-effect, we offer a short internalised proof http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)

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References (62)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2015 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2811263
Publisher site
See Article on Publisher Site

Abstract

Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer) SIMON KRAMER, SK-R&D LLC (Switzerland) We produce a decidable super-intuitionistic normal modal logic of internalised intuitionistic (and thus disjunctive and monotonic) interactive proofs (LIiP) from an existing classical counterpart of classical monotonic non-disjunctive interactive proofs (LiP). Intuitionistic interactive proofs effect a durable epistemic impact in the possibly adversarial communication medium CM (which is imagined as a distinguished agent) and only in that, that consists in the permanent induction of the perfect and thus disjunctive knowledge of their proof goal by means of CM's knowledge of the proof: If CM knew my proof then CM would persistently and also disjunctively know that my proof goal is true. So intuitionistic interactive proofs effect a lasting transfer of disjunctive propositional knowledge (disjunctively knowable facts) in the communication medium of multiagent distributed systems via the transmission of certain individual knowledge (knowable intuitionistic proofs). Our (necessarily) CM-centred notion of proof is also a disjunctive explicit refinement of KD45-belief, and yields also such a refinement of standard S5-knowledge. Monotonicity but not communality is a commonality of LiP, LIiP, and their internalised notions of proof. As a side-effect, we offer a short internalised proof

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Sep 17, 2015

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