Notre Dame Journal of Formal Logic

Intermediate Logics and Visser's Rules

Rosalie Iemhoff

Abstract

Visser's rules form a basis for the admissible rules of ${\sf IPC}$. 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 ${\sf L}$ for which they are admissible. This implies that if Visser's rules are derivable for ${\sf L}$ then ${\sf L}$ 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.

Article information

Source
Notre Dame J. Formal Logic Volume 46, Number 1 (2005), 65-81.

Dates
First available: 31 January 2005

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1107220674

Digital Object Identifier
doi:10.1305/ndjfl/1107220674

Mathematical Reviews number (MathSciNet)
MR2131547

Zentralblatt MATH identifier
02186751

Subjects
Primary: 03B55: Intermediate logics
Secondary: 03B35: Mechanization of proofs and logical operations [See also 68T15]

Keywords
intermediate logics intuitionistic logic admissible rules projective formulas

Citation

Iemhoff, Rosalie. Intermediate Logics and Visser's Rules. Notre Dame Journal of Formal Logic 46 (2005), no. 1, 65--81. doi:10.1305/ndjfl/1107220674. http://projecteuclid.org/euclid.ndjfl/1107220674.


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