Entropy, Vol. 19, Pages 622: Inquiry Calculus and the Issue of Negative Higher Order Informations (Entropy)

In this paper, we will give the derivation of an inquiry calculus, or, equivalently, a Bayesian information theory. From simple ordering follow lattices, or, equivalently, algebras. Lattices admit a quantification, or, equivalently, algebras may be extended to calculi. The general rules of quantification are the sum and chain rules. Probability theory follows from a quantification on the specific lattice of statements that has an upper context. Inquiry calculus follows from a quantification on the specific lattice of questions that has a lower context. There will be given here a relevance measure and a product rule for relevances, which, taken together with the sum rule of relevances, will allow us to perform inquiry analyses in an algorithmic manner.