Skip Navigation


Journal of Logic and Computation Advance Access originally published online on December 21, 2007
Journal of Logic and Computation 2008 18(4):589-600; doi:10.1093/logcom/exm084
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
18/4/589    most recent
exm084v1
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Zimmermann, E.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2007. Published by Oxford University Press on behalf of the Association of Physicians. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Lambek Calculus in Natural Deduction

Ernst Zimmermann

Boeblingen, Germany

E-mail: ernstzimmermann{at}de.ibm.com

Received 21 June 2007.


  Abstract

A formulation of Lambek calculus in natural deduction is given. New rules for Lambek's multiplicative, non-commutative conjunction are proposed, rules for Lambek's two implications are standard. Rules for Lambek's conjunction are variants of general elimination rules: a symmetric elimination rule and its specializations, left elimination rule and right elimination rule. Conversions hold for all these rules, but only the symmetric elimination rule is fully permutable. Due to a natural transformation for left and right elimination rules to the symmetric elimination rule with partial empty sequences of assumptions and vice versa, there hold two normalization theorems, one with a minimal set and one with a maximal set of permutations.

Keywords: Natural deduction; Lambek calculus


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.