Derivation rules as anti-axioms in modal logic

Journal of Symbolic Logic 58 (3):1003-1034 (1993)
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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 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

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Yde Venema
University of Amsterdam

Citations of this work

Multi-Dimensional Modal Logic.Maarten Marx - 1996 - Dordrecht, Netherland: Kluwer Academic Publishers.
Hierarchies of modal and temporal logics with reference pointers.Valentin Goranko - 1996 - Journal of Logic, Language and Information 5 (1):1-24.

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Language in action.Johan Van Benthem - 1991 - Journal of Philosophical Logic 20 (3):225-263.
Varieties of complex algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
Modal Logic and Classical Logic.R. A. Bull - 1987 - Journal of Symbolic Logic 52 (2):557-558.
Decidability for branching time.John P. Burgess - 1980 - Studia Logica 39 (2-3):203-218.

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