Skip Navigation


Journal of Logic and Computation Advance Access originally published online on April 22, 2008
Journal of Logic and Computation 2008 18(4):669-695; doi:10.1093/logcom/exn001
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
18/4/669    most recent
exn001v1
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 Colson, L.
Right arrow Articles by Michel, D.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Pedagogical Second-order Propositional Calculi

Loïc Colson and David Michel

University of Metz, Metz, France. E-mail: colson{at}univ-metz.fr; david.michel{at}univ-metz.fr

Received 18 June 2007.


  Abstract

The present work introduces the notion of pedagogical natural deduction systems, which are natural deduction systems with the following additional constraint: all hypotheses made in a proof must be motivated by an example. Technically speaking, we replace the rule (Hyp):


Formula

with the rule (PHyp):


Formula

with {sigma} denoting a substitution replacing all variables of {Gamma} with an example. This substitution is called the motivation of {Gamma}. These systems are in essence negationless. In the present article, we study the second-order propositional calculus, since it is the simplest non-trivial natural deduction system in which the negation is definable. Some pedagogical versions of the second-order propositional calculus are proposed. We argue that these pedagogical calculi are negationless and we study their expressive power.

Keywords: Constructive mathematics; mathematical logic; natural deduction; negationless mathematics; typed {lambda}-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.