Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T05:29:47.359Z Has data issue: false hasContentIssue false
  • English
  • Français

Four Simple Systems of Modal Propositional Logic

Published online by Cambridge University Press:  14 March 2022

Gerald J. Massey
Gerald J. Massey*
Affiliation:
Michigan State University
Get access Rights & Permissions [Opens in a new window]

Abstract

Four progressively ambitious systems of modal propositional logic are set forth, together with decision procedures. The simultaneous employment of parenthesis notation and parenthesis-free notation, the dual use of symbols as primitive and defined, and the introduction of a new modal operator (the truth operator) are the principal devices used to effect the development of these logics. The first two logics turn out to be “the same” as two of von Wright's systems.

Type
Research Article
Information
Philosophy of Science , Volume 32 , Issue 4 , October 1965 , pp. 342 - 355
Copyright
Copyright © 1965 by The Philosophy of Science Association

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.)

References

[1] Carnap, R., “Intellectual Autobiography” Schilpp, in P., ed., The Philosophy of Rudolf Carnap. LaSalle: Open Court Publishing Co.; 1963.Google Scholar
[2] Carnap, R., Meaning and Necessity. Chicago: U. of Chicago Press; 1960.Google Scholar
[3] Church, A., Introduction to Mathematical Logic, Vol. I. Princeton: Princeton U. Press; 1956.Google Scholar
[4] Feys, R., “Carnap on Modalities” in P. Schilpp, ed., The Philosophy of Rudolf Carnap.Google Scholar
[5] Feys, R., Modal Logics. Louvain: E. Nauwelaerts; 1965.Google Scholar
[6] Hintikka, J., “The Modes of Modality”, Acta Philosophica Fennica, v. 16 (1963), pp. 65–82.Google Scholar
[7] Kripke, S., “A completeness theorem in modal logic”, Journal of Symbolic Logic, v. 24 (1959), pp. 1–14.Google Scholar
[8] Kripke, S., “Semantical Considerations on Modal Logic”, Acta Philosophica Fennica, v. 16 (1963), pp. 83–94.Google Scholar
[9] Leonard, H., “Two-Valued Truth Tables for Modal Functions” in Henle, Kallen & Langer, , eds., Structure, Method and Meaning. New York: Liberal Arts Press; 1951.Google Scholar
[10] Lewis, C. & Langford, C., Symbolic Logic. New York: Dover Publications, Inc.; 1959.Google Scholar
[11] Montague, R., “Syntactical Treatments of Modality with Corollaries on Reflexion Principles and Finite Axiomatizability”, Acta Philosophica Fennica, v. 16 (1963), pp. 153–168.Google Scholar
[12] Prior, A., Formal Logic. Oxford: Clarendon Press; 1962.Google Scholar
[13] Quine, W., Methods of Logic. New York: Henry Holt & Co.; 1960.Google Scholar
[14] Quine, W., Set Theory and Its Logic. Cambridge: Harvard U. Press; 1963.CrossRefGoogle Scholar
[15] von Wright, G., An Essay in Modal Logic. Amsterdam: North Holland Publishing Co.; 1951.Google Scholar