# Finding Proofs in Tarskian Geometry

@article{Beeson2016FindingPI, title={Finding Proofs in Tarskian Geometry}, author={Michael Beeson and Larry Wos}, journal={Journal of Automated Reasoning}, year={2016}, volume={58}, pages={181-207} }

We report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betweenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski’s axioms of Hilbert’s 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some OTTER proofs in Tarskian geometry (solving challenges issued in Wos’s 1998…

## 11 Citations

From Hilbert to Tarski

- Mathematics
- 2016

In this paper, we describe the formal proof using the Coq proof assistant that Tarski's axioms for plane neutral geometry (excluding continuity axioms) can be derived from the corresponding Hilbert's…

From Tarski to Descartes: Formalization of the Arithmetization of Euclidean Geometry

- Mathematics, Computer ScienceSCSS
- 2016

The formalization of the arithmetization of Euclidean geometry in the Coq proof assistant is described, derived from Tarski's system of geometry a formal proof of the nine-point circle theorem using the Grobner basis method.

On the formalization of foundations of geometry

- Computer Science
- 2018

A new proof is exposed that Euclid’s parallel postulate is not derivable from the other axioms of first-order Euclidean geometry, and Pejas’ classification of parallel postulates is refined.

Formalization of the arithmetization of Euclidean plane geometry and applications

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2019

Portfolio theorem proving and prover runtime prediction for geometry

- Computer ScienceAnnals of Mathematics and Artificial Intelligence
- 2018

This paper proposes a set of features which characterize a specific geometric theorem, so that machine learning techniques can be used in geometry and constructed several portfolios for theorem proving in geometry, and also runtime prediction models for provers involved.

Euclid After Computer Proof-checking

- Philosophy
- 2021

Euclid pioneered the concept of a mathematical theory developed from axioms by a series of justified proof steps. From the outset there were critics and improvers. In this century the use of…

Formalization of the Poincaré Disc Model of Hyperbolic Geometry

- Computer ScienceJournal of Automated Reasoning
- 2020

The Poincaré disc model of hyperbolic geometry within the Isabelle/HOL proof assistant is described and is shown to satisfy Tarski’s axioms except for Euclid's axiom.

Learning to solve geometric construction problems from images

- Computer ScienceCICM
- 2021

A purely image-based method for finding geometric constructions with a ruler and compass in the Euclidea geometric game based on adapting the Mask R-CNN state-of-theart visual recognition neural architecture and adding a tree-based search procedure to it.

Larry Wos: Visions of Automated Reasoning

- Computer ScienceJournal of Automated Reasoning
- 2022

This paper celebrates the scientific discoveries and the service to the automated reasoning community of Lawrence (Larry) T. Wos, who passed away in August 2020. The narrative covers Larry’s most…

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