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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
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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

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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