This paper describes the design and implementation of a new operating system authorization architecture to support trustworthy computing. Called logical attestation, this architecture provides a sound framework for reasoning about run time behavior of applications. Logical attestation is based on attributable, unforgeable statements about program properties, expressed in a logic. These statements are suitable for mechanical processing, proof construction, and verification; they can serve as credentials, support authorization based on expressive authorization policies, and enable remote principals to trust software components without restricting the local user’s choice of binary implementations. We have implemented logical attestation in a new operating system called the Nexus. The Nexus executes natively on x86 platforms equipped with secure coprocessors. It supports both native Linux applications and uses logical attestation to support new trustworthy-computing applications. When deployed on a trustworthy cloud-computing stack, logical attestation is efficient, achieves high-performance, and can run applications that provide qualitative guarantees not possible with existing modes of attestation.