Skip Navigation


Journal of Logic and Computation Advance Access originally published online on September 16, 2006
Journal of Logic and Computation 2006 16(5):697-710; doi:10.1093/logcom/exl032
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
16/5/697    most recent
exl032v1
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 arrow Search for citing articles in:
ISI Web of Science (1)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Yavorskaya, T.
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

Logic of Proofs and Labels with a Complete Set of Operations

Tatiana Yavorskaya, Sidon

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

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

We develop a framework in which operations on proofs can be specified and studied. Proofs are treated as structures built from atomic proofs and references by means of computable operations.

Our approach extends the ideas of Logic of Proofs (Artemov, 1995, Bull. Symb. Logic, 7, 1–36) in which the proof predicate ‘t is a proof of F ’ is incorporated into the propositional language. We introduce an additional storage predicate ‘x is a label for F ’ (Yavorskaya, 2005, J. Logic Comput., 15, 517–537).

In this article which is essentially a continuation of Yavorskaya's work, we study a natural example of a logic with operations on proofs and labels. This logic Formula is decidable and complete with respect to its intended semantics. Formula is capable to internalize its own proofs, and operations of Formula suffice to realize all operations specified in the language with proofs and labels.

Keywords: Logic of proofs; justification logic; modal logic; provability logic


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.