A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multi-sorted) .rst-order logic can be used to represent and reason about policies. Because we use first-order logic, policies have a clear syntax and semantics. We show that further restricting the fragment results in a language that is still quite expressive yet is also tractable. More precisely, questions about entailment, such as ?May Alice access the file??, can be answered in time that is a low-order polynomial (indeed, almost linear in some cases), as can questions about the consistency of policy sets. We also give a brief overview of a prototype that we have built whose reasoning engine is based on the logic and whose interface is designed for non-logicians, allowing them to enter both policies and background information, such as ?Alice is a student?, and to ask questions about the policies.