Intermediate Logics and Visser's Rules


Authors
Rosalie Iemhoff
Utrecht University
Abstract
Visser's rules form a basis for the admissible rules of . Here we show that this result can be generalized to arbitrary intermediate logics: Visser's rules form a basis for the admissible rules of any intermediate logic for which they are admissible. This implies that if Visser's rules are derivable for then has no nonderivable admissible rules. We also provide a necessary and sufficient condition for the admissibility of Visser's rules. We apply these results to some specific intermediate logics and obtain that Visser's rules form a basis for the admissible rules of, for example, De Morgan logic, and that Dummett's logic and the propositional Gödel logics do not have nonderivable admissible rules
Keywords intermediate logics   intuitionistic logic   admissible rules   projective formulas
Categories (categorize this paper)
DOI 10.1305/ndjfl/1107220674
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 42,204
Through your library

References found in this work BETA

Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.
A Characterization of Intuitionistic Propositional Logic.Rosalie Iemhoff - 2001 - Annals of Pure and Applied Logic 113 (1-3):161-173.

View all 6 references / Add more references

Citations of this work BETA

Consequence Relations and Admissible Rules.Rosalie Iemhoff - 2016 - Journal of Philosophical Logic 45 (3):327-348.
Proof Theory for Admissible Rules.Rosalie Iemhoff & George Metcalfe - 2009 - Annals of Pure and Applied Logic 159 (1-2):171-186.
Complexity of Admissible Rules.Emil Jeřábek - 2007 - Archive for Mathematical Logic 46 (2):73-92.
Independent Bases of Admissible Rules.Emil Jerábek - 2008 - Logic Journal of the IGPL 16 (3):249-267.

View all 17 citations / Add more citations

Similar books and articles

The Density of Truth in Monadic Fragments of Some Intermediate Logics.Zofia Kostrzycka - 2007 - Journal of Logic, Language and Information 16 (3):283-302.

Analytics

Added to PP index
2010-08-24

Total views
59 ( #134,822 of 2,253,791 )

Recent downloads (6 months)
15 ( #58,693 of 2,253,791 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature