Hostname: page-component-5f745c7db-j9pcf Total loading time: 0 Render date: 2025-01-06T12:26:47.912Z Has data issue: true hasContentIssue false
  • English
  • Français

Systematization of finite many-valued logics through the method of tableaux

Published online by Cambridge University Press:  12 March 2014

Walter A. Carnielli
Walter A. Carnielli*
Affiliation:
Department of Mathematics, University of Campinas, 13081 Campinas, Brazil
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a unified treatment of the propositional and first-order many-valued logics through the method of tableaux. It is shown that several important results on the proof theory and model theory of those logics can be obtained in a general way.

We obtain, in this direction, abstract versions of the completeness theorem, model existence theorem (using a generalization of the classical analytic consistency properties), compactness theorem and Löwenheim-Skolem theorem.

The paper is completely self-contained and includes examples of application to particular many-valued formal systems.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 2 , June 1987 , pp. 473 - 493
Copyright
Copyright © Association for Symbolic Logic 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[0]Borowik, P., On Gentzen's axiomatization of the reducts of many-valued logics, this Journal, vol. 48 (1983), pp. 1224–1225 (abstract).Google Scholar
[1]Carnielli, W. A., Sobre o método dos tableaux em lógicas polivalentes finitáias, Ph.D. thesis, University of Campinas, Brazil, 1982.Google Scholar
[2]Carnielli, W. A., The problem of quantificational completeness and the characterization of all perfect quantifiers in 3-valued logics, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik (to appear).Google Scholar
[3]D'Ottaviano, I. M. L., Sobre uma teoria de modelos trivalente, Ph.D. thesis, University of Campinas, Brazil, 1982.Google Scholar
[4]Fitting, M., Model-existence theorems for modal and intuitionistic logics, this Journal, vol. 38 (1973), pp. 613–627.Google Scholar
[5]Rasiowa, H. and Sikorski, R., The mathematics of metamathematics, PWN, Warsaw, 1970.Google Scholar
[6]Rosenberg, I., The number of maximal closed classes in the set of functions over a finite domain, Journal of Combinatorial Theory Series A, vol. 14 (1973), pp. 1–7.CrossRefGoogle Scholar
[7]Sette, A. M., On the propositional calculus p1, Mathematica Japonicae, vol. 16 (1973), pp. 173–180.Google Scholar
[8]Smullyan, R. M., A unifying principle in quantification theory, Proceedings of the National Academy of Sciences of the United States of America, vol. 49 (1963), pp. 828–832.CrossRefGoogle Scholar
[9]Smullyan, R. M., First order logic. Springer-Verlag, Berlin, 1968.CrossRefGoogle Scholar
[10]Surma, S. J., An algorithm for axiomatizing very finite logic, Computer science and multiple-valued logic: theory and applications (Rine, D. C., editor), North-Holland, Amsterdam, 1977, pp. 137–143.CrossRefGoogle Scholar