Common knowledge does not have the Beth property

Authors:
Thomas Studer
Affiliations:
Institut für Informatik und angewandte Mathematik, Universität Bern, Neubrückstrasse 10, CH-3012 Bern, Switzerland
Venue:
Information Processing Letters
Year:
2009

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Abstract

Common knowledge is an essential notion for coordination among agents. We show that the logic of common knowledge does not have the Beth property and thus it also lacks interpolation. The proof we present is a variant of Maksimova's proof that temporal logics with 'the next' do not have the Beth property. Our result also provides an explanation why it is so difficult to find 'nice' deductive systems for common knowledge.