A proof procedure for quantification theory

Abstract

The purpose of this paper is to present and justify a simple proof procedure for quantification theory. The procedure will take the form of a method for proving a quantificational schema to be inconsistent, i.e., satisfiable in no non-empty universe. But it serves equally for proving validity, since we can show a schema valid by showing its negation inconsistent.Method A, as I shall call it, will appear first, followed by a more practical adaptation which I shall call B. The soundness and completeness of A will be established, and the equivalence of A and B. Method A, as will appear, is not new.The reader need be conversant with little more than the fairly conventional use (as in [8]) of such terms as ‘quantificational schema’, ‘interpretation’, ‘valid’, ‘consistent’, ‘prenex’, and my notation (as in [7]) of quasi-quotation.