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Media type:
E-Article
Title:
Derivation Rules as Anti-Axioms in Modal Logic
Contributor:
Venema, Yde
imprint:
Association for Symbolic Logic, Inc., 1993
Published in:The Journal of Symbolic Logic
Language:
English
ISSN:
0022-4812
Origination:
Footnote:
Description:
<p>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 Λ is a derivation system having a set of axioms that are special Sahlqvist formulas and Λ⁺ is the extension of Λ with a set of non-ξ rules, then Λ⁺ is strongly sound and complete with respect to the class of frames determined by the axioms and the rules.</p>