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Studia Logica

, Volume 45, Issue 1, pp 39–53 | Cite as

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

  • Branislav R. Boričić
Article

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.

Keywords

Mathematical Logic Computational Linguistic Classical Logic Propositional Logic Sequent Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Polish Academy of Sciences 1986

Authors and Affiliations

  • Branislav R. Boričić
    • 1
  1. 1.Ekonomski FakultetUniverzitet u BeograduBeogradJugoslavija

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