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Modal reduction principles

Published online by Cambridge University Press:  12 March 2014

J.F.A.K. van Benthem
J.F.A.K. van Benthem*
Affiliation:
Instituut Voor Grondslagenonderzoek, Universiteit van Amsterdam, Amsterdam, The Netherlands
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Extract

Modal reduction principles (MRPs) are modal formulas of the following form: Mp → Np, where M, N are (possibly empty) sequences of modal operators (i.e. □ or ◊). The notation M, N will be used to abbreviate such an MRP. We study a certain semantic correspondence between modal formulas and relational properties and obtain two main results. (1) On transitive semantic structures every MRP corresponds to a first-order relational property. (2) For the general case a syntactic criterion exists for distinguishing modal formulas with corresponding first-order properties from the others.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 2 , June 1976 , pp. 301 - 312
Copyright
Copyright © Association for Symbolic Logic 1976

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References

REFERENCES

[1] van Benthem, J. F. A. K., A note on modal formulae and relational properties, this Journal, vol. 40 (1975), pp. 55–58.Google Scholar
[2] van Benthem, J. F. A. K., Some correspondence results in modal logic, Department of Mathematics, University of Amsterdam, Report 74-05.Google Scholar
[3] Fitch, F. B., A correlation between modal reduction principles and properties of relations, The Journal of Philosophical Logic, vol. 2 (1973), pp. 97–101.CrossRefGoogle Scholar
[4] Sahlqvist, H., Completeness and correspondence in the first and second order semantics for modal logic, revised version of cand. real.-thesis submitted to the University of Oslo, Department of Mathematics, Spring 1973.Google Scholar