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A unified completeness theorem for quantified modal logics

Published online by Cambridge University Press:  12 March 2014

Giovanna Corsi
Giovanna Corsi*
Affiliation:
Dipartimento Di Filosofia, Università di Bologna, Via Zamboni, 38 -I-40126 Bologna, Italy, E-mail: [email protected]
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Abstract

A general strategy for proving completeness theorems for quantified modal logics is provided. Starting from free quantified modal logic K. with or without identity, extensions obtained either by adding the principle of universal instantiation or the converse of the Barcan formula or the Barcan formula are considered and proved complete in a uniform way. Completeness theorems are also shown for systems with the extended Barcan rule as well as for some quantified extensions of the modal logic B. The incompleteness of Q°.B + BF is also proved.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 4 , December 2002 , pp. 1483 - 1510
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

[1]Corsi, Giovanna, Quantified modal logic with rigid terms, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 34 (1988), pp. 251–259.CrossRefGoogle Scholar
[2]Corsi, Giovanna, Counterparts and possible worlds. A study on quantified modal logics, Preprint, Dipartimento di Filosofia, Università di Bologna, vol. 21 (2001), pp. 1–61.Google Scholar
[3]Fitting, Melvin and Mendelsohn, Richard L., First-order modal logic, Kluwer A P, 1998.CrossRefGoogle Scholar
[4]Garson, James, Quantification in modal logic, Handbook of philosophical logic (Gabbay, D. and Guenthner, F., editors), vol. II, Kluwer A P, Dordrecht, 1984, pp. 249–307.CrossRefGoogle Scholar
[5]Garson, James, Quantification in modal logic, Handbook of philosophical logic (Gabbay, D. and Guenthner, F., editors), vol. II, Kluwer A P, Dordrecht, 2nd ed., 2002, pp. 249–307.Google Scholar
[6]Hughes, George and Cresswell, Max, A new introduction to modal logic, Routledge, London, 1996.CrossRefGoogle Scholar
[7]Kripke, Saul, Semantical considerations on modal logics, Acta Philosophica Fennica, vol. 16 (1963), pp. 83–94.Google Scholar
[8]Thomason, Richmond H., Some completeness results for modal predicate calculi, Philosophical problems in logic: Some recent developments (Lambert, Karel, editor), Kluwer A P, Dordrecht, 1970, pp. 56–76.CrossRefGoogle Scholar