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Improved decision procedures for Lewis's calculus S4 and von Wright's calculus M

Published online by Cambridge University Press:  12 March 2014

Alan Ross Anderson
Alan Ross Anderson*
Affiliation:
Yale University
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Extract

The decision procedures to be described in this paper constitute simplifications of methods previously developed by G. H. von Wright. The decision problems for both the systems under consideration have already been solved, but the known solutions are hopelessly impractical. Our methods for S4 and M, while not “practical” in the sense that they can be applied quickly and easily to any formula, do constitute a vast improvement over any other known methods. It appears, for example, that our methods (with the aid of very little ingenuity) will yield decisions readily when applied to modal functions of degree two (or less) with three (or fewer) distinct propositional variables.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 19 , Issue 3 , September 1954 , pp. 201 - 214
Copyright
Copyright © Association for Symbolic Logic 1954

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References

REFERENCES

[1]Anderson, A. R., abstract of the present paper, this Journal, vol. 18 (1953), pp. 187–188.Google Scholar
[2]Anderson, A. R., Alternative formulations of a modal system of Feys-von Wright, forthcoming in the Journal of computing systems.Google Scholar
[3]Anderson, A. R., Review of von Wright [11], this Journal, vol. 18 (1953), pp. 174–176.Google Scholar
[4]Carnap, R., Modalities and quantification, this Journal, vol. 11 (1946), pp. 33–64.Google Scholar
[5]Lewis, C. I. and Langford, C. H., Symbolic logic, New York, 1932.Google Scholar
[6]McKinsey, J. C. C., A solution of the decision problem for the Lewis systems S2 and S4, with an application to topology, this Journal, vol. 6 (1941), pp. 117–134.Google Scholar
[7]McKinsey, J. C. C. and Tarski, A., Some theorems about the sentential calculi of Lewis and Heyting, this Journal, vol. 13 (1948), pp. 1–15.Google Scholar
[8]Parry, W. T., Modalities in the “Survey” system of strict implication, this Journal, vol. 4 (1939), pp. 137–154.Google Scholar
[9]Quine, W. V., Mathematical logic, Cambridge, Mass., 1947.Google Scholar
[10]Simons, L., New axiomatizations of S3 and S4, this Journal, vol. 18 (1953), pp. 309–316.Google Scholar
[11]von Wright, G. H., An essay in modal logic. Amsterdam, 1951.Google Scholar