Proceedings The 13th International Workshop on Theorem proving components for Educational software

The ThEdu series pursues the smooth transition from an intuitive way of doing mathematics at secondary school to a more formal approach to the subject in STEM education while favoring software support for this transition by exploiting the power of theorem-proving technologies. What follows is a brief description of how the present volume contributes to this enterprise. The 13th International Workshop on Theorem Proving Components for Educational Software (ThEdu'24), was a satellite event of the CADE29, part of IJCAR 2024, Nancy, France. ThEdu'24 was a vibrant workshop, with one invited talk by Jeremy Avigad (Carnegie Mellon University) and 14 submitted talks. An open call for papers was then issued and attracted 9 submissions. Eight of those submissions have been accepted by our reviewers. The resulting revised papers are collected in the present volume. The contributions in this volume are a faithful representation of the wide spectrum of ThEdu, ranging from those more focused on the automated deduction research, not losing track of the possible applications in an educational setting, to those focused on the applications, in educational settings, of automated deduction tools and methods. We, the volume editors, hope that this collection of papers will further promote the development of theorem-proving-based software and that it will allow to improve the mutual understanding between computer scientists, mathematicians, and stakeholders in education. While this volume goes to press, the next edition of the ThEdu workshop is being prepared: ThEdu'25 will be a satellite event of the 30th international Conference on Automated DEduction (CADE-30), July 28th - August 2nd, 2025, Stuttgart, Germany.

Proceedings 12th International Workshop on Theorem proving components for Educational software

The ThEdu series pursues the smooth transition from an intuitive way of doing mathematics at secondary school to a more formal approach to the subject in STEM education, while favouring software support for this transition by exploiting the power of theorem-proving technologies. What follows is a brief description of how the present volume contributes to this enterprise. The 12th International Workshop on Theorem Proving Components for Educational Software(ThEdu'23), was a satellite event of the 29th international Conference on Automated Deduction (CADE 2023), July 1-4, 2023, Rome, Italy. ThEdu'23 was very successful, with one invited talk, by Yves Bertot (Inria, France), "The challenges of using Type Theory to teach Mathematics", and seven regular contributions. An open call for papers was then issued, to which eight contributions were submitted. Seven submissions have been accepted by our reviewers, who jointly produced at least three careful reports on each of the contributions. The resulting revised papers are collected in the present volume. We, the volume editors, hope that this collection of papers will further promote the development of theorem-proving based software, and that it will allow to improve the mutual understanding between computer scientists, mathematicians and stakeholders in education. PC Chairs:Julien Narboux (University of Strasbourg, France); Walther Neuper (JKU, Johannes Kepler University, Linz, Austria); Pedro Quaresma (University of Coimbra, Portugal)

Automated Completion of Statements and Proofs in Synthetic Geometry: an Approach based on Constraint Solving

Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn a conjecture with missing assumptions and with an under-specified goal into a proper theorem. Also, the proposed framework can help in completing a proof sketch into a human-readable and machine-checkable proof. Our approach is focused on synthetic geometry, and uses coherent logic and constraint solving. The proposed approach is uniform for all three kinds of tasks, flexible and, to our knowledge, unique such approach.