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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,357
External links
  • Through your library Configure
    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..

    View all 6 references

    Citations of this work BETA
    Similar books and articles
    Analytics

    Monthly downloads

    Added to index

    2009-01-28

    Total downloads

    8 ( #138,593 of 1,088,811 )

    Recent downloads (6 months)

    0

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.