This paper identifies the need for a new theory of information and develops a mathematical model which distinguishes between: (1) data, as directly observable facts; (2) information, as structured collections of data; and (3) knowledge, as methods of using information. The model is based on the ideas of the binary relational model and uses the concept of semantic categories to develop a semantic information retrieval system. Originally conceived to provide a firm foundation for information science, the model may also be used as the basis for an advanced information retrieval system. (EW)