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Derivation rules as anti-axioms in modal logic

Published online by Cambridge University Press:  12 March 2014

Yde Venema
Yde Venema*
Affiliation:
Faculteit der Wijsbegeerte, Rijksuniversiteit Utrecht, 3584 CS Utrecht, The Netherlands, E-mail: yde@phil.ruu.nl
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Abstract

We discuss a ‘negative’ way of defining frame classes in (multi)modal logic, and address the question of whether these classes can be axiomatized by derivation rules, the ‘non-ξ rules’, styled after Gabbay's Irreflexivity Rule. The main result of this paper is a metatheorem on completeness, of the following kind: If ⋀ is a derivation system having a set of axioms that are special Sahlqvist formulas and ⋀+ is the extension of ⋀ with a set of non-ξ rules, then ⋀+ is strongly sound and complete with respect to the class of frames determined by the axioms and the rules.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 3 , September 1993 , pp. 1003 - 1034
Copyright
Copyright © Association for Symbolic Logic 1993

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