CHAPTER 7
LANGUAGE AND INFORMATION
Information often concerns the values of variables or the truth of propositions satisfying equations or logical formulae. It is in many cases stated through linguistic constructs with a determined interpretation. This general situation is a source of many valuation algebras that all have the interesting property of idempotent combination. Moreover, they always provide neutral and null elements and therefore adopt the structure of an information algebra according to Section 4.2.1. In such cases, the computations are usually not carried out on the level of the information or valuations, but rather in the corresponding linguistic system using syntactic procedures. In this chapter, we illustrate the general concept of representing information by formal languages with a determined interpretation. We first give two important examples of such formalisms and then derive a more general concept that serves as a generic construction to produce the two previous examples and many other instances.
In the first section, we show how propositional logic serves to state the truth about propositions or logical variables. The interpretation of propositional formulae represents the information expressed by the formulae. We shall show that such pieces of information form a valuation algebra and more particularly an information algebra. The second example presented in Section 7.2 concerns systems of linear equations whose solutions provide information about the values ...
