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Media type:
E-Article
Title:
Derivation rules as anti-axioms in modal logic
Contributor:
Venema, Yde
imprint:
Cambridge University Press (CUP), 1993
Published in:Journal of Symbolic Logic
Language:
English
DOI:
10.2307/2275109
ISSN:
0022-4812;
1943-5886
Origination:
Footnote:
Description:
<jats:title>Abstract</jats:title><jats: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<jats:italic>derivation rules</jats:italic>, 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<jats:italic>⋀</jats:italic>is a derivation system having a set of axioms that are special Sahlqvist formulas and<jats:italic>⋀</jats:italic><jats:sup>+</jats:sup>is the extension of<jats:italic>⋀</jats:italic>with a set of non-ξ rules, then<jats:italic>⋀</jats:italic><jats:sup>+</jats:sup>is strongly sound and complete with respect to the class of frames determined by the axioms and the rules.</jats:p>