Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Proof search in Hájek's basic logic

Proof search in Hájek's basic logic We introduce a proof system for Hájek's logic BL based on a relational hypersequents framework. We prove that the rules of our logical calculus, called RHBL , are sound and invertible with respect to any valuation of BL into a suitable algebra, called (ω)0,1. Refining the notion of reduction tree that arises naturally from RHBL , we obtain a decision algorithm for BL provability whose running time upper bound is 2 O ( n ) , where n is the number of connectives of the input formula. Moreover, if a formula is unprovable, we exploit the constructiveness of a polynomial time algorithm for leaves validity for providing a procedure to build countermodels in (ω)0, 1. Finally, since the size of the reduction tree branches is O ( n 3 ), we can describe a polynomial time verification algorithm for BL unprovability. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Proof search in Hájek's basic logic

Download PDF
26 pages

Loading next page...
 
/lp/association-for-computing-machinery/proof-search-in-h-jek-s-basic-logic-pG70uyVxP0

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
Association for Computing Machinery
Copyright
Copyright © 2008 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/1352582.1352589
Publisher site
See Article on Publisher Site

Abstract

We introduce a proof system for Hájek's logic BL based on a relational hypersequents framework. We prove that the rules of our logical calculus, called RHBL , are sound and invertible with respect to any valuation of BL into a suitable algebra, called (ω)0,1. Refining the notion of reduction tree that arises naturally from RHBL , we obtain a decision algorithm for BL provability whose running time upper bound is 2 O ( n ) , where n is the number of connectives of the input formula. Moreover, if a formula is unprovable, we exploit the constructiveness of a polynomial time algorithm for leaves validity for providing a procedure to build countermodels in (ω)0, 1. Finally, since the size of the reduction tree branches is O ( n 3 ), we can describe a polynomial time verification algorithm for BL unprovability.

Journal

ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Jun 1, 2008

There are no references for this article.