Current information technologies allow people to acquire personal data related to their health, lifestyle, behavior, and activities, often using wearable and mobile devices. Personal data management technologies have emerged recently, in order to cope with the requirements of this type of data, ranging from personal clouds to self-storage solutions. Pryv.io is a comprehensive solution for managing this particularly sensible type of data streams, focusing both on data privacy and decentralization. In this paper, we describe SemPryv, a system aiming at providing a semantization mechanism for enriching personal data streams with standardized specialized vocabularies from third-party providers. It relies on third providers of semantic concepts, and includes rule-based mechanisms for facilitating the semantization process. A full implementation of SemPryv has been produced, pluggable to the existing Pryv.io platform, showing the feasibility of the approach.