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December 2009 Canonical rules
Emil Jeřábek
J. Symbolic Logic 74(4): 1171-1205 (December 2009). DOI: 10.2178/jsl/1254748686

Abstract

We develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of the Blok—Esakia theorem and the theory of modal companions to systems of multiple-conclusion rules or (finitary structural global) consequence relations, and a characterization of splittings in the lattices of consequence relations over monomodal or superintuitionistic logics with the finite model property.

Citation

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Emil Jeřábek. "Canonical rules." J. Symbolic Logic 74 (4) 1171 - 1205, December 2009. https://doi.org/10.2178/jsl/1254748686

Information

Published: December 2009
First available in Project Euclid: 5 October 2009

zbMATH: 1186.03045
MathSciNet: MR2583815
Digital Object Identifier: 10.2178/jsl/1254748686

Subjects:
Primary: 03B45, 03B55

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 4 • December 2009
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