On the Predictability of Classical Propositional Logic

Abstract: In this work we provide a statistical form of empirical analysis of classical propositional logic decision methods called SAT solvers. This work is perceived as an empirical counterpart of a theoretical movement, called the enduring scandal of deduction, that opposes considering Boolean Logic as trivial in any sense. For that, we study the predictability of classical logic, which we take to be the distribution of the runtime of its decision process. We present a series of experiments that determines the run distribution of SAT solvers and discover a varying landscape of distributions, following the known existence of a transition of easy-hard-easy cases of propositional formulas. We find clear distributions for the easy areas and the transitions easy-hard and hard-easy. The hard cases are shown to be hard also for the detection of statistical distributions, indicating that several independent processes may be at play in those cases.