We propose a logic for specifying security policies at a very high level of abstraction. The logic accommodates the subjective nature of affirmations for authorization and knowledge without compromising the objective nature of logical inference. In order to accurately model consumable authorizations and resources, we construct our logic as a modal enrichment of linear logic. We show that the logic satisfies cut elimination, which is a proof-theoretic expression of its soundness. We also demonstrate that the logic is amenable to meta-reasoning about specifications expressed in it through several examples.