Skip Navigation


Journal of Logic and Computation Advance Access originally published online on September 12, 2006
Journal of Logic and Computation 2006 16(5):645-661; doi:10.1093/logcom/exl028
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
16/5/645    most recent
exl028v1
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 Krupski, V. N.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Reference Constructions in the Single-conclusion Proof Logic

Vladimir N. Krupski

Department of Mathematical Logic and Theory of Algorithms, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119992, Russia.

E-mail: krupski{at}lpcs.math.msu.su

We propose an extension of the propositional proof logic language by the second-order variables denoting the reference constructors (like ‘the formula which is proven by x’). The proof logic in this weak second-order language is axiomatized via the calculus Formula ref, the (Functional) Logic of Proofs with References. It is supplied with the formal arithmetical semantics: we prove that Formula ref is sound with respect to arithmetical interpretations and is a conservative extension of propositional single-conclusion proof logic Formula . Finally, we demonstrate how the language of Formula ref can be used as a scheme language for arithmetic and provide the corresponding proof conversion method.

Keywords: Proof theory; explicit modal logic; single conclusion logic of proofs; proof term; reference; unification


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.