Abstract: The goal of a mediator system is to provide users a uniform interface to the multitude of information sources. To translate user queries, given in a mediated schema, to queries on the data sources, mediators rely on explicit mappings between the contents of the data sources and the meanings of the relations in the mediated schema.

Thus far, contents of data sources were described qualitatively. In this paper we describe the use of quantitative information in the form of probabilistic knowledge in mediator systems. We consider several kinds of probabilistic information: information about overlap between collections in the mediated schema, coverage of the information sources, and degrees of overlap between information sources. We address the problem of ordering accesses to multiple information sources, in order to maximize the likelihood of obtaining answers as early as possible. We describe a declarative formalism for specifying these kinds of probabilistic information, and we propose algorithms for ordering the information sources. Finally, we discuss a preliminary experimental evaluation of these algorithms on the domain of bibliographic sources available on the WWW.