Tautology testing with a generalized matrix reduction method

AbstractA formalization of the tautology problem in terms of matrices is given. From that a generalized matrix reduction method is derived. Its application to a couple of selected examples indicates a relatively efficient behaviour in testing the validity of a given formula in propositional logic—not only for machines but also for humans. A further result from that formalization is a reduction of the tautology problem to a part of Presburger arithmetic which involves formulas of the ∀∃∃⋯∃-type where all quantifiers have finite range