Logical Theories for Fragments of Elementary Geometry [chapter]

Philippe Balbiani, Valentin Goranko, Ruaan Kellerman, Dimiter Vakarelov
2007 Handbook of Spatial Logics  
We survey models and theories of geometric structures of parallelism, orthogonality, incidence, betweenness and order, thus gradually building towards full elementary geometry of Euclidean spaces, in Tarski's sense. Besides the geometric aspects of such structures we look at their logical (first-order and modal) theories and discuss logical issues such as: expressiveness and definability, axiomatizations and representation results, completeness and decidability, and interpretations between structures and theories.
doi:10.1007/978-1-4020-5587-4_7 fatcat:wx2kmogq2zgidm2ybmf2hvubkq