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Distributed Knowledge Justification Logics

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Abstract

Justification logics are a family of modal epistemic logics which enables us to reasoning about justifications and evidences. In this paper, we introduce evidence-based multi-agent distributed knowledge logics, called distributed knowledge justification logics. The language of our justification logics contain evidence-based knowledge operators for individual agents and for distributed knowledge , which are interpreted respectively as “t is a justification that agent i accepts for F”, and “t is a justification that all agents accept for F if they combine their knowledge and justifications”. We study basic properties of our logics and prove the conservativity of distributed knowledge justification logics over multi-agent justification logics. We present Kripke style models, pseudo-Fitting and Fitting models, as well as Mkrtychev models (single world Fitting models) and prove soundness and completeness theorems. We also find a class of Fitting models which satisfies the principle of full communication. Finally, we establish the realization theorem, which states that distributed knowledge justification logics can be embedded into the modal distributed knowledge logics, and vise versa.

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Notes

  1. Letia and Groza in [18] proposed a logic named “distributed justification logic”. Their work is not about distributed knowledge, rather it is on argumentation theory.

  2. This paper is an extended and improved version of [11, 12].

  3. We conjecture that this statement holds for non-empty \(\mathcal{CS}\), and also holds for \({\sf JS5_{n}^{D}}\).

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Acknowledgements

I would like to thank the referee for useful comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran

    Meghdad Ghari

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  1. Meghdad Ghari
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Correspondence to Meghdad Ghari.

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This research was in part supported by a grant from IPM. (No. 91030416).

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Ghari, M. Distributed Knowledge Justification Logics. Theory Comput Syst 55, 1–40 (2014). https://doi.org/10.1007/s00224-013-9492-x

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