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

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. ...

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

1996
*
Lecture Notes in Computer Science
*

quantifiers
p. 161

doi:10.1007/3-540-61511-3_64
fatcat:iizfu32trnfadmj4z7xcvwds5y
*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 ...##
###
GeoThms — a Web System for Euclidean Constructive Geometry

2007
*
Electronical Notes in Theoretical Computer Science
*

GeoThms is

doi:10.1016/j.entcs.2006.09.020
fatcat:tloosukxrrd5venmpmgix25v7e
*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 ...##
###
Automated Theorem Proving in GeoGebra: Current Achievements

2015
*
Journal of automated reasoning
*

mature stage, we embarked on

doi:10.1007/s10817-015-9326-4
fatcat:rh7lvmmy75eipaqmkvf3dqxs3a
*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] ). ...##
###
Towards a Geometry Automated Provers Competition

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

doi:10.4204/eptcs.313.6
fatcat:7qd6linvqnbifeh4lxwe75ii6y
*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 ...##
###
The SymbolicData GEO Records – A Public Repository of Geometry Theorem Proof Schemes
[chapter]

2004
*
Lecture Notes in Computer Science
*

Such facilities are part of integrated

doi:10.1007/978-3-540-24616-9_5
fatcat:5uctg5wepzgblp2oyxajlym74i
*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 ...##
###
Geometry Constructions Language

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*...

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

2010
*
arXiv
*
pre-print

By integrating an external geometric

arXiv:1005.0080v1
fatcat:3odyuvxtcvfarbj4kfpoqjizjq
*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. ...##
###
Automated Discovery in Elementary Extrema Problems
[chapter]

2006
*
Lecture Notes in Computer Science
*

This paper describes an enhancement of GDI,

doi:10.1007/11758525_63
fatcat:o3tdrxc37bemtmyw6p4s377zlq
*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*). ...##
###
Formalization and Implementation of Algebraic Methods in Geometry

2012
*
Electronic Proceedings in Theoretical Computer Science
*

We describe our ongoing project of formalization of algebraic methods for

doi:10.4204/eptcs.79.4
fatcat:j7pyqmy6nvbpraduv6tbkhmmt4
*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] . ...##
###
Combining algebraic computing and term-rewriting for geometry theorem proving
[chapter]

1998
*
Lecture Notes in Computer Science
*

This note reports some of our investigations on combining algebraic computing and term-rewriting techniques for automated

doi:10.1007/bfb0055909
fatcat:wvc5fdfi6fhrxkz4i7ujlnltt4
*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 ...##
###
Automatically Building Diagrams for Olympiad Geometry Problems
[article]

2021
*
arXiv
*
pre-print

We present

arXiv:2012.02590v2
fatcat:iw67yzylkrgsjaxbfvimesphbi
*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. ...##
###
Automated Generation of Geometric Theorems from Images of Diagrams
[article]

2014
*
arXiv
*
pre-print

Experiments with

arXiv:1406.1638v1
fatcat:oy47uzea7vdd5m4dgff4derbwi
*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*. ...##
###
Formalization of Wu's Simple Method in Coq
[chapter]

2011
*
Lecture Notes in Computer Science
*

We present in this paper the integration within the Coq proof assistant, of

doi:10.1007/978-3-642-25379-9_8
fatcat:yk3yueuenreatdwxiiumaosc3e
*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 ...##
###
Automatic Verification of Regular Constructions in Dynamic Geometry Systems
[chapter]

*
Automated Deduction in Geometry
*

We present an application of automatic

doi:10.1007/978-3-540-77356-6_3
dblp:conf/adg/JanicicQ06
fatcat:5lbvtew56fgo3bgguztplh7i5q
*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). ...
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