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Logic Journal of IGPL Advance Access published online on September 9, 2009
Logic Journal of IGPL, doi:10.1093/jigpal/jzp048
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

On the directional Lambek calculus

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


  Abstract

The article presents a calculus of syntactic types which differs from the calculi L and NL of J. Lambek in that, in its Gentzen-like form, sequent antecedents are neither strings (as in L) nor phrase structures (as in NL) but functor-argument structures. The product-free part of the calculus is shown to be equivalent to the system AB due to Ajdukiewicz and Bar-Hillel. However, if the empty sequent antecedent is admitted, the resulting product-free calculus is not finitely cut-rule axiomatizable.

Key Words: Lambek calculus • Gentzen formalism • axiomatization


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