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The modal logic of affine planes is not finitely axiomatisable

Published online by Cambridge University Press:  12 March 2014

Ian Hodkinson  and
Altaf Hussain
Ian Hodkinson
Affiliation:
Department of Computing, Imperial College London, London, SW7 2AZ, UK, E-mail: imh@doc.ic.ac.uk, URL: http://www.doc.ic.ac.uk/~imh
Altaf Hussain
Affiliation:
Department of Computing, Imperial College London, London, SW7 2AZ, UK, E-mail: E-mail: altaf.a.hussain@googlemail.com, URL: http://www.doc.ic.ac.uk/~imh
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Abstract

We consider a modal language for affine planes, with two sorts of formulas (for points and lines) and three modal boxes. To evaluate formulas, we regard an affine plane as a Kripke frame with two sorts (points and lines) and three modal accessibility relations, namely the point-line and line-point incidence relations and the parallelism relation between lines. We show that the modal logic of affine planes in this language is not finitely axiomatisable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 3 , September 2008 , pp. 940 - 952
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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