Classes of Spatiotemporal Objects and Their Closure Properties

TL;DR

This paper introduces a new data model for spatio-temporal databases, defining classes of objects and analyzing their closure properties under set operations, with extensions for improved practical utility.

Contribution

It proposes a novel spatio-temporal data model with classes of objects and analyzes their closure properties, extending the model for better applicability.

Findings

Certain classes are closed under all set operators

Extension of the model improves closure properties

A normal form for the extended model is discussed

Abstract

We present a data model for spatio-temporal databases. In this model spatio-temporal data is represented as a finite union of objects described by means of a spatial reference object, a temporal object and a geometric transformation function that determines the change or movement of the reference object in time. We define a number of practically relevant classes of spatio-temporal objects, and give complete results concerning closure under Boolean set operators for these classes. Since only few classes are closed under all set operators, we suggest an extension of the model, which leads to better closure properties, and therefore increased practical applicability. We also discuss a normal form for this extended data model.