We investigate the problem of sharing private information on the Web, where the information is hosted on different machines that may use different access control and distribution schemes. We introduce a distributed knowledge-base model, termed WebdamExchange, that comprises logical statements for specifying data, access control, distribution and knowledge about other peers. The statements can be communicated, replicated, queried, and updated, while keeping track of time and provenance. This unified base allows applications to reason declaratively about what data is accessible, where it resides, and how to retrieve it securely.