Hostname: page-component-cb9f654ff-5kfdg Total loading time: 0 Render date: 2025-09-06T12:21:38.222Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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