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Modal sequents and definability

Published online by Cambridge University Press:  12 March 2014

Bruce M. Kapron
Bruce M. Kapron*
Affiliation:
Department of Computer Science, University of Toronto, Toronto, Ontario M5S 1A4, Canada
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Abstract

The language of propositional modal logic is extended by the introduction of sequents. Validity of a modal sequent on a frame is defined, and modal sequent-axiomatic classes of frames are introduced. Through the use of modal algebras and general frames, a study of the properties of such classes is begun.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 3 , September 1987 , pp. 756 - 762
Copyright
Copyright © Association for Symbolic Logic 1987

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Footnotes

1

The results of this article are based on an M.Sc. thesis written at Simon Fraser University under the supervision of Dr. S. K. Thomason. The author gratefully acknowledges his supervisor's contribution.

References

REFERENCES

[BS] Bell, J. L. and Slomson, A. B., Models and ultraproducts, North-Holland, Amsterdam, 1969.Google Scholar
[BuS] Burris, S. and Sankappanavar, H. P., A course in universal algebra, Springer-Verlag, Berlin, 1981.CrossRefGoogle Scholar
[vB1] van Benthem, J., Modal correspondence theory, Ph.D. Thesis, University of Amsterdam, Amsterdam, 1976.Google Scholar
[vB2] van Benthem, J., Modal logic and classical logic, Bibliopolis, Naples, 1985.Google Scholar
[vB3] van Benthem, J., Notes on modal definability, Report 86–11, Department of Mathematics, University of Amsterdam, Amsterdam, 1986.Google Scholar
[G] Goldblatt, R. I., Metamathematics of modal logic. I, II, Reports on Mathematical Logic, vol. 6 (1976), pp. 41–78; vol. 7 (1976), pp. 21–52.Google Scholar
[GT] Goldblatt, R. I. and Thomason, S. K., Axiomatic classes in propositional modal logic, Algebra and logic (Crossley, J., editor), Lecture Notes in Mathematics, vol. 450, Springer-Verlag, Berlin, 1975, pp. 163–173.CrossRefGoogle Scholar
[LS] Lemmon, E. J. and Scott, D. S., An introduction to modal logic, American PhilosophicalQuarterly Monograph no. 11, Blackwell, Oxford, 1977.Google Scholar
[S] Segerberg, K., Classical propositional operators, Oxford University Press, Oxford, 1982.Google Scholar
[T] Thomason, S. K., Reduction of second-order logic to modal logic, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 21 (1975), pp. 107–114.CrossRefGoogle Scholar