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Replacement in some modal systems

Published online by Cambridge University Press:  12 March 2014

Ivo Thomas
Ivo Thomas*
Affiliation:
University of Notre Dame
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Extract

In the original formulations of Lewis's S1–S5 in [1], Feys's S1°, S2° in [2], and Sobociński's S3°, S4° in [3], a primitive rule is that of replacement for strict equivalents which it is enough to express formally as:

RI: where γ′ is like γ except for having β at one place where γ has α.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 4 , January 1969 , pp. 569 - 570
Copyright
Copyright © Association for Symbolic Logic 1969

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References

[1]Lewis, C. I. and Langford, C. H., Symbolic logic, 2nd ed., Dover, New York, 1959.Google Scholar
[2]Feys, R., Les systèmes formalisés des modalités aristotéliciennes, Revue néo-scholastiqut de philosophie, vol. 40 (1937), pp. 517–553 and vol. 41 (1938), pp. 217–252.CrossRefGoogle Scholar
[3]Sobociński, B., A contribution to the axiomatization of Lewis's system S5, Notre Dame journal of formal logic, vol. 3 (1962), pp. 51–60.CrossRefGoogle Scholar
[4]Lemmon, E. J., New foundations for Lewis modal systems, this Journal, vol. 21 (1957), pp. 176–186.Google Scholar
[5]Canty, J. T., Systems classically axiomatized and properly contained in Lewis's S3, Notre Dame journal of formal logic, vol. 6 (1965), pp. 309–318.CrossRefGoogle Scholar
[6]Zeman, J. J., Lemmon-style bases for the systems S1°-S4°, this Journal (to appear).Google Scholar