Derivation rules as anti-axioms in modal logic

Journal of Symbolic Logic 58 (3):1003-1034 (1993)
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
Keywords (multi)modal logic   completeness   derivation rules   modal definability
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DOI 10.2307/2275109
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Maarten de Rijke (1998). A System of Dynamic Modal Logic. Journal of Philosophical Logic 27 (2):109-142.
Maarten De Rijke (1995). The Logic of Peirce Algebras. Journal of Logic, Language and Information 4 (3):227-250.

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