On definability in multimodal logic

Review of Symbolic Logic 2 (3):451-468 (2009)

Authors
Joseph Y. Halpern
Cornell University
Abstract
Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth’s theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, reducibility, is introduced; it is shown that in multimodal logics, explicit definability is equivalent to the combination of implicit definability and reducibility. The three notions of definability are characterized semantically using (modal) algebras. The use of algebras, rather than frames, is shown to be necessary for these characterizations
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DOI 10.1017/S175502030999013X
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Synonymous Logics.Francis Jeffry Pelletier & Alasdair Urquhart - 2003 - Journal of Philosophical Logic 32 (3):259-285.

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