Abstract
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 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.
Work funded with Grant AFRÂ 894328 from the National Research Fund Luxembourg cofunded under the Marie-Curie Actions of the European Commission (FP7-COFUND), and finalised during an invited stay at the Institute of Mathematical Sciences, Chennai, India.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kramer, S.: Logic of non-monotonic interactive proofs (formal theory of temporary knowledge transfer). Technical Report 1208.1842, arXiv (2012), http://arxiv.org/abs/1208.1842
Kramer, S.: A logic of interactive proofs (formal theory of knowledge transfer). Technical Report 1201.3667, arXiv (2012), http://arxiv.org/abs/1201.3667
Makinson, D.: How To Go Nonmonotonic. In: Handbook of Philosophical Logic, 2nd edn., vol. 12. Springer (2005)
Meyer, J.J., Veltman, F.: Intelligent Agents and Common Sense Reasoning. In: [5]
Blackburn, P., van Benthem, J., Wolter, F. (eds.): Handbook of Modal Logic. Studies in Logic and Practical Reasoning, vol. 3. Elsevier (2007)
Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning about Knowledge. MIT Press (1995)
Hendricks, V., Roy, O. (eds.): Epistemic Logic: 5 Questions. Automatic Press (2010)
Katz, J.: Digital Signatures. Springer (2010)
Anderson, R.: Security Engineering: A Guide to Building Dependable Distributed Systems, 2nd edn. Wiley (2008)
Artemov, S.: The logic of justifications. The Review of Symbolic Logic 1(4) (2008)
Hindley, J., Seldin, J.: Lambda-Calculus and Combinators, 2nd edn. Cambridge University Press (2008)
Baltag, A., Renne, B., Smets, S.: The Logic of Justified Belief Change, Soft Evidence and Defeasible Knowledge. In: Ong, L., de Queiroz, R. (eds.) WoLLIC 2012. LNCS, vol. 7456, pp. 168–190. Springer, Heidelberg (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kramer, S. (2013). Logic of Non-monotonic Interactive Proofs. In: Lodaya, K. (eds) Logic and Its Applications. ICLA 2013. Lecture Notes in Computer Science, vol 7750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36039-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-36039-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36038-1
Online ISBN: 978-3-642-36039-8
eBook Packages: Computer ScienceComputer Science (R0)