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COMPLETENESS RESULTS FOR SOME TWO-DIMENSIONAL LOGICS OF ACTUALITY

Published online by Cambridge University Press:  25 January 2012

DAVID R. GILBERT  and
EDWIN D. MARES
DAVID R. GILBERT*
Affiliation:
Centre for logic, language and computation, Victoria University of Wellington
EDWIN D. MARES*
Affiliation:
Centre for logic, language and computation, Victoria University of Wellington
*
*CENTRE FOR LOGIC, LANGUAGE AND COMPUTATION, VICTORIA UNIVERSITY OF WELLINGTON, NEW ZEALAND. E-mail: [email protected]
†CENTRE FOR LOGIC, LANGUAGE AND COMPUTATION, VICTORIA UNIVERSITY OF WELLINGTON, NEW ZEALAND. E-mail: [email protected]
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Abstract

We provide a Hilbert-style axiomatization of the logic of ‘actually’, as well as a two-dimensional semantics with respect to which our logics are sound and complete. Our completeness results are quite general, pertaining to all such actuality logics that extend a normal and canonical modal basis. We also show that our logics have the strong finite model property and permit straightforward first-order extensions.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 5 , Issue 2 , June 2012 , pp. 239 - 258
Copyright
Copyright © Association for Symbolic Logic 2012

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References

BIBLIOGRAPHY

Areces, C., & ten Cate, B. (2007). Hybrid logics. In Blackburn, P., van Benthem, J., and Wolter, F., editors. Handbook of Modal Logic. Amsterdam, The Netherlands: Elsevier.Google Scholar
Blackburn, P., de Rijke, M., & Venema, Y. (2004). Modal Logic. Cambridge, UK: Cambridge University Press.Google Scholar
Blackburn, P., & Marx, M. (2001). Remarks on Gregory’s “actually” operator. Journal of Philosophical Logic, 31, 281–288.CrossRefGoogle Scholar
Blackburn, P., & Seligman, J. (1998). What are hybrid languages? In Kracht, M., de Rijke, M., Wansing, H., and Zakharyaschev, M., editors. Advances in Modal Logic, Vol. 1. Stanford, CA: CSLI.Google Scholar
Fara, M., & Williamson, T. (2005). Counterparts and actuality. Mind, 114, 1–30.CrossRefGoogle Scholar
Forbes, G. (1989). Languages of Possibility. Oxford, UK: Basil Blackwell.Google Scholar
Goldblatt, R., & Mares, E. (2006). A general semantics for quantified modal logic. In Governatori, G., Hodkinson, I., and Venema, Y., editors. Advances in Modal Logic, Vol. 6. Stanford, CA: CSLI.Google Scholar
Gregory, D. (2001). Completeness and decidability results for some propositional modal logics containing “actually” operators. Journal of Philosophical Logic, 30, 57–78.CrossRefGoogle Scholar
Hodes, H. (1984a). Axioms for actuality. Journal of Philosophical Logic, 13, 27–34.CrossRefGoogle Scholar
Hodes, H. (1984b). Some theorems on the expressive limitations of modal languages. Journal of Philosophical Logic, 13, 13–26.CrossRefGoogle Scholar
Lewis, D. (1986). On the Plurality of Worlds. Oxford, UK: Blackwell.Google Scholar
Stephanou, Y. (2005). First-order modal logic with an ‘actually’ operator. Notre Dame Journal of Formal Logic, 46(4), 381–405.CrossRefGoogle Scholar