The Expressive Power of Higher-Order Datalog

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.