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Journal of Logic and Computation Advance Access originally published online on December 12, 2008
Journal of Logic and Computation 2009 19(2):305-321; doi:10.1093/logcom/exn099
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Corner Article

Algebras of Relations and Relevance Logic

Szabolcs Mikulás

School of Computer Science and Information Systems, Birkbeck College, University of London, Malet Street, London WC1E 7HX, UK.
E-mail: szabolcs{at}dcs.bbk.ac.uk

Received 6 May 2008.


  Abstract

We prove that algebras of binary relations whose similarity type includes intersection, composition, converse negation and the identity constant form a non-finitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of relevant logic with respect to binary relations.

Keywords: relevance logic; completeness; De Morgan monoids; relation algebras; finite axiomatizability

This article is dedicated to the memory of Professor Imre Ruzsa (1921–2008)


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