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Journal of Logic and Computation Advance Access published online on July 25, 2006
Journal of Logic and Computation, doi:10.1093/logcom/exl001
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
Received September 10, 2005

Original Papers

Proof Theory for Casari's Comparative Logics

George Metcalfe 1 *

1 University of Technology, Vienna, Austria

* To whom correspondence should be addressed.
George Metcalfe, E-mail: metcalfe{at}logic.at


  Abstract

Comparative logics were introduced by Casari in the 1980s to treat aspects of comparative reasoning occurring in natural language. In this article Gentzen systems are defined for these logics by means of a special mix rule that combines calculi for various substructural logics with a hypersequent calculus for Meyer and Slaney's Abelian logic. Cut-elimination is established for all these systems, and as a consequence, a positive answer is given to an open problem on the decidability of the basic comparative logic.

Keywords: Comparative logics; substructural logics; Abelian logic; sequents; hypersequents.
Work supported by Marie Curie Fellowship HPMF-CT-2004-501043.
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