Line-based affine reasoning in Euclidean plane |
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Authors: | Philippe Balbiani Tinko Tinchev |
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Affiliation: | aInstitut de recherche en informatique de Toulouse, France;bSofia University, Bulgaria |
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Abstract: | We consider the binary relations of parallelism and convergence between lines in a 2-dimensional affine space. 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. |
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Keywords: | Spatial reasoning Euclidean geometry First-order theories of space Spatial logics |
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