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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

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