CHAPTER 1
VALUATION ALGEBRAS
The valuation algebra framework provides the algebraic foundation for the application of all generic inference mechanisms introduced in this book and therefore marks the beginning of our studies. Comparable to the total order that is required for the application of sorting procedures, all formalisms must satisfy the structure of a valuation algebra in order to be processed by these generic inference tools. Further, this framework mirrors all the essential properties we naturally associate with the rather imprecise notions of knowledge and information. Let us engross ourselves in this thought and put our daily perception of information into words: information exists in pieces and comes from different sources. A piece of information refers to some specific questions that we later call the domain of an information piece. Also, there are two principal operations to manipulate information: we may combine or aggregate pieces of information to a new information piece and we may project a piece of information to some specific question which corresponds to information extraction. Depending on the operation, we either get a broader or more focused information. In the following section, we give a formal definition of the valuation algebra framework consisting of its operations and axioms. Along the way, we further bear on our idea of valuations as pieces of knowledge or information to clarify the rather abstract and formal structures.
1.1 OPERATIONS AND AXIOMS ...
