A note on sequent calculi intermediate between LJ and LK

Studia Logica 47 (2):151 - 157 (1988)
We prove that every finitely axiomatizable extension of Heyting's intuitionistic logic has a corresponding cut-free Gentzen-type formulation. It is shown how one can use this result to find the corresponding normalizable natural deduction system and to give a criterion for separability of considered logic. Obviously, the question how to obtain an effective definition of a sequent calculus which corresponds to a concrete logic remains a separate problem for every logic.
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DOI 10.1007/BF00370289
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References found in this work BETA
Gaisi Takeuti (1987). Proof Theory. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
Toshio Umezawa (1959). On Intermediate Propositional Logics. Journal of Symbolic Logic 24 (1):20-36.

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