These intermediate formulae will be useful for the explicit computations carried out in our applications.
They do not show mathematical formulae, but they refer to mathematical principles by name, with discussion of the significance, and ample references.
From a knowledge base of classical (non-defeasible) formulae, plus defeasible (meta-level) rules, arguments "for" and "against" any particular inference can be constructed.
Presumably, their theory was that their formulae represent not only historical realities but synchronic realities of some sort as well.
Unlike many other textbooks, this one takes special care in explaining the intuition behind the basic learning formulae.
Alternatively, attempts to use sophisticated mathematical techniques, such as high order polynomial equations, may fail because the formulae are too complex for statistical treatment.
Each extension is a set of classical formulae.
After this step, traditional formulae of symbolic summation can be applied and polytope volumes are expressed by polynomials whose variables are symbolic sizes.
