Improving QED-Tutrix by Automating the Generation of Proofs

The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects. QED-Tutrix is an intelligent tutor for geometry offering an interface to help high school students in the resolution of demonstration problems. It focuses on specific goals: 1) to allow the student to freely explore the problem and its figure, 2) to accept proofs elements in any order, 3) to handle a variety of proofs, which can be customized by the teacher, and 4) to be able to help the student at any step of the resolution of the problem, if the need arises. The software is also independent from the intervention of the teacher. QED-Tutrix offers an interesting approach to geometry education, but is currently crippled by the lengthiness of the process of implementing new problems, a task that must still be done manually. Therefore, one of the main focuses of the QED-Tutrix' research team is to ease the implementation of new problems, by automating the tedious step of finding all possible proofs for a given problem. This automation must follow fundamental constraints in order to create problems compatible with QED-Tutrix: 1) readability of the proofs, 2) accessibility at a high school level, and 3) possibility for the teacher to modify the parameters defining the "acceptability" of a proof. We present in this paper the result of our preliminary exploration of possible avenues for this task. Automated theorem proving in geometry is a widely studied subject, and various provers exist. However, our constraints are quite specific and some adaptation would be required to use an existing prover. We have therefore implemented a prototype of automated prover to suit our needs. The future goal is to compare performances and usability in our specific use-case between the existing provers and our implementation.Comment: In Proceedings ThEdu'17, arXiv:1803.0072

Text Summarization by Sentence Extraction and Syntactic Pruning

Nous présentons une méthode hybride pour le résumé de texte, en combinant l'extraction de phrases et l'élagage syntaxique des phrases extraites. L'élagage syntaxique est effectué sur la base d’une analyse complète des phrases selon un parseur de dépendances, analyse réalisée par la grammaire développée au sein d'un logiciel commercial de correction grammaticale, le Correcteur 101. Des sous-arbres de l'analyse syntaxique sont supprimés quand ils sont identifiés par les relations ciblées. L'analyse est réalisée sur un corpus de divers textes. Le taux de réduction des phrases extraites est d’en moyenne environ 74%, tout en conservant la grammaticalité ou la lisibilité dans une proportion de plus de 64%. Étant donné ces premiers résultats sur un ensemble limité de relations syntaxiques, cela laisse entrevoir des possibilités pour une application de résumé automatique de texte.CRSN

Assessing and Improving Domain Knowledge Representation in DBpedia

With the development of knowledge graphs and the billions of triples generated on the Linked Data cloud, it is paramount to ensure the quality of data. In this work, we focus on one of the central hubs of the Linked Data cloud, DBpedia. In particular, we assess the quality of DBpedia for domain knowledge representation. Our results show that DBpedia has still much room for improvement in this regard, especially for the description of concepts and their linkage with the DBpedia ontology. Based on this analysis, we leverage open relation extraction and the information already available on DBpedia to partly correct the issue, by providing novel relations extracted from Wikipedia abstracts and discovering entity types using the dbo:type predicate. Our results show that open relation extraction can indeed help enrich domain knowledge representation in DBpedia

FICLONE: Improving DBpedia Spotlight Using Named Entity Recognition and Collective Disambiguation

In this paper we present FICLONE, which aims to improve the performance of DBpedia Spotlight, not only for the task of semantic annotation (SA), but also for the sub-task of named entity disambiguation (NED). To achieve this aim, first we enhance the spotting phase by combining a named entity recognition system (Stanford NER ) with the results of DBpedia Spotlight. Second, we improve the disambiguation phase by using coreference resolution and exploiting a lexicon that associates a list of potential entities of Wikipedia to surface forms. Finally, to select the correct entity among the candidates found for one mention, FICLONE relies on collective disambiguation, an approach that has proved successful in many other annotators, and that takes into consideration the other mentions in the text. Our experiments show that FICLONE not only substantially improves the performance of DBpedia Spotlight for the NED sub-task but also generally outperforms other state-of-the-art systems. For the SA sub-task, FICLONE also outperforms DBpedia Spotlight against the dataset provided by the DBpedia Spotlight team

Actes de la Conférence nationale et du 13e Colloque de l'AQPC

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Automating the Generation of High School Geometry Proofs using Prolog in an Educational Context

When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing, beforehand, the possible ways to solve a problem. Hence the need for an automated theorem prover that provide proofs as they would be written by a student. To achieve this objective, logic programming is a natural tool due to the similarity of its reasoning with a mathematical proof by inference. In this paper, we present the core ideas we used to implement such a prover, from its encoding in Prolog to the generation of the complete set of proofs. However, when dealing with educational aspects, there are many challenges to overcome. We also present the main issues we encountered, as well as the chosen solutions.Comment: In Proceedings ThEdu'19, arXiv:2002.1189