The main objective of this paper is to establish a coherent framework for information retrieval based on the axiomatic decision theory. In information retrieval one has to deal with two difficult problems (knowledge representation and query formulation), both of which are absent in conventional database systems. It is argued that the axiomatic decision theory provides a useful framework to study these complex issues. Two quantitative representation systems are introduced. One is developed from the expected utility model and the other is derived from the concepts of evidential reasoning. An inductive learning algorithm is suggested for constructing a user query. The experimental results seem to provide some support for the theoretical arguments presented here. Although the focus in this paper is mainly on information retrieval, the current work may be viewed as a preliminary effort towards unifying symbolic and numeric reasoning with incomplete or uncertain information.