Temporal Logic of Minkowski Spacetime
Robin Hirsch, Brett McLean

TL;DR
This paper proves the decidability and PSPACE-completeness of the temporal logic for two-dimensional Minkowski spacetime, extends the proof to slower-than-light signals, and applies it to real intervals with 'during' as the relation.
Contribution
It introduces a novel proof technique using two-dimensional mosaics and extends the results to more general spacetime models and interval logics.
Findings
Temporal logic of 2D Minkowski spacetime is PSPACE-complete.
The proof technique applies to slower-than-light signals.
The logic of real intervals with 'during' is also PSPACE-complete.
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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Taxonomy
TopicsQuantum Mechanics and Applications · Cellular Automata and Applications · Semiconductor Lasers and Optical Devices
