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GEOTHER 1.1: Handling and Proving Geometric Theorems Automatically [chapter]

Dongming Wang
2004 Lecture Notes in Computer Science  
GEOTHER provides an environment for handling and proving theorems in geometry automatically. In this environment, geometric theorems are represented by means of predicate specifications.  ...  ) geometry.  ...  The current version GEOTHER 1.1 provides a user-friendly environment for handling and proving theorems in geometry automatically.  ... 
doi:10.1007/978-3-540-24616-9_12 fatcat:prtb6iijcrfhpcy7vmnparwa34

Saturation-based theorem proving: Past successes and future potential [chapter]

Harald Ganzinger
1996 Lecture Notes in Computer Science  
quantifiers p. 161 GEOTHER: a geometry theorem prover p. 166 Structuring metatheory on inductive definitions p. 171 An embedding of Ruby in Isabelle p. 186 Mechanical verification of mutually  ...  prolog technology theorem prover for default reasoning: a system description p. 293 IMPS: an updated system description p. 298 The tableau-based theorem prover [subscript 3]T[superscript A]P, version  ... 
doi:10.1007/3-540-61511-3_64 fatcat:iizfu32trnfadmj4z7xcvwds5y

GeoThms — a Web System for Euclidean Constructive Geometry

Pedro Quaresma, Predrag Janičić
2007 Electronical Notes in Theoretical Computer Science  
GeoThms is a web-based framework for exploring geometrical knowledge that integrates Dynamic Geometry Software (DGS), Automatic Theorem Provers (ATP), and a repository of geometrical constructions, figures  ...  GeoThms is a publicly accessible system with a growing body of geometrical constructions and formally proven geometrical theorems.  ...  Framework Components GeoThms, is a framework that links dynamic geometry software, geometry automatic theorem provers, and a repository of geometry problems providing a common web interface for all these  ... 
doi:10.1016/j.entcs.2006.09.020 fatcat:tloosukxrrd5venmpmgix25v7e

Automated Theorem Proving in GeoGebra: Current Achievements

Francisco Botana, Markus Hohenwarter, Predrag Janičić, Zoltán Kovács, Ivan Petrović, Tomás Recio, Simon Weitzhofer
2015 Journal of automated reasoning  
mature stage, we embarked on a project of incorporating and testing a number of dierent automated provers for geometry in GeoGebra.  ...  Since including automated deduction tools in GeoGebra could bring a whole new range of teaching and learning scenarios, and since automated theorem proving and discovery in geometry has reached a rather  ...  An early example (from the late 70's) is Geom, a Prolog-based geometry theorem-prover ( [Coelho & al., 1986] ).  ... 
doi:10.1007/s10817-015-9326-4 fatcat:rh7lvmmy75eipaqmkvf3dqxs3a

Towards a Geometry Automated Provers Competition

Nuno Baeta, Pedro Quaresma, Zoltán Kovács
2020 Electronic Proceedings in Theoretical Computer Science  
CPU time), the possibility of visual and/or readable proofs is also an expected output against which the geometry automated theorem provers (GATP) should be measured.  ...  The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals  ...  There are many other GATPs to be considered: ArgoCLP, a Coherent Logic Based Geometry Theorem Prover [34] , GEOTHER [36] , Gex [12, 13, 15] , JGEX [39] , MMP [14] ; different formalizations in Coq  ... 
doi:10.4204/eptcs.313.6 fatcat:7qd6linvqnbifeh4lxwe75ii6y

The SymbolicData GEO Records – A Public Repository of Geometry Theorem Proof Schemes [chapter]

Hans-Gert Gräbe
2004 Lecture Notes in Computer Science  
Such facilities are part of integrated geometry theorem provers as, e.g., D. Wang's GEOTHER prover [14, 16] or the Geometry Expert, [5] .  ...  It is a special design decision of many geometry theorem provers, e.g., D.Wang's GEOTHER [14] , not to introduce the latter objects as basic but to take only point objects as primitives.  ...  A proof scheme for the Cathedral example [11, 5.3] as GEO record  ... 
doi:10.1007/978-3-540-24616-9_5 fatcat:5uctg5wepzgblp2oyxajlym74i

Geometry Constructions Language

Predrag Janičić
2009 Journal of automated reasoning  
Geometry Constructions Language (gcl) is a language for explicit descriptions of constructions in Euclidean plane and of their properties.  ...  These features make the tools gclc and Wingclc powerful mechanized geometry systems and they have thousands of users worldwide.  ...  Built-in Theorem Provers The system gclc has three geometry theorem provers for Euclidean constructive theorems built in (for a survey of automated deduction in geometry, see, for instance [26] ): a theorem  ... 
doi:10.1007/s10817-009-9135-8 fatcat:ecv4j425evhuhdry5m5gnrqlre

Electronic Geometry Textbook: A Geometric Textbook Knowledge Management System [article]

Xiaoyu Chen
2010 arXiv   pre-print
By integrating an external geometric theorem prover and an external dynamic geometry software package, the system offers the facilities for automatically proving theorems and generating dynamic figures  ...  This paper provides a comprehensive account of the current version of Electronic Geometry Textbook.  ...  For example, the theorems in the textbooks can be automatically proved by invoking geometric theorem provers, and the figures are automatically constructed by applying dynamic geometry software.  ... 
arXiv:1005.0080v1 fatcat:3odyuvxtcvfarbj4kfpoqjizjq

Automated Discovery in Elementary Extrema Problems [chapter]

Francisco Botana, José L. Valcarce
2006 Lecture Notes in Computer Science  
This paper describes an enhancement of GDI, a dynamic geometry environment that uses symbolic techniques for performing automatic proof and discovery in elementary geometry.  ...  Based in classical one variable calculus, the new module, Optimus, is a step ahead in the cooperation between dynamic geometry and computer algebra systems.  ...  8 3 theorem).  ... 
doi:10.1007/11758525_63 fatcat:o3tdrxc37bemtmyw6p4s377zlq

Formalization and Implementation of Algebraic Methods in Geometry

Filip Marić, Ivan Petrović, Danijela Petrović, Predrag Janičić
2012 Electronic Proceedings in Theoretical Computer Science  
We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools  ...  should enable new applications of theorem proving in education.  ...  Quaife used a resolution theorem prover to prove theorems in Tarski's geometry [38] .  ... 
doi:10.4204/eptcs.79.4 fatcat:j7pyqmy6nvbpraduv6tbkhmmt4

Combining algebraic computing and term-rewriting for geometry theorem proving [chapter]

Stéphane Fèvre, Dongming Wang
1998 Lecture Notes in Computer Science  
This note reports some of our investigations on combining algebraic computing and term-rewriting techniques for automated geometry theorem proving.  ...  A general approach is proposed that requires both Clifford algebraic reduction and term-rewriting.  ...  Design The architecture of our prototype is simple and allows one to use the user interface of GEOTHER [11] , a geometry theorem prover developed by the second author using several methods (Wu's characteristic  ... 
doi:10.1007/bfb0055909 fatcat:wvc5fdfi6fhrxkz4i7ujlnltt4

Automatically Building Diagrams for Olympiad Geometry Problems [article]

Ryan Krueger, Jesse Michael Han, Daniel Selsam
2021 arXiv   pre-print
We present a method for automatically building diagrams for olympiad-level geometry problems and implement our approach in a new open-source software tool, the Geometry Model Builder (GMB).  ...  Central to our method is a new domain-specific language, the Geometry Model-Building Language (GMBL), for specifying geometry problems along with additional metadata useful for building diagrams.  ...  Our program can be run both as a command-line tool for integration with theorem provers or as a locally-hosted web server.  ... 
arXiv:2012.02590v2 fatcat:iw67yzylkrgsjaxbfvimesphbi

Automated Generation of Geometric Theorems from Images of Diagrams [article]

Xiaoyu Chen, Dan Song, Dongming Wang
2014 arXiv   pre-print
Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams.  ...  We propose an approach to generate geometric theorems from electronic images of diagrams automatically.  ...  For the efficiency of theorem mining, false propositions need be ruled out first, so that each proposition submitted to a theorem prover is a potential theorem.  ... 
arXiv:1406.1638v1 fatcat:oy47uzea7vdd5m4dgff4derbwi

Formalization of Wu's Simple Method in Coq [chapter]

Jean-David Génevaux, Julien Narboux, Pascal Schreck
2011 Lecture Notes in Computer Science  
We present in this paper the integration within the Coq proof assistant, of a method for automatic theorem proving in geometry. We use an approach based on the validation of a certificate.  ...  The certificate is generated by an implementation in Ocaml of a simple version of Wu's method.  ...  Stating the conjecture As most automatic theorem provers in geometry, to state a theorem, we will assume that the user provides the assumptions as a list of geometric predicates taking only points as parameters  ... 
doi:10.1007/978-3-642-25379-9_8 fatcat:yk3yueuenreatdwxiiumaosc3e

Automatic Verification of Regular Constructions in Dynamic Geometry Systems [chapter]

Predrag Janičić, Pedro Quaresma
Automated Deduction in Geometry  
We present an application of automatic theorem proving (ATP) in the verification of constructions made with dynamic geometry software (DGS).  ...  This gives a real-world application of ATP in dynamic geometry tools.  ...  The Geometric Framework GeoThms 4 is a framework that links dynamic geometry software (GCLC, Eukleides), geometry theorem provers (GCLCprover), and a repository of geometry problems (geoDB).  ... 
doi:10.1007/978-3-540-77356-6_3 dblp:conf/adg/JanicicQ06 fatcat:5lbvtew56fgo3bgguztplh7i5q
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