Towards Ranking Geometric Automated Theorem Provers

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.Comment: In Proceedings ThEdu'18, arXiv:1903.1240

O método do ângulo completo no sistema OpenGeoProver

Dissertação de Mestrado em Matemática apresentada à Faculdade de Ciências e Tecnologia da Universidade de CoimbraO método do ângulo completo para geometria euclideana construtiva foi proposto por Chou, Gao e Zhang no início dos anos 1990. Este método, uma extensão do método da área proposto pelos mesmos autores, produz demonstrações legíveis e de um modo eficiente demonstra muitos teoremas não triviais. Pode ser considerado como um dos métodos mais interessante e de maior sucesso na demonstração de teoremas em geometria e, possivelmente, o mais bem sucedido na produção de demonstrações automáticas legíveis. Nesta dissertação de mestrado faz-se a apresentação do mêtodo do ângulo completo e demonstram-se muitos dos seus lemas. Descreve-se ainda a planificação da implementação, em código livre, do método do ângulo completo.The full-angle method for euclidean constructive geometry was proposed by Chou, Gao, Zhang in early 1990’s. The method, an extension of the area method proposed by the same authors, produces humanreadable proofs and can efficiently prove many non-trivial theorems. It can be considered as one of the most interesting and most successful methods in geometry theorem proving and probably the most successful in the domain of automated production of readable proofs. In this master thesis a presentation of the full-angle method is made and several of its lemmas are proved. A plannification of the implementation, in open source code, of the full-angle method is also described

Exchange of Geometric Information Between Applications

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

Towards a Geometry Automated Provers Competition

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

Inferência de percursos dos utentes de um transporte coletivo

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Redes de Comunicações e MultimédiaNos dias de hoje, os dispositivos móveis inteligentes com o Smartphone fazem parte do dia-a-dia de cerca 46% dos utilizadores de telemóvel, representando por isso quase metade da população portuguesa. Estes dispositivos são dotados de muitas funcionalidades que permitem a deteção do movimento dos seus utilizadores, quer através dos seus sensores GPS e acelerómetro, quer por via dos módulos de comunicação sem fios Bluetooth e WiFi, e por isso podem ser usados para passivamente colherem dados da mobilidade destes. Este facto, embora controverso devido a questões de privacidade de dados e de possível identificação do seu utilizador, está a revolucionar a forma como se avalia os hábitos, tendências, contagens e mobilidade dos fluxos de população, quer dentro de grandes superfícies ou de espaços públicos. A proposta deste trabalho é a elaboração de uma prova de conceito que explora as tecnologias de deteção e contagem baseadas em dispositivos WiFi, aplicadas à problemática da contabilização de passageiros num transporte público específico – os autocarros. A informação sobre o número de passageiros bem como a mobilidade entre origem e destinos é informação extremamente difícil e onerosa de obter de forma recorrente. Esta informação é bastante valiosa para a correta gestão de um sistema de transportes. O contacto com a empresa Tecmic ajudou a perceber este problema, que hoje ainda não tem uma solução ideal.Abstract: Nowadays smart mobile devices like the Smartphone are part of the everyday life of about 46% from the mobile phone user’s base, representing almost half of total Portuguese population. These devices are equipped with many features that enable motion detection of its users, either through the GPS and accelerometer sensors, or by the WiFi or Bluetooth wireless communication modules, making possible passive collection of mobility data of its users. This fact, although controversial due to issues with privacy of personal data and possible user identification, is changing the way on how to evaluate habits and trends, mobility and population flows, both within large service infrastructures, or in public open spaces. The purpose of this work is to develop a proof of concept that exploits sensing and counting technologies based on WiFi devices, applied to the problem of passenger counting for a specific public transport: the BUS. Information about passenger counting as well as mobility between origin and destination are extremely difficult and costly to obtain on a recurring basis. This information is very valuable for the proper management of a transport system. The Contact with Tecmic Company helped to realize this problem, which today does not have yet an ideal solution

Open Geometry Prover Community Project

In Proceedings ADG 2021, arXiv:2112.14770Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely. To avoid disparate efforts,the Open Geometry Prover Community Project aims at the integration of the different efforts for the development of geometry automated theorem provers, under a common "umbrella". In this article the necessary steps to such integration are specified and the current implementation of some of those steps is described

Mining users mobility at public transportation

In this research work we propose a new approach to estimate the number of passengers in a public transportation and determinate the users’ route path based on a passive approach without user intervention. The method is based on the probe requests of users mobile device through the collected data in wireless access point. This data is manipulated to extract the information about the numbers of users with mobile devices and track their route path and time. This data can be manipulated to extract useful knowledge related with users’ habits at public transportation and extract user mobility patterns.info:eu-repo/semantics/publishedVersio