A cut-free Gentzen-type system for the logic of the weak law of excluded middle

Studia Logica 45 (1):39 - 53 (1986)
The logic of the weak law of excluded middleKC p is obtained by adding the formula A A as an axiom scheme to Heyting's intuitionistic logicH p . A cut-free sequent calculus for this logic is given. As the consequences of the cut-elimination theorem, we get the decidability of the propositional part of this calculus, its separability, equality of the negationless fragments ofKC p andH p , interpolation theorems and so on. From the proof-theoretical point of view, the formulation presented in this paper makes clearer the relations betweenKC p ,H p , and the classical logic. In the end, an interpretation of classical propositional logic in the propositional part ofKC p is given.
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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..
M. E. Szabo (1978). Algebra of Proofs. Sole Distributors for the U.S.A. And Canada, Elsevier North-Holland.
William Craig (1957). Replacement of Auxiliary Expressions. Journal of Symbolic Logic 22 (3):317-318.

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