Learning Concepts Definable in First-Order Logic with Counting

We study classification problems over relational background structures for hypotheses that are defined using logics with counting. The aim of this paper is to find learning algorithms running in time sublinear in the size of the background structure. We show that hypotheses defined by FOCN(P)-formulas over structures of polylogarithmic degree can be learned in sublinear time. Furthermore, we prove that for structures of unbounded degree there is no sublinear learning algorithm for first-order formulas.