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.

翻译：均匀一阶逻辑片段U1是一种自然地将双变量逻辑扩展到包含所有元数关系的上下文中的形式系统。我们综述了U1的性质，并研究了其与专为容纳更高元数关系而设计的描述逻辑（特别是DLR_reg）之间的关系。我们还定义了U1变体的描述逻辑版本，并证明了关于U1及相关逻辑表达力的一系列新成果。