On first glance agent technology seems more like a hostile intruder into the database world. On the other hand, the two could easily complement each other, since agents carry out information processes whereas databases supply information to processes. Nonetheless, to view agent technology from a database perspective seems to question some of the basic paradigms of database technology, particularly the premise of semantic consistency of a database. The paper argues that the ensuing uncertainty in distributed databases can be modelled by beliefs, and develops the basic concepts for adjusting peer-to-peer databases to the individual beliefs in single nodes and collective beliefs in the entire distributed database.