On the uniform one-dimensional fragment
This work addresses foundational logic and knowledge representation problems for researchers in formal methods and AI, but it is incremental as it builds on existing logics.
The paper surveys the uniform one-dimensional fragment (U1) of first-order logic, which extends two-variable logic to handle relations of all arities, and investigates its relationship to description logics like DLR_reg, proving new results about their expressivity.
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.