Inquiry calculus and the issue of negative higher order informations
Noel van Erp (TU Delft - Safety and Security Science)
Ronald Linger (TU Delft - Safety and Security Science)
Pieter van Gelder (TU Delft - Safety and Security Science)
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Abstract
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
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