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The elimination of De Re modalities

Published online by Cambridge University Press:  12 March 2014

M. J. Cresswell
M. J. Cresswell*
Affiliation:
Victoria University of Wellington Wellington, New Zealand
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Extract

A formula α of modal LPC is a de re modality iff it contains a free individual variable within the scope of a modal operator; otherwise α is de dicto.1 We shall say that de re modalities are eliminable in a system S of modal LPC iff there is a transformation R on wffs of S such that R(α) is de dicto and ├sα ≡ R(α). We shall show that where S is LPC + S5 + Pr2 then de re modalities are not eliminable in S.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 3 , 17 November 1969 , pp. 329 - 330
Copyright
Copyright © Association for Symbolic Logic 1969

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References

[1]Hughes, G. E. and Cresswell, M. J., An introduction to modal logic, Methuen, London, 1968.Google Scholar
[2]Prior, A. N., Formal logic, Oxford University Press, Oxford, 1955.Google Scholar
[3]Von Wright, G. H., An essay in modal logic, North-Holland, Amsterdam, 1951.Google Scholar