David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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References found in this work BETA
Krister Segerberg (1968). Decidability of S4. Theoria 34 (1):7-20.
Citations of this work BETA
Thomas Müller & Niko Strobach (2012). A Letter on the Present State of Affairs. Synthese 188 (3):469-485.
Sara L. Uckelman & Joel Uckelman (2007). Modal and Temporal Logics for Abstract Space–Time Structures. Studies in History and Philosophy of Science Part B 38 (3):673-681.
Marco Aiello, Guram Bezhanishvili, Isabelle Bloch & Valentin Goranko (2012). Logic for Physical Space. Synthese 186 (3):619-632.
V. B. Shehtman (1983). Modal Logics of Domains on the Real Plane. Studia Logica 42 (1):63 - 80.
Philip Kremer (forthcoming). Quantified Modal Logic on the Rational Line. Review of Symbolic Logic:1-16.
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