Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T23:40:54.121Z Has data issue: false hasContentIssue false
  • English
  • Français

There are infinitely many Diodorean modal functions1

Published online by Cambridge University Press:  12 March 2014

D. C Makinson
D. C Makinson*
Affiliation:
Worcester College, Oxford, England
Get access Rights & Permissions [Opens in a new window]

Extract

It is well known that the modal calculus S4 has infinitely many non-equivalent formulae in a single proposition letter (in standard terminology, infinitely many modal functions), whilst S5 has only finitely many. However, the situation regarding the intermediate modal calculi S4.2, S4.3, and Prior's Diodorean tense-logic D does not seem to have been settled. In this note we show that each of these systems, together with a certain proper supersystem D* of D, has infinitely many modal functions.

This is in contrast with the fact that in the intermediate propositional logics KC and LC, which correspond under the McKinsey-Tarski translations to S4.2 and S4.3, there are only finitely many non-equivalent formulae in a single proposition letter.2

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 406 - 408
Copyright
Copyright © Association for Symbolic Logic 1996

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.)

Footnotes

1

Based on a section of the author's D. Phil, thesis, Rules of truth for modal logic, submitted to the University of Oxford in June 1965.

References

[1]Dummett, M. and Lemmon, E., Modal logics between S4 and S5, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 3 (1959), pp. 250–264.CrossRefGoogle Scholar
[2]Nishimura, I., On formulas of one variable in intuitionistic propositional calculus, this Journal, Vol. 25 (1960), pp. 327–331.Google Scholar
[3]Prior, A. N., Time and modality (Oxford University Press), 1957.Google Scholar
[4]Prior, A. N., Diodorus and modal logic: a correction, Philosophical quarterly, vol. 8 (1958), pp. 226–230.CrossRefGoogle Scholar