On the Uniform One-dimensional Fragment

The uniform one-dimensional fragment of first-order logic, U1, is a recently introduced 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 DLRreg . 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.