We present an architecture for authentication and authorization on the Web that is based on the Self-Sovereign Identity paradigm. Using our architecture, we aim to achieve semantic interoperability across different approaches to SSI. We build on the underlying RDF data model of the W3C’s recommendation for Verifiable Credentials and specify semantic access control rules using SHACL. Our communication protocol for an authorization process is based on Decentralised Identifiers and extends the Hyperledger Aries Present Proof protocol. We propose a modular architecture that allows for flexible extension, e. g., for supporting more signature schemes or Decentralised Identifier Methods. For evaluation, we implemented a Proof-of-Concept: We show that a Web-based approach to SSI outperfoms a blockchain-based approach to SSI in terms of End-to-End execution time.