Diodorean modality in Minkowski spacetime

Studia Logica 39 (2-3):219 - 236 (1980)
The Diodorean interpretation of modality reads the operator as it is now and always will be the case that. In this paper time is modelled by the four-dimensional Minkowskian geometry that forms the basis of Einstein's special theory of relativity, with event y coming after event x just in case a signal can be sent from x to y at a speed at most that of the speed of light (so that y is in the causal future of x).It is shown that the modal sentences valid in this structure are precisely the theorems of the well-known logic S4.2, and that this system axiomatises the logics of two and three dimensional spacetimes as well.
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Niko Strobach (2007). Fooling Around with Tenses. Studies in History and Philosophy of Science Part B 38 (3):653-672.

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