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Logical connectives for intuitionistic propositional logic

Published online by Cambridge University Press:  12 March 2014

Dean P. McCullough
Dean P. McCullough*
Affiliation:
University of Illinois, Urbana, Illinois
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Extract

In classical propositional logic it is well known that {7, ⊃ } is a functionally complete set with respect to a two-valued truth function modeling. I.e. all definable logical connectives are definable from 7 and ⊃. Other modelings of classical type propositional logics may have different functionally complete sets; for example, multivalued truth function modelings.

This paper examines the question of a functionally complete set of logical connectives for intuitionistic propositional logic with respect to S. Kripke's modeling for intuitionistic logic.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 1 , March 1971 , pp. 15 - 20
Copyright
Copyright © Association for Symbolic Logic 1971

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References

[1]Fitting, Melvin, Intuitionistic model theory and the Cohen independence proofs, Proceedings of the Conference on Proof Theory and Intuitionism, Buffalo, 1968 (Mimeographed).Google Scholar
[2]Kripke, Saul A., Semantical analysis of intuitionistic logic. I, Formal systems and recursive functions, Crossley, J. N. and Dummett, M. A. E., editors, North-Holland, Amsterdam, 1965, pp. 92–130.CrossRefGoogle Scholar