Abstract
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.
Our research is partly supported by the Centre national de la recherche scientifique, the RILA project 06288TF and the ECONET project 08111TL.
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Balbiani, P., Tinchev, T. (2004). Line-Based Affine Reasoning in Euclidean Plane. In: Alferes, J.J., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2004. Lecture Notes in Computer Science(), vol 3229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30227-8_40
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DOI: https://doi.org/10.1007/978-3-540-30227-8_40
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