  We study the complexity of evaluating positive equality-free sentences of
first-order (FO) logic over a fixed, finite structure B. This may be seen as a
natural generalisation of the non-uniform quantified constraint satisfaction
problem QCSP(B). We introduce surjective hyper-endomorphisms and use them in
proving a Galois connection that characterises definability in positive
equality-free FO. Through an algebraic method, we derive a complete complexity
classification for our problems as B ranges over structures of size at most
three. Specifically, each problem is either in Logspace, is NP-complete, is
co-NP-complete or is Pspace-complete.
