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2005 Intermediate Logics and Visser's Rules
Rosalie Iemhoff
Notre Dame J. Formal Logic 46(1): 65-81 (2005). DOI: 10.1305/ndjfl/1107220674

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.

Citation

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Rosalie Iemhoff. "Intermediate Logics and Visser's Rules." Notre Dame J. Formal Logic 46 (1) 65 - 81, 2005. https://doi.org/10.1305/ndjfl/1107220674

Information

Published: 2005
First available in Project Euclid: 31 January 2005

zbMATH: 1102.03032
MathSciNet: MR2131547
Digital Object Identifier: 10.1305/ndjfl/1107220674

Subjects:
Primary: 03B55
Secondary: 03B35

Rights: Copyright © 2005 University of Notre Dame

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Vol.46 • No. 1 • 2005
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