Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-16T19:21:47.376Z Has data issue: false hasContentIssue false
  • English
  • Français

A conjunctive normal form for S3.5

Published online by Cambridge University Press:  12 March 2014

M. J. Cresswell
M. J. Cresswell*
Affiliation:
Victoria University of Wellington
Get access Rights & Permissions [Opens in a new window]

Extract

In this note we sketch a decision procedure for S3.51 based on reduction to conjunctive normal form. Using the following theorem of S3.5: and its dual for M over a conjunction, any formula can be reduced by standard methods (as in S52) to a conjunction of disjunctions of the form where Í is (p ⊃ p), 0 is ∼(p ⊃ p) and α — λ are all PC-wffs (i.e. they contain no modal operators).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 2 , 25 July 1969 , pp. 253 - 255
Copyright
Copyright © Association for Symbolic Logic 1969

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] Åqvist, L., Results concerning some modal systems that contain S2, this Journal , vol. 29 (1964), pp. 79–87.Google Scholar
[2] Cresswell, M. J., Note on a system of Åqvist, this Journal , vol. 32 (1967), pp. 58–60.Google Scholar
[3] Cresswell, M. J., The interpretation of some Lewis systems of modal logic, Australian Journal of philosophy, vol. 45 (1967), pp. 185–205.Google Scholar
[4] Hughes, G. E. and Cresswell, M. J., An introduction to modal logic, Methuen, London, 1968.Google Scholar
[5] Kripke, S. A., Semantical analysis of modal logic II non-normal modal prepositional calculi, The theory of models (ed. Addison, J. W., Henkin, L., Tarski, A.), North-Holland, Amsterdam, 1965, pp. 206–220.Google Scholar
[6] Lemmon, E. J., New foundations for Lewis modal systems, this Journal , vol. 22 (1957), pp. 176–186.Google Scholar
[7] Lemmon, E. J., Algebraic semantics for modal logics. II, this Journal , vol. 31 (1966), pp. 191–218.Google Scholar