arXiv subjects

Pedro Quaresma

Publications and source records attributed to Pedro Quaresma.

23 records · Page 2Linked to original sources

arXiv2014

Querying Geometric Figures Using a Controlled Language, Ontological Graphs and Dependency Lattices

Dynamic geometry systems (DGS) have become basic tools in many areas of geometry as, for example, in education. Geometry Automated Theorem Provers (GATP) are an active area of research and are considered as being basic tools in future enhanced educational software as well as in a next generation of mechanized mathematics assistants. Recently emerged Web repositories of geometric knowledge, like TGTP and Intergeo, are an attempt to make the already vast data set of geometric knowledge widely available. Considering the large amount of geometric information already available, we face the need of a query mechanism for descriptions of geometric constructions. In this paper we discuss two approaches for describing geometric figures (declarative and procedural), and present algorithms for querying geometric figures in declaratively and procedurally described corpora, by using a DGS or a dedicated controlled natural language for queries.

cs.CG↗

arXiv2013

The Web Geometry Laboratory Project

The "Web Geometry Laboratory" (WGL) project's goal is to build an adaptive and collaborative blended-learning Web-environment for geometry. In its current version (1.0) the WGL is already a collaborative blended-learning Web-environment integrating a dynamic geometry system (DGS) and having some adaptive features. All the base features needed to implement the adaptive module and to allow the integration of a geometry automated theorem prover (GATP) are also already implemented. The actual testing of the WGL platform by high-school teachers is underway and a field-test with high-school students is being prepared. The adaptive module and the GATP integration will be the next steps of this project.

cs.CY↗

arXiv2012

An XML-Format for Conjectures in Geometry (Work-in-Progress)

With a large number of software tools dedicated to the visualisation and/or demonstration of properties of geometric constructions and also with the emerging of repositories of geometric constructions, there is a strong need of linking them, and making them and their corpora, widely usable. A common setting for interoperable interactive geometry was already proposed, the i2g format, but, in this format, the conjectures and proofs counterparts are missing. A common format capable of linking all the tools in the field of geometry is missing. In this paper an extension of the i2g format is proposed, this extension is capable of describing not only the geometric constructions but also the geometric conjectures. The integration of this format into the Web-based GeoThms, TGTP and Web Geometry Laboratory systems is also discussed.

cs.CG↗

arXiv2012

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

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.

cs.CG↗

arXiv2012

Proceedings First Workshop on CTP Components for Educational Software

The THedu'11 workshop received thirteen submissions, twelve of which were accepted and presented during the workshop. For the post-conference proceedings nine submission where received and accepted. The submissions are within the scope of the following points, which have been announced in the call of papers: CTP-based software tools for education; CTP technology combined with novel interfaces, drag and drop, etc.; technologies to access ITP knowledge relevant for a certain step of problem solving; usability considerations on representing ITP knowledge; combination of deduction and computation; formal problem specifications; effectiveness of ATP in checking user input; formats for deductive content in proof documents, geometric constructions, etc; formal domain models for e-learning in mathematics and applications.

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