Computer-Generated Geometry Proofs in a Learning Context

Quaresma, Pedro; Santos, Vanda

doi:10.1007/978-3-030-28483-1_11

Cited by 3 publications

(3 citation statements)

References 29 publications

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“…Wu's (algebraic) method), but there is also the need of readable proof scripts (e.g. Area Method, semi-synthetic) and this two objectives are difficult to attain together [12,13]. There is also the need of an automated deduction method that is adapted to the secondary Listing 1 Rule D1 schools learning, i.e.…”

Section: Rendering Considerationsmentioning

confidence: 99%

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Towards a geometry deductive database prover

Baeta

Quaresma

2023

Ann Math Artif Intell

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The Geometry Automated-Theorem-Provers (GATP) based on the deductive database method use a data-based search strategy to improve the efficiency of forward chaining. An implementation of such a method is expected to be able to efficiently prove a large set of geometric conjectures, producing readable proofs. The number of conjectures a given implementation can prove will depend on the set of inference rules chosen, the deductive database method is not a decision procedure. Using an approach based in an SQL database library and using an in-memory database, the implementation described in this paper tries to achieve the following goals. Efficiency in the management of the inference rules, the set of already known facts and the new facts discovered, by the use of the efficient data manipulation techniques of the SQL library. Flexibility, by transforming the inference rules in SQL data manipulation language queries, will open the possibility of meta-development of GATP based on a provided set of rules. Natural language and visual renderings, possible by the use of a synthetic forward chaining method. Implemented as an open source library, that will open its use by third-party programs, e.g. the dynamic geometry systems.

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Section: Rendering Considerationsmentioning

confidence: 99%

“…The OGP-GDDM is hosted at GitHub. 9 It is code is be made available under the GNU General Public Licence, 13 version 3 or later, and the documentation under the GNU Free Documentation Licence, 14 version 1 or later. It is available only as sourcecode.…”

Section: Source Repositorymentioning

confidence: 99%

Towards a geometry deductive database prover

Baeta

Quaresma

2023

Ann Math Artif Intell

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“…The WGL→TGTP interconnection will provide to the WGL users a large set of geometric constructions, giving them the possibility of browsing constructions and exploring conjectures and proofs. Teachers and students will gain the possibility of visualising geometric problems and link them with formal proofs [18].…”

Section: Clients and Servers Of Geometric Informationmentioning

confidence: 99%

Exchange of Geometric Information Between Applications

Quaresma

Santos

Baeta

2018

Electron. Proc. Theor. Comput. Sci.

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The Web Geometry Laboratory (WGL) is a collaborative and adaptive e-learning Web platform integrating a well known dynamic geometry system. Thousands of Geometric problems for Geometric Theorem Provers (TGTP) is a Web-based repository of geometric problems to support the testing and evaluation of geometric automated theorem proving systems.The users of these systems should be able to profit from each other. The TGTP corpus must be made available to the WGL user, allowing, in this way, the exploration of TGTP problems and their proofs. On the other direction TGTP could gain by the possibility of a wider users base submitting new problems.Such information exchange between clients (e.g. WGL) and servers (e.g. TGTP) raises many issues: geometric search-someone, working in a geometric problem, must be able to ask for more information regarding that construction; levels of geometric knowledge and interest-the problems in the servers must be classified in such a way that, in response to a client query, only the problems in the user's level and/or interest are returned; different aims of each tool-e.g. WGL is about secondary school geometry, TGTP is about formal proofs in semi-analytic and algebraic proof methods, not a perfect match indeed; localisation issues, e.g. a Portuguese user obliged to make the query and process the answer in English; technical issues-many technical issues need to be addressed to make this exchange of geometric information possible and useful.Instead of a giant (difficult to maintain) tool, trying to cover all, the interconnection of specialised tools seems much more promising. The challenges to make that connection work are many and difficult, but, it is the authors impression, not insurmountable.

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