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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: david.gilbert@vuw.ac.nz
†CENTRE FOR LOGIC, LANGUAGE AND COMPUTATION, VICTORIA UNIVERSITY OF WELLINGTON, NEW ZEALAND. E-mail: edwin.mares@vuw.ac.nz
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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

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