Abstract
The logic of the weak law of excluded middleKC p is obtained by adding the formula ℸA ∨ ℸ ℸA 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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Boričić, B.R. A cut-free gentzen-type system for the logic of the weak law of excluded middle. Stud Logica 45, 39–53 (1986). https://doi.org/10.1007/BF01881548
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DOI: https://doi.org/10.1007/BF01881548