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

Studia Logica 45 (1):39 - 53 (1986)
Abstract
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
William Craig (1957). [Omnibus Review]. Journal of Symbolic Logic 22 (4):360-363.
M. E. Szabo (1978). Algebra of Proofs. Sole Distributors for the U.S.A. And Canada, Elsevier North-Holland.
Gaisi Takeuti (1987). Proof Theory. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..

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