Abstract
The proof theory of multi-agent epistemic logic extended with operators for distributed knowledge is studied. A proposition A is distributed knowledge within a group G if A follows from the totality of what the individual members of G know. There are known axiomatizations for epistemic logics with the distributed knowledge operator, but apparently no cut-free proof system for such logics has yet been presented. A Gentzen-style contraction-free sequent calculus system for propositional epistemic logic with operators for distributed knowledge is given, and a cut-elimination theorem for the system is proved. Examples of reasoning about distributed knowledge that use the calculus are given.
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Hakli, R., Negri, S. (2008). Proof Theory for Distributed Knowledge. In: Sadri, F., Satoh, K. (eds) Computational Logic in Multi-Agent Systems. CLIMA 2007. Lecture Notes in Computer Science(), vol 5056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88833-8_6
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DOI: https://doi.org/10.1007/978-3-540-88833-8_6
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