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A Formalism for Primitive Logic and Mechanical Proof-Checking

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono
Katuzi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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The universal character of the primitive logic LO in the sense that popular logics such as the lower classical predicate logic LK, the intuitionistic predicate logic LJ, Johansson’s minimal predicate logic LM, etc. can be faithfully interpreted in LO is very remarkable even from the view point of mechanical proof-checking. Since LO is very simple, deductions in LO could be mechanized in a simple form if a suitable formalism for LO is found out. Main purpose of this paper is to introduce a practical formalism for LO, practical in the sense that it is suitable at least for mechanical proof-checking business.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 26 , February 1966 , pp. 195 - 203
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Church, A. [1] Introduction to Mathematical Logic, I, Princeton, 1956.Google Scholar
[2] Fitch, F. B., [1] A basic logic, J. Symb. Log., vol. 7 (1942), pp. 105–114.CrossRefGoogle Scholar
[3] Johansson, L., [1] Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus, Compositio Mathematica, vol. 4(1936), pp. 119–136.Google Scholar
[4] Lukasiewicz, J. and Tarski, A., [1] Untersuchungen über den Aussagenkalkül, Comptes Rendus des séances de la Société des Sciences et des Lettres de Varsovie, vol. 23 (1930), vol. III, pp. 31–2.Google Scholar
[5] Ono, K., [1] On universal character of the primitive logic, Nagoya Math. J., vol. 27-1 (1966), 331–353.CrossRefGoogle Scholar
[6] Ono, K., [2] A certain kind of formal theories, Nagoya Math. J., vol. 25 (1965), pp. 59–86.Google Scholar
[7] Ono, K., [3] On a practical way of describing formal deductions, Nagoya Math. J., vol. 21 (1962), pp. 115–121.Google Scholar