In mobile and ambient environments, devices need to become autonomous, managing and resolving problems without interference from a user. The database of a (mobile) device can be seen as its knowledge about objects in the 'real world'. Data exchange between small and/or large computing devices can be used to supplement and update this knowledge whenever a connection gets established. In many situations, however, data from different data sources referring to the same real world objects, may conflict. It is the task of the data management system of the device to resolve such conflicts without interference from a user. In this paper, we take a first step in the development of a probabilistic XML DBMS. The main idea is to drop the assumption that data in the database should be certain: subtrees in XML documents may denote possible views on the real world. We formally define the notion of probabilistic XML tree and several operations thereon. We also present an approach for determining a logical semantics for queries on probabilistic XML data. Finally, we introduce an approach for XML data integration where conflicts are resolved by the introduction of possibilities in the database.