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Functional completeness and canonical forms in many-valued logics1

Published online by Cambridge University Press:  12 March 2014

William H. Jobe
William H. Jobe*
Affiliation:
University of Tulsa and University of Kansas
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Extract

This paper examines the questions of functional completeness and canonical completeness in many-valued logics, offering proofs for several theorems on these topics.

A skeletal description of the domain for these theorems is as follows. We are concerned with a proper logic L, containing a denumerably infinite class of propositional symbols, P, Q, R, …, a finite set of unary operations, U1, U2,…, Ub, and a finite set of binary operations, B1, B2, …, Bc. Well-formed formulas in L are recursively defined by the conventional set of rules. With L there is associated an integer, M ≧ 2, and the integers m, where (1 ≦m≦M), are the truth values of L.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 27 , Issue 4 , December 1962 , pp. 409 - 422
Copyright
Copyright © Association for Symbolic Logic 1962

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Footnotes

1

The author gratefully acknowledges the aid of Walter E. Stuermann, Professor of Philosophy at the University of Tulsa, in bringing this paper into its published form.

References

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