Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 46, Number 1 (2005), 65-81.
Intermediate Logics and Visser's Rules
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.
Notre Dame J. Formal Logic Volume 46, Number 1 (2005), 65-81.
First available in Project Euclid: 31 January 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03B55: Intermediate logics
Secondary: 03B35: Mechanization of proofs and logical operations [See also 68T15]
Iemhoff, Rosalie. Intermediate Logics and Visser's Rules. Notre Dame J. Formal Logic 46 (2005), no. 1, 65--81. doi:10.1305/ndjfl/1107220674. http://projecteuclid.org/euclid.ndjfl/1107220674.