 One should distinguish sharply between logical frameworks, that is, choices as to what kind of thing a sequent is (e.g., Set-Fmla vs. Set-Set), on the one hand, and approaches to logic, that is, choices as to what kind of sequent-to-sequent rules are to be used (e.g., natural deduction vs. sequent calculus), on the other. Gentzen (1934) used Set-Set for a classical sequent calculus and Set-Fmla for the intuitionistic case. (More accurately, since he had finite sequences of formulas in mind rather than sets, and in the latter case allowed empty but not multiple succedents, we should really say something long the lines of Seq-Seq and Seq-Fmla0, respectively. Additional structural rules are then needed to allow permutation of formulas in a sequence.) Rudolf Carnap (1943) had a rather different reason for passing from Set-Fmla to Set-Set, one which is semantically based rather than grounded in considerations of proof-theoretic elegance.