Evolution of Automated Deduction and Dynamic Constructions in Geometry

Quaresma, Pedro

doi:10.1007/978-3-030-86909-0_1

Cited by 4 publications

(4 citation statements)

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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%

“…The OGPCP, aims to integrate different efforts in the development of GATP, namely: to provide a common open access repository for the development of GATPs; to provide an API to the different GATP in such a way that they can be easily used by users; to develop a portfolio strategies to allow choosing the best GATP for any given geometric conjecture; to interface with repositories of geometric knowledge, e.g. TGTP, 12 TPTP; to develop a GATP System Competition (GASC) to allow rating GATPs [2].…”

Section: Open Source Librarymentioning

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%

Section: Open Source Librarymentioning

confidence: 99%

Towards a geometry deductive database prover

Baeta

Quaresma

2023

Ann Math Artif Intell

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“…Automated deduction in geometry has been, since 1960s, an important field in the area of automated reasoning. Various methods and techniques have been studied and developed for automatically proving and discovering geometric theorems [22]. Focusing in the DGS/GATP platforms, i.e., platforms that combine the DGS with one (or several) GATP(s) we can highlight (some have been mentioned already): Cinderella, with a randomised prover; GCLC [16], which include several provers (area method, Wu's method and Gröbner basis method) [17]; GeoGebra, which include several algebraic provers [18,19] and JGEx which include several provers (area method, full-angle method, deductive databases method, Wu's method and Gröbner basis method).…”

Section: Geometry Automated Theorem Proversmentioning

confidence: 99%

“…Since the early attempts, linked to artificial intelligence, synthetic provers based on inference rules and using forward chaining reasoning has been seen has a more suited approach for education. Using an appropriated set of rules and using forward chaining they can more easily mimic the expected behaviour of a student when developing a proof [2,22].…”

Section: A Rule-based Geometry Automated Theorem Provermentioning

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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