Line-Based Affine Reasoning in Euclidean Plane
Résumé
We consider the binary relations of parallelism and convergence between lines in a 2-dimensional affinespace. Associating with parallelism and convergence the binary predicates P and C and the modal connectives [ P] and [C], we consider a first-order theory based on these predicates and a modal logic based on these modal connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic.