Temporal Logic of Minkowski Spacetime

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.