Abstract
We present the proof that the temporal logic of two-dimensional Minkowski spacetime is decidable, PSPACE-complete. The proof is based on a type of two-dimensional mosaic. Then, we present the modification of the proof so as to work for slower-than-light signals. Finally, a subframe of the slower-than-light Minkowski frame is used to prove the new result that the temporal logic of real intervals with during as the accessibility relation is also PSPACE-complete.
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J. Madarász
Alfréd Rényi Institute of Mathematics
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Acknowledgements
The authors would like to thank our reviewer, Judit Madarász, for constructive suggestions—we believe the chapter is considerably improved!
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Hirsch, R., McLean, B. (2022). Temporal Logic of Minkowski Spacetime. In: Düntsch, I., Mares, E. (eds) Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Outstanding Contributions to Logic, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-030-71430-7_15
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