Skip Navigation


Logic Journal of IGPL Advance Access originally published online on February 26, 2008
Logic Journal of IGPL 2008 16(3):233-248; doi:10.1093/jigpal/jzn002
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
16/3/233    most recent
jzn002v1
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 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 Voutsadakis, G.
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

Categorical Abstract Algebraic Logic: Bloom's Theorem for Rule-Based {pi}-Institutions

George Voutsadakis

School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USA.

E-mail: gvoutsad{at}lssu.edu


  Abstract

A syntactic machinery is developed for {pi}-institutions based on the notion of a category of natural transformations on their sentence functors. Rules of inference, similar to the ones traditionally used in the sentential logic framework to define the best known sentential logics, are, then, introduced for {pi}-institutions. A {pi}-institution is said to be rule-based if its closure system is induced by a collection of rules of inference. A logical matrix-like semantics is introduced for rule-based {pi}-institutions and a version of Bloom's Lemma and Bloom's Theorem are proved for rule-based {pi}-institutions.

Key Words: Closure Operators • Deductive Systems • Logical Matrices • Universal Horn Logic Without Equality • Bloom's Theorem • {pi}-Institutions • Rules of Inference • Filtered Products • Ultraproducts • 2000 AMS Subject Classification: • Primary: 03G99 • 18C15 • Secondary: 68N30

Received for publication .
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.