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  1. Derivation rules as anti-axioms in modal logic.Yde Venema - 1993 - Journal of Symbolic Logic 58 (3):1003-1034.
    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 (...)
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  • Two-dimensional adventures.Lloyd Humberstone - 2004 - Philosophical Studies 118 (1-2):17--65.
    This paper recalls some applications of two-dimensional modal logic from the 1980s, including work on the logic of Actually and on a somewhat idealized version of the indicative/subjunctive distinction, as well as on absolute and relative necessity. There is some discussion of reactions this material has aroused in commentators since. We also survey related work by Leslie Tharp from roughly the same period.
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  • Squares in Fork Arrow Logic.Renata P. de Freitas, Jorge P. Viana, Mario R. F. Benevides, Sheila R. M. Veloso & Paulo A. S. Veloso - 2003 - Journal of Philosophical Logic 32 (4):343-355.
    In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational (...)
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  • Dynamic squares.Patrick Blackburn & Yde Venema - 1995 - Journal of Philosophical Logic 24 (5):469 - 523.
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  • Multi-dimensional modal logic.Maarten Marx - 1997 - Boston, Mass.: Kluwer Academic Publishers. Edited by Yde Venema.
    Over the last twenty years, in all of these neighbouring fields, modal systems have been developed that we call multi-dimensional. (Our definition of multi ...
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