An axiomatisation of the temporal logic of two dimensional Minkowski spacetime

TL;DR

This paper develops a formal logical system with axioms that precisely characterize the valid temporal statements in two-dimensional Minkowski spacetime, providing a rigorous foundation for reasoning about such spacetime structures.

Contribution

It introduces a complete set of axioms specifically tailored for the temporal logic of two-dimensional Minkowski spacetime, filling a gap in formal logical characterizations.

Findings

Axioms are sound and complete for the temporal validities over ( eals^2, <)

Provides a formal framework for reasoning about 2D Minkowski spacetime

Establishes a foundation for further logical analysis of spacetime structures

Abstract

We define temporal axioms that are sound and complete for the temporal validities over $(\reals^2, <)$.