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Certain Method for Generating a Series of Logics

Published online by Cambridge University Press:  22 January 2016

Satoshi Miura  and
Shûrô Nagata
Satoshi Miura
Affiliation:
Toyota Technical College and Mathematical Institute, Nagoya University
Shûrô Nagata
Affiliation:
Toyota Technical College and Mathematical Institute, Nagoya University
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At first, we define three relations ⊇, =, and ⊃ in connection with a pair of logics L and L* as follows:

  • L ⊇ L*, if and only if every proposition provable in L* is also provable in L;

  • L = L*, if and only if L ⊇ L* and L* ⊇ L;

  • L ⊃ L*, if and only if L, ⊇ L* but not L* ⊇ L.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 31 , January 1968 , pp. 125 - 129
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

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