The Closed-World Assumption (CWA) on a database expresses that an atom not in the database is false. The CWA is only applicable in domains where the database has complete knowledge. In many cases, for example in the context of distributed databases, a data source has only complete knowledge about part of the domain of discourse. In this paper, we introduce an expressive and intuitively appealing method of representing a local closed-world assumption (LCWA) of autonomous data-sources. This approach distinguishes between the data that is conveyed by a data-source and the meta-knowledge about the area in which these data is complete. The data is stored in a relational database that can be queried in the standard way, whereas the meta-knowledge about its completeness is expressed by a first order theory that can be processed by an independent reasoning system (for example a mediator). We consider different ways of representing our approach, relate it to other methods of representing local closed-word assumptions of data-sources, and show some useful properties of our framework which facilitate its application in real-life systems.