Studia Logica

, Volume 46, Issue 1, pp 37–54 | Cite as

Definability and Quantifier Elimination for J3-theories

  • Ítala M. L. D'Ottaviano
Article

Abstract

The Joint Non-Trivialization Theorem, two Definability Theorems and the generalized Quantifier Elimination Theorem are proved for J3-theories. These theories are three-valued with more than one distinguished truth-value, reflect certain aspects of model type logics and can. be paraconsistent. J3-theories were introduced in the author's doctoral dissertation.

Keywords

Mathematical Logic Doctoral Dissertation Model Type Computational Linguistic Generalize Quantifier 
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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References

  1. [1]
    A. I. Arruda, A survey of paraconsistent logic, Mathematical Logic in Latin America, North-Holland, Amsterdam, 1980, pp. 1–41.Google Scholar
  2. [2]
    L. Borkowski (Ed.), Selected Works of J. Łukasiewicz, North-Holland, Amsterdam, 1970.Google Scholar
  3. [3]
    I. M. L. D'Ottaviano and N. C. A. da Costa, Sur un problème de Jaśkcowski, C. R. Acad. Sc. Paris, 270A, 1970, pp. 1349–1353.Google Scholar
  4. [4]
    I. M. L. D'Ottaviano, Sobre uma teoria de modelos trivalente (Thesis), Universidade Estadual de Campinas, 1982.Google Scholar
  5. [5]
    I. M. L. D'Ottaviano, The completeness and compactness of a three-valued first-order logic, Revista Colombiana de Matemáticas, vol. XIX, 1–2, Proceedings of the Fifth Latin-American Symposium on Mathematical Logic, 1985, pp. 31–42.Google Scholar
  6. [6]
    I. M. L. D'Ottaviano, The model extension theorems for J 3-theories, Methods in Mathematical Logic, Lecture Notes in Mathematics, 1130, Springer Verlag, 1985, pp. 157–173.Google Scholar
  7. [7]
    J. Łukasiewicz and A. Tarski, Untersuchunger Über den Aussagenkalküll, C. R. Soc. Sci. Lett. Varsovie 23, 1930, pp. 39–50 (Translation to English in [2], pp. 131–152).Google Scholar
  8. [8]
    N. Rescher, Many-valued Logics, McGraw-Hill, N. York, 1969.Google Scholar
  9. [9]
    J. B. Rosser and A. Turquette, Many-valued Logics, North-Holland, Amsterdam, 1952.Google Scholar
  10. [10]
    J. R. Shoenfield, Mathematical Logic, Addison Wesley, Reading, 1967.Google Scholar

Copyright information

© Polish Academy of Sciences 1987

Authors and Affiliations

  • Ítala M. L. D'Ottaviano
    • 1
  1. 1.Institute of Mathematics, Statistics and Computer SciencesState University of CampinasCampinasBrazil

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