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Logic Journal of IGPL Advance Access originally published online on March 26, 2007
Logic Journal of IGPL 2007 15(2):165-181; doi:10.1093/jigpal/jzm005
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The Relevant Equivalence Property

Lloyd Humberstone

Department of Philosophy, Monash University, Clayton Victoria 3800, Australia. E-mail: Lloyd.Humberstone{at}arts.monash.edu.au

Robert K. Meyer

Automated Reasoning Group, Computer Sciences Laboratory, RSISE, ANU, Canberra, ACT 0200, Australia. E-mail: bob.meyer{at}anu.edu.au


  Abstract

The pure implicational and the multiplicative fragments of a range of propositional relevant (and other) logics are shown to have the property that any two formulas equivalent in such a logic are constructed from exactly the same propositional variables – as opposed to merely having (as the definition of relevance itself would require) some propositional variable in common.

Key Words: relevance • implicational logics • substructural logics

Received for publication 4 January 2007.
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