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MIPC as the formalisation of an intuitionist concept of modality

Published online by Cambridge University Press:  12 March 2014

R. A. Bull
R. A. Bull*
Affiliation:
Wadham College, Oxford
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Extract

In the course of a recent paper on modal' extensions of the intuitionist propositional calculus, [1], I made some suggestions as to the relationships between the system MIPC, the intuitionist predicate calculus, and the question of producing a genuine intuitionist concept of modality. This paper may be regarded as a clarification of those rather inaccurate ideas in the light of Kripke's outstanding analysis of the intuitionist predicate calculus, [2]. (I use Kripke's notation and terminology here without explanation — this work is intended to be read in conjunction with [2].) In particular, I shall adapt his interpretation of his modelling to give an account of MIPC in terms of differing mathematical intuitions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 4 , December 1966 , pp. 609 - 616
Copyright
Copyright © Association for Symbolic Logic 1997

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References

[1]Bull, R. A., A modal extension of intuitionist logic. Notre Dame Journal of Formal Logic, vol. 6, No. 2 (April 1965), pp. 142–146.CrossRefGoogle Scholar
[2]Kripke, Saul A., Semantical analysis of intuitionist logic. Formal Systems and Recursive Functions, ed. Crossley, J. N. and Dummett, M. A. E.. Amsterdam, 1965.Google Scholar
[3]Kripke, Saul A., A completeness theorem in modal logic. This Journal, Vol. 24 (1959), pp. 1–14.Google Scholar
[4]Fitch, F. B., Intuitionistic modal logic with quantifiers. Portugaliae Mathematicae, vol. 7 (1948), pp. 113–118.Google Scholar