# The Expressive Power of Higher-Order Datalog

## TL;DR

This paper extends classical descriptive complexity results to higher-order Datalog, showing that on ordered databases, k-order Datalog captures (k-1)-EXPTIME, indicating increased expressive power.

## Contribution

It generalizes the expressive power of Datalog to higher orders, establishing a precise complexity characterization for k-order Datalog on ordered databases.

## Key findings

- k-order Datalog captures (k-1)-EXPTIME on ordered databases
- Higher-order Datalog has greater expressive power than classical Datalog
- The results open avenues for further theoretical and practical research

## Abstract

A classical result in descriptive complexity theory states that Datalog expresses exactly the class of polynomially computable queries on ordered databases. In this paper we extend this result to the case of higher-order Datalog. In particular, we demonstrate that on ordered databases, for all $k\geq2$, $k$-order Datalog captures $(k-1)$-EXPTIME. This result suggests that higher-order extensions of Datalog possess superior expressive power and they are worthwhile of further investigation both in theory and in practice. This paper is under consideration for acceptance in TPLP.