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Binary connectives functionally complete by themselves in S5 modal logic

Published online by Cambridge University Press:  12 March 2014

Gerald J. Massey
Gerald J. Massey*
Affiliation:
Michigan State University
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Extract

This paper answers affirmatively the open question of Massey [1] concerning the existence of binary connectives functionally complete by themselves in two-valued truth tabular logic, i.e. in the modal theory S5. Since {∼, ⊃, ◊} is a functionally complete set of connectives (Massey [1, § 4]), the following definitions show that the binary operator ф, the semantics of which is given below, is functionally complete by itself:

It is left to the reader to verify, by means of complete sets of truth tables (see Massey [1, §§ 1 and 3]), that the foregoing definitions are correct.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 1 , June 1967 , pp. 91 - 92
Copyright
Copyright © Association for Symbolic Logic 1967

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References

[1]Massey, G. J., The theory of truth tabular connectives, both truth functional and modal, this Journal (forthcoming).Google Scholar