This paper generalizes some results of BELNA1? 1959b (presented more elaborately in Anmanson and BELNAP 1962), to a non-classical system of quantification theory, based on an intensional relation of entailment. The fundamental idea behind the present quantiiicational treatment is most easily made clear by reference to the propositional calculus E (for which see Annnnson 1959, together with works cited above). Let A —-> B be an entailment in which only truthiunctions occur in A and B. In the system E we can rewrite A in disjunctive normal form, and B in conjunctive normal form, obtaining an equivalent formula (in the sense of the double arrow <—>):