  Constraint satisfaction problems (CSPs) for first-order reducts of finitely
bounded homogeneous structures form a large class of computational problems
that might exhibit a complexity dichotomy, P versus NP-complete. A powerful
method to obtain polynomial-time tractability results for such CSPs is a
certain reduction to polynomial-time tractable finite-domain CSPs defined over
k-types, for a sufficiently large k. We give sufficient conditions when this
method can be applied and illustrate how to use the general results to prove a
new complexity dichotomy for first-order expansions of the basic relations of
the well-studied spatial reasoning formalism RCC5. We also classify which of
these CSPs can be expressed in Datalog. Our method relies on Ramsey theory; we
prove that RCC5 has a Ramsey order expansion.
