Hirsch, R;
McLean, B;
(2018)
The temporal logic of two-dimensional Minkowski spacetime with slower-than-light accessibility is decidable.
In: Bezhanishvili, G and D'Agostino, G and Metcalfe, G and Studer, T, (eds.)
Advances in Modal Logic, Volume 12.
(pp. pp. 347-366).
AiML: Bern, Switzerland.
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Abstract
We work primarily with the Kripke frame consisting of two-dimensional Minkowski spacetime with the irreflexive accessibility relation ‘can reach with a slower-than-light signal’. We show that in the basic temporal language, the set of validities over this frame is decidable. We then refine this to PSPACE-complete. In both cases the same result for the corresponding reflexive frame follows immediately. With a little more work we obtain PSPACE-completeness for the validities of the Halpern–Shoham logic of intervals on the real line with two different combinations of modalities.
| Type: | Proceedings paper |
|---|---|
| Title: | The temporal logic of two-dimensional Minkowski spacetime with slower-than-light accessibility is decidable |
| Event: | Twelfth conference on "Advances in Modal logic," |
| ISBN: | 1904987206 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://www.aiml.net/volumes/volume12/ |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | temporal logic, basic temporal language, Minkowski spacetime, frame validity, Halpern–Shoham logic. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10090241 |
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