  The uniform one-dimensional fragment of first-order logic, U1, is a formalism
that extends two-variable logic in a natural way to contexts with relations of
all arities. We survey properties of U1 and investigate its relationship to
description logics designed to accommodate higher arity relations, with
particular attention given to DLR_reg. We also define a description logic
version of a variant of U1 and prove a range of new results concerning the
expressivity of U1 and related logics.
