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 

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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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