The coinductive formulation of common knowledge

Baston, Colm and Capretta, Venanzio (2018) The coinductive formulation of common knowledge. In: ITP 2018 - Interactive Theorem Proving, 9-12 August 2018, Oxford, UK.

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Abstract

We study the coinductive formulation of common knowledge in type theory. We formalise both the traditional relational semantics and an operator semantics, similar in form to the epistemic system S5, but at the level of events on possible worlds rather than as a logical derivation system. We have two major new results. Firstly, the operator semantics is equivalent to the relational semantics: we discovered that this requires a new hypothesis of semantic entailment on operators, not known in previous literature. Secondly, the coinductive version of common knowledge is equivalent to the traditional transitive closure on the relational interpretation. All results are formalised in the proof assistants Agda and Coq.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Baston C., Capretta V. (2018) The Coinductive Formulation of Common Knowledge. In: Avigad J., Mahboubi A. (eds) Interactive Theorem Proving. ITP 2018. Lecture Notes in Computer Science, vol 10895. Springer, Cham. ISBN 9783319948201. The final authenticated version is available online at https://doi.org/10.1007/978-3-319-94821-8_8.
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Computer Science
Identification Number: https://doi.org/10.1007/978-3-319-94821-8_8
Depositing User: Eprints, Support
Date Deposited: 31 Aug 2018 10:13
Last Modified: 31 Aug 2018 10:13
URI: http://eprints.nottingham.ac.uk/id/eprint/53576

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