Notre Dame Journal of Formal Logic

Multi-Dimensional Semantics for Modal Logics

Maarten Marx


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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Notre Dame J. Formal Logic, Volume 37, Number 1 (1996), 25-34.

First available in Project Euclid: 16 December 2002

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Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}


Marx, Maarten. Multi-Dimensional Semantics for Modal Logics. Notre Dame J. Formal Logic 37 (1996), no. 1, 25--34. doi:10.1305/ndjfl/1040067313.

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