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
Philip Kremer (2014). Quantified Modal Logic on the Rational Line. Review of Symbolic Logic 7 (3):439-454.
Peter Øhrstrøm & Per Hasle (1993). A. N. Prior's Rediscovery of Tense Logic. Erkenntnis 39 (1):23 - 50.
Attila Molnár & Gergely Székely (2015). Axiomatizing Relativistic Dynamics Using Formal Thought Experiments. Synthese 192 (7):2183-2222.
Johan van Benthem, Guram Bezhanishvili, Balder ten Cate & Darko Sarenac (2006). Multimo Dal Logics of Products of Topologies. Studia Logica 84 (3):369-392.
John F. Phillips (2001). Modal Logics of Succession for 2-Dimensional Integral Spacetime. Journal of Philosophical Logic 30 (1):1-25.
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