Multi-Dimensional Semantics for Modal Logics

Notre Dame Journal of Formal Logic 37 (1):25-34 (1996)
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Abstract

We show that every modal logic (with arbitrary many modalities of arbitrary arity) can be seen as a multi-dimensional modal logic in the sense of Venema. This result shows that we can give every modal logic a uniform "concrete" semantics, as advocated by Henkin et al. This can also be obtained using the unravelling method described by de Rijke. The advantage of our construction is that the obtained class of frames is easily seen to be elementary and that the worlds have a more uniform character

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References found in this work

Cylindric modal logic.Yde Venema - 1995 - Journal of Symbolic Logic 60 (2):591-623.
Generalized quantifiers and modal logic.Wiebe Van Der Hoek & Maarten De Rijke - 1993 - Journal of Logic, Language and Information 2 (1):19-58.
Generalized quantifiers and modal logic.Wiebe Hoek & Maarten Rijke - 1993 - Journal of Logic, Language and Information 2 (1):19-58.

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