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A short note about case distinctions in Tarski's geometry

Pierre Boutry 1 Julien Narboux 2 Pascal Schreck 1 Gabriel Braun 1 
ICube - Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie
Abstract : In this paper we study some decidability properties in the context of Tarski's axiom system for geometry. We removed excluded middle from our assumptions and studied how our formal proof of the first thirteen chapters of [SST83] are impacted. We show that decidability of equality is equivalent to the decidability of the two other given predicates of the theory: congruence and betweenness. We prove that the decidability of the other predicates used in [SST83] can be derived except for the predicate stating the existence of the intersection of two lines. All results have been proved formally using the Coq proof assistant.
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Submitted on : Wednesday, June 25, 2014 - 9:36:37 AM
Last modification on : Wednesday, December 1, 2021 - 3:32:14 PM
Long-term archiving on: : Thursday, September 25, 2014 - 10:41:54 AM


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  • HAL Id : hal-00989785, version 2


Pierre Boutry, Julien Narboux, Pascal Schreck, Gabriel Braun. A short note about case distinctions in Tarski's geometry. Automated Deduction in Geometry 2014, Jul 2014, Coimbra, Portugal. pp.1-15. ⟨hal-00989785v2⟩



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