First-order Complete and Computationally Complete Query Languages for Spatio-Temporal Databases

TL;DR

This paper characterizes the exact nature of spatio-temporal queries in databases, defining their computability and invariance under geometric transformations that respect time, and identifies complete query languages for these classes.

Contribution

It introduces a formal framework for spatio-temporal queries based on invariance under specific geometric transformations and provides sound and complete languages for first-order and computable queries within these classes.

Findings

Identifies classes of genericity based on geometric transformations.

Defines sound and complete query languages for these classes.

Distinguishes between time-invariant and time-dependent genericity.

Abstract

We address a fundamental question concerning spatio-temporal database systems: ``What are exactly spatio-temporal queries?'' We define spatio-temporal queries to be computable mappings that are also generic, meaning that the result of a query may only depend to a limited extent on the actual internal representation of the spatio-temporal data. Genericity is defined as invariance under groups of geometric transformations that preserve certain characteristics of spatio-temporal data (e.g., collinearity, distance, velocity, acceleration, ...). These groups depend on the notions that are relevant in particular spatio-temporal database applications. These transformations also have the distinctive property that they respect the monotone and unidirectional nature of time. We investigate different genericity classes with respect to the constraint database model for spatio-temporal databases and we identify sound and complete languages for the first-order and the computable queries in these genericity classes. We distinguish between genericity determined by time-invariant transformations, genericity notions concerning physical quantities and genericity determined by time-dependent transformations.