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Lemmon-style bases for the systems S1°-S4°

Published online by Cambridge University Press:  12 March 2014

J. Jay Zeman
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Extract

In [1], Lemmon provides us with his now well-known formulations of the Lewis-modal systems S1 through S4. This paper will present similar bases for the related systems S1° and S2° of Feys [2], and S3° and S4° of Sobocinski [3]. Notation and definitions here will be as in [1]. Standard bases for the Lewis-modal systems may be drawn from the following stock of axioms and rules, as is done in [1].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 3 , 10 October 1968 , pp. 458 - 461
Copyright
Copyright © Association for Symbolic Logic 1968

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References

[1]Lemmon, E. J., New foundations for Lewis modal systems, this Journal, vol. 22 (1957), pp. 176–186.Google Scholar
[2]Feys, R., Les systèmes formalisés des modalités aristotéliciennes, Revue Philosophique de Louvain, vol. 48 (1950), pp. 478–509.CrossRefGoogle Scholar
[3]Soboci, B.ński, A contribution to the axiomatization of Lewis' system S5, Notre Dame journal of formal logic, vol. 3 (1962), pp. 51–60.Google Scholar
[4]Feys, R., Modal logics (ed. with some complements by Dopp, Joseph), E. Nauwelaerts, Louvain and Paris, 1965.Google Scholar
[5]Thomas, Ivo, Decision procedures for S2° and T°, Notre Dame journal of formal logic, vol. 5 (1964), pp. 319–320.Google Scholar