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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
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

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
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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