UM CÁLCULO DE SEQUENTES A PARTIR DO SISTEMA TRIVALENTE E FRACAMENTE INTUICIONISTA I1

Authors

  • Elias Oliveira Vieira dos Santos Mestrando em Matemática Aplicada e Computacional da Unesp, Campus de Presidente Prudente
  • Luiz Henrique da Cruz Silvestrini Professor do Departamento de Matemática da Unesp, Campus de Bauru, e professor do Programa de Pós-Graduação em Filosofia da Unesp, Campus de Marília

DOI:

https://doi.org/10.36311/1984-8900.2023.v15n38.p174-206

Keywords:

Intuitionistic logics, Logic I1, Sequent Calculus

Abstract

The logic I1, a three-valued system with an weakly-intuitionistic character, was introduced by Sette and Carnielli in 1995 via axiomatic (Hilbertian) system. The aim of this paper is to present this system in a logical formalism by sequent calculus, called GI1, which presents itself as a theorem proof system, characterized as an algorithm, being more applicable from a computational point of view, by means of the dualization of the analytical tableaux TI1. Furthermore, the deductive equivalence between the sequent system GI1 and the Hilbertian system I1 is presented.

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References

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CARNIELLI, W. A. On sequents and tableaux for many-valued logics. Journal of Non-Classical Logic, v. 8, p. 59-76, 1991.

GENTZEN G. The collected papers of Gerhard Gentzen (M. E. Szabo, ed.), NorthHolland Publishing Company, 1969.

SANTOS, E. O. V.; SILVESTRINI, L. H. C. O Método dos tableaux aplicado ao Cálculo Trivalente e Intuicionista I1. Trends in Computational and Applied Mathematics, v. 22, n. 3, p. 393-412, 2021.

SANTOS, J. B. Infraestrutura para provadores interativos de teoremas na web. Dissertação de Mestrado, PUC-RIO, Rio de Janeiro, 2010.

SETTE, A. M.; CARNIELLI. W. A. Maximal weakly-intuicionistic logics. StudiaLogica, v. 55, p. 181-203, 1995.

SUNDHOLM. G. Systems of deduction. In D. Gabbay and R Guenthner, editors, Handbook of Philosophical Logic, v. I, chapter I.2, p. 133–188. Reidel, Dordrecht, 1983.

SMULLYAN, R. M. First-order logic. New York: Dover Publication, 1968.

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Published

2023-07-28

Issue

Vol. 15 No. 38 (2023)

Section

Artigos

License

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