Modal and Temporal Logics for Abstract Space-Time Structures
Sara L. Uckelman, Joel Uckelman

Abstract:
In the 4th century BC, the Greek philosopher Diodoros Chronos gave a
temporal definition of necessity.  Because it connects modality and
temporality, this definition is of interest to philosophers working
within branching time or branching space-time models.  This definition
of necessity can be formalized and treated within a logical framework.
We give a survey of the several known modal and temporal logics of
abstract space-time structures based on the real numbers and the
integers, considering three different accessibility relations between
spatio-temporal points.