Definitions: the primitive concept of logics or The Leśniewski-Tarski legacy

E. G. K. López-Escobar; Francisco Miraglia

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Displaying similar documents to “Definitions: the primitive concept of logics or The Leśniewski-Tarski legacy”

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Shokoofeh Ghorbani (2020)

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In this paper, we introduce and study a corresponding logic to equality-algebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equality-algebras and local deduction theorem. We show that this logic is regularly algebraizable with respect to the variety of equality∆-algebras but it is not Fregean. Then we introduce the concept of (prelinear) equality∆-algebras and investigate some related properties. Also, we study ∆-deductive...

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An Alternative Natural Deduction for the Intuitionistic Propositional Logic

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A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via translations from sequent calculus derivations to natural deduction derivations and back.

Intuitionistic logic considered as an extension of classical logic : some critical remarks

Javier Legris, Jorge A. Molina (2001)

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In this paper we analyze the consideration of intuitionistic logic as an extension of classical logic. This — at first sight surprising — point of view has been sustained explicitly by Jan Łukasiewicz on the basis of a mapping of classical propositional logic into intuitionistic propositional logic by Kurt Gödel in 1933. Simultaneously with Gödel, Gerhard Gentzen had proposed another mapping of Peano´s arithmetic into Heyting´s arithmetic. We shall discuss these mappings in connection...

Provability in arithmetic and a schema of Grzegorczyk

George Boolos (1980)

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