The umbilical cord of finite model theory

TL;DR

Finite model theory, rooted in mathematical logic, was significantly shaped by its early focus on relational databases, influencing its development more than its original motivation from complexity theory.

Contribution

This paper explores how relational database theory influenced the development of finite model theory, highlighting its impact beyond traditional mathematical logic.

Findings

Finite model theory was initially driven by relational database applications.

Relational database theory significantly shaped finite model theory's development.

Finite model theory's evolution was also influenced by complexity theory considerations.

Abstract

Model theory was born and developed as a part of mathematical logic. It has various application domains but is not beholden to any of them. A priori, the research area known as finite model theory would be just a part of model theory but didn't turn out that way. There is one application domain -- relational database management -- that finite model theory had been beholden to during a substantial early period when databases provided the motivation and were the main application target for finite model theory. Arguably, finite model theory was motivated even more by complexity theory. But the subject of this paper is how relational database theory influenced finite model theory. This is NOT a scholarly history of the subject with proper credits to all participants. My original intent was to cover just the developments that I witnessed or participated in. The need to make the story coherent forced me to cover some additional developments.