 A quantitative attempt at specifying the information yield of deductions was undertaken by Jaakko Hintikka with his theory of surface information and depth information (Hintikka 1970, 1973). The theory of surface and depth information extends Bar-Hillel and Carnap’s theory of semantic information from the monadic predicate calculus all the way up to the full polyadic predicate calculus. This itself is a considerable achievement, but although technically astounding, a serious restriction of this approach is that it is only a fragment of the deductions carried out within full first-order logic that yield a non-zero information measure. The rest of the deductions in the full polyadic predicate calculus, as well as all of those in the monadic predicate calculus and propositional calculus, measure 0, (see Sequoiah-Grayson 2008). 