Consequence and Confirmation

Gentzen's account of logical consequence is extended so as to be- come a matter of degree. We characterize and study two kinds of function G, where G(X, Y) takes values between 0 and 1, which represent the degree to which the set X of statements (understood conjunctively) logically implies the set Y of statements (understood disjunctively). It is then shown that these func- tions are essentially the same as the absolute and the relative probability func- tions described by Carnap.