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Journal of Logic and Computation Advance Access originally published online on December 27, 2006
Journal of Logic and Computation 2007 17(2):299-310; doi:10.1093/logcom/exl041
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

On Reduction Systems Equivalent to the Non-associative Lambek Calculus with the Empty String

Wojciech Zielonka

University of Warmia and Mazury, Faculty of Mathematics and Computer Science, Zolnierska 14a, 10-561 Olsztyn, Poland.

E-mail: zielonka{at}uwm.edu.pl

Received 20 June 2005.


  Abstract

The article concludes a series of results on cut-rule axiomatizability of the Lambek calculus. It is proved that the non-associative product-free Lambek calculus with the empty string (NL0) is not finitely axiomatizable if the only rule of inference admitted is Lambek's cut rule. The proof makes use of the (infinitely) cut-rule axiomatized calculus NC designed by the author exactly for that purpose.

Keywords: Lambek calculus; cut rule; axiomatizability


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W. Zielonka
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[Abstract] [PDF]


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