Four Geometry Problems to Introduce Automated Deduction in Secondary Schools

Quaresma, Pedro; Santos, Vanda

doi:10.4204/eptcs.354.3

Cited by 6 publications

(5 citation statements)

References 19 publications

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“…Even if many of the items of such reports can be of a matter of taste and coding style, a detailed study of these messages seems unavoidable for the long term. Some recent work [1,8,9] confirm that continuing the pioneer work being put in JGEX is an important step towards the more general use of automated reasoning in the classroom. One possibility is to copy the algorithms and modify them accordingly (this way was chosen by Baeta and Quaresma, using C++), but another option (we chose this) is to use the original source code and do the modifications on it directly.…”

Section: Discussionmentioning

confidence: 94%

Open Source Prover in the Attic

Kovács,

Vujic

2024

Electron. Proc. Theor. Comput. Sci.

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The well known JGEX program became open source a few years ago, but seemingly, further development of the program can only be done without the original authors. In our project, we are looking at whether it is possible to continue such a large project as a newcomer without the involvement of the original authors. Is there a way to internationalize, fix bugs, improve the code base, add new features? In other words, to save a relic found in the attic and polish it into a useful everyday tool.

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Section: Discussionmentioning

confidence: 94%

Open Source Prover in the Attic

Kovács,

Vujic

2024

Electron. Proc. Theor. Comput. Sci.

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“…In a parallel project devoted to the use of automated deduction tools and methods in secondary schools, where the authors also participate, it is claimed that, one of the bottlenecks that the introduction of automated deduction systems in secondary schools face is the difficulty of tackling the task by automatic means [14]. There is the need of efficient provers (e.g.…”

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 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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“…The introduction of automated deduction systems in secondary schools faces several bottlenecks. The absence of the subject geometry itself, of rigorous mathematical demonstrations, not to mention formal proofs, in many of the national curricula, the lack of knowledge (and/or training) by the teachers about the subject [25], the dissonance between the outcomes of the available Geometry Automated Theorem Provers (GATP) and the normal practice of conjecturing and proving in the secondary education [23], are the most important in our opinion.…”

Section: Introductionmentioning

confidence: 99%

A Rule Based Theorem Prover: an Introduction to Proofs in Secondary Schools

Teles

Santos

Quaresma

2023

Electron. Proc. Theor. Comput. Sci.

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The introduction of automated deduction systems in secondary schools faces several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers and the normal practice of conjecturing and proving in schools is a major barrier to a wider use of such tools in an educational environment.Since the early implementations of geometry automated theorem provers, applications of artificial intelligence methods, synthetic provers based on inference rules and using forward chaining reasoning are considered to be best suited for education proposes.Choosing an appropriate set of rules and an automated method that can use those rules is a major challenge. We discuss one such rule set and its implementation using the geometry deductive databases method (GDDM). The approach is tested using some chosen geometric conjectures that could be the goal of a 7th year class (≈12-year-old students). A lesson plan is presented, its goal is the introduction of formal demonstration of proving geometric theorems, trying to motivate students to that goal.

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Four Geometry Problems to Introduce Automated Deduction in Secondary Schools

Cited by 6 publications

References 19 publications

Open Source Prover in the Attic

Open Source Prover in the Attic

Towards a geometry deductive database prover

A Rule Based Theorem Prover: an Introduction to Proofs in Secondary Schools

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