The next meeting of the Algebra and Logic Seminar will be held
First-order theory of Euclidean plane, based on lines as only primitive notion
Abstract. The paper [1] gives qualitative spatial reasoning in Euclidean plane based solely on lines. The relations of parallelism and convergence between lines are considered. In this presentation I consider a continuation of [1] by adding a new predicate – perpendicularity. I introduce a first-order theory of lines in Euclidean plane with predicates parallelism, convergence and perpendicularity. The logic is complete with respect to the Euclidean plane, ω – categorical and not categorical in every uncountable cardinality. The membership problem of the logic is PSPACE-complete.
The proof that the membership problem of the logic is PSPACE-complete is a joint work with Prof. Tinko Tinchev.
[1] Balbiani, P. and Tinchev, T., Line-Based Affine Reasoning in Euclidean Plane, Journal of Applied Logic, vol. 5 (2007), no. 3, pp. 421–434.