Automatic Verification of Regular Constructions in Dynamic Geometry Systems

Janicic, Predrag; Quaresma, Pedro

doi:10.1007/978-3-540-77356-6_3

Cited by 13 publications

(11 citation statements)

References 16 publications

(21 reference statements)

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“…Given the fact that it is a client/server system the incorporation of a GATP (on the server) should not be difficult. One of the authors has already experience on that type of integration [11], [12], [13].…”

Section: Discussionmentioning

confidence: 99%

Collaborative environment for geometry

Santos

Quaresma

2013

2013 2nd Experiment@ International Conference (exp.at'13)

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The Web Geometry Laboratory is a collaborative blended-learning Web-environment integrating a dynamic geometry system and where each user has a personalised scrapbook of geometric constructions. All the base features needed to implement an adaptive module and to allow the integration of a geometry automated theorem prover are also already implemented.The actual testing of the Web Geometry Laboratory by highschool teachers is underway and a first field-test with high-school students is due to the spring term of 2013.

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Section: Discussionmentioning

confidence: 99%

Collaborative environment for geometry

Santos

Quaresma

2013

2013 2nd Experiment@ International Conference (exp.at'13)

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“…The intended use is also important. For example, in education two uses of a GATP are foreseen, the validation of a given conjecture and/or construction [1,16] and the proof itself as object of study.…”

Section: Test Benchmentioning

confidence: 99%

Towards Ranking Geometric Automated Theorem Provers

Baeta

Quaresma

2019

Electron. Proc. Theor. Comput. Sci.

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The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers.The geometry automated deduction area differs from other areas by the strong connection between the axiomatic theories and its standard models. In many cases the geometric constructions are used to establish the theorems' statements, geometric constructions are, in some provers, used to conduct the proof, used as counter-examples to close some branches of the automatic proof. Synthetic geometry proofs are done using geometric properties, proofs that can have a visual counterpart in the supporting geometric construction.With the growing use of geometry automatic deduction tools as applications in other areas, e.g. in education, the need to evaluate them, using different criteria, is felt. Establishing a ranking among geometric automated theorem provers will be useful for the improvement of the current methods/implementations. Improvements could concern wider scope, better efficiency, proof readability and proof reliability.To achieve the goal of being able to compare geometric automated theorem provers a common test bench is needed: a common language to describe the geometric problems; a comprehensive repository of geometric problems and a set of quality measures.

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“…GCLC has a built-in mechanism (using GCLCprover) for checking if a construction step is illegal, i.e., if it is always impossible [30]. [5] will be used to illustrate the mechanism for automatic verification of regular constructions built into GCLC.…”

Section: Automatic Verif Ication Of Regular Constructionsmentioning

confidence: 99%

“…This description of the area method should be sufficient for a complete understanding of the method, and for making a new implementation a straightforward task. This paper also summarises our results, experiences, and descriptions of our software systems related to the area method [30,33,43,45,50,52].…”

Section: Introductionmentioning

confidence: 98%

The Area Method

2010

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The area method for Euclidean constructive geometry was proposed by Chou, Gao and Zhang in the early 1990's. The method can efficiently prove many non-trivial geometry theorems and is one of the most interesting and most successful methods for automated theorem proving in geometry. The method produces proofs that are often very concise and human-readable. In this paper, we provide a first complete presentation of the method. We provide both algorithmic and implementation details that were omitted in the original presentations. We also give a variant of Chou, Gao and Zhang's axiom system. Based on this axiom system, we proved formally all the lemmas needed by the method and its soundness using the Coq proof assistant. To our knowledge, apart from the original implementation by the authors who first proposed the method, there are only three implementations more. Although the basic idea of the method is simple, implementing it is a very challenging task because of a number of details that has to be dealt with. With the description of the method given in this paper, implementing the method should be still complex, but a straightforward task. In the paper we describe all these implementations and also some of their applications. 490 P. Janičić et al.

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Automatic Verification of Regular Constructions in Dynamic Geometry Systems

Cited by 13 publications

References 16 publications

Collaborative environment for geometry

Collaborative environment for geometry

Towards Ranking Geometric Automated Theorem Provers

The Area Method

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