4 research outputs found

    Towards a Geometry Automated Provers Competition

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    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 and applications (from research in the area of artificial intelligence to applications in education). Apart from the usual measures of efficiency (e.g. CPU time), the possibility of visual and/or readable proofs is also an expected output against which the geometry automated theorem provers (GATP) should be measured. The implementation of a competition between GATP would allow to create a test bench for GATP developers to improve the existing ones and to propose new ones. It would also allow to establish a ranking for GATP that could be used by "clients" (e.g. developers of educational e-learning systems) to choose the best implementation for a given intended use.Comment: In Proceedings ThEdu'19, arXiv:2002.1189

    Exchange of Geometric Information Between Applications

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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.Comment: In Proceedings ThEdu'17, arXiv:1803.0072

    Integrating DGSs and GATPs in an Adaptative and Collaborative Blended-Learning Web-Environment

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    The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant way, the learning environments. The dynamic geometry software systems (DGSs) can be used to explore the visual contents of geometry. This already mature tools allows an easy construction of geometric figures build from free objects and elementary constructions. The geometric automated theorem provers (GATPs) allows formal deductive reasoning about geometric constructions, extending the reasoning via concrete instances in a given model to formal deductive reasoning in a geometric theory. An adaptative and collaborative blended-learning environment where the DGS and GATP features could be fully explored would be, in our opinion a very rich and challenging learning environment for teachers and students. In this text we will describe the Web Geometry Laboratory a Web environment incorporating a DGS and a repository of geometric problems, that can be used in a synchronous and asynchronous fashion and with some adaptative and collaborative features. As future work we want to enhance the adaptative and collaborative aspects of the environment and also to incorporate a GATP, constructing a dynamic and individualised learning environment for geometry.Comment: In Proceedings THedu'11, arXiv:1202.453
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