Skip Navigation

Journal of Logic and Computation 1998 8(5):637-664; doi:10.1093/logcom/8.5.637
© 1998 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 YASHIN, A. D.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Original Articles

New Solutions to Novikov's Problem for Intuitionistic Connectives

A. D. YASHIN

Udmurtia State University Lichvintzeva str., 68a-14, lzhevsk 426034, Russia E-mail:yashin{at}uni.udm.ru

D. Gabbay gave an example of the extension of the intuitionistic propositional logic dealing with a certain kind of the ’irreflexive modality‘. In this paper it is proved that Gabbay's logic satisfies the syntactical approach to the notion of a new intuitionistic connective suggested by P. Novikov in the 1950s: this logic is conservative over intuitionistic propositional logic, contains the Replacement Axiom for extra connective and does not allow to add any explicit expression for it. Also we describe the unique, according to Novikov's approach, complete (maximal conservative) extension of Gabbay's logic. Finally, an example of complete logic determining binary extra connective (Bowen's antiimplication) is constructed with the use of an appropriate variant of the translation technique.

Keywords: New intuitionistic connective; Novikov completeness; irreflexive modality


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.