The modal logic of affine planes is not finitely axiomatisable

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: Journal
• Year: 2008
• Where: JSYML
• Authors: Ian Hodkinson, Altaf Hussain
• Keywords: Affine Planes, JSYML 2008, Modal Accessibility Relations, Modal Language