Reasoning Theory

Reasoning Theory asks what is the least a system needs in order to reason, and what reasoning costs at that minimum. It has two halves: a floor, which says what cannot be removed, and a ceiling, stated as conjecture, which says that nothing more is needed. From an operational definition and eleven axioms, separation theorems identify three functions that no reasoner can drop under a stated requirement, identification apart from fit, a gate between candidates and claims, and an evaluation boundary, and a fourth, grammar extension, that transformational novelty requires if a stated conjecture holds. The theorems make no assumption about the substrate. On cost, what remains once verified control is reused is fresh work; that this remainder is the whole irreducible cost is the central conjecture, stated in a measurable form. The theory also gives the objects with which reasoners are described and built, a reading of language models in the same terms, and, for each conjecture, the experiment that would settle it. If the central conjecture holds, a system built to that minimum would leave nothing in its reasoning to optimise.