Skip Navigation

Logic Journal of IGPL 2002 10(1):85-103; doi:10.1093/jigpal/10.1.85
© 2002 by Oxford University Press
This Article
Right arrow Full Text (PDF)
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 Siekman, J
Right arrow Articles by Wrightson, G
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

An open research problem: strong completeness of R Kowalski's connection graph proof procedure

J SiekmanZ and G WrightsonZZ

Z Universität des Saarlandes, Stuhlsatzenhausweg, D-66123 Saarbrücken, Germany E-mail: siekmann@dfki.de ZZ Department of Computer Science and Software Engineering, The University of Newcastle, NSW 2308, Australia E-mail: graham@cs.newcastle.edu.au

The connection graph proof procedure (or clause graph resolution as it is more commonly called today) is a theorem proving technique due to Robert Kowalski. It is a negative test calculus (a refutation procedure) based on resolution. Due to an intricate deletion mechanism that generalises the well-known purity principle, it substantially refines the usual notions of resolution-based systems and leads to a largely reduced search space. The dynamic nature of the clause graph upon which this refutation procedure is based, poses novel meta-logical problems previously unencountered in logical deduction systems. Ever since its invention in 1975 the soundness, confluence and (strong) completeness of the procedure have been in doubt in spite of many partial results. This paper provides an introduction to the problem as well as an overview of the main results that have been obtained in the last twenty-five years.


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.