Automated Deduction and Knowledge Management in Geometry

Computer Assisted Proofs and Automated Methods in Mathematics Education

“…New topics or renewed topics can be proposed and explored, at an earlier stage of the student's cursus than in the past, whence a need to analyse new didactic situations and didactic transposition [16,17]. All this is part of the new paradigms evoked by P. Quaresma [61] (v.s. Section 1).…”

“…But the world has changed profoundly, and the various available technologies transformed mathematics into an experimental domain, and discovering novelties at an early stage of education. P. Quaresma says ( [61]): "Scientific research and education at all levels are concerned primarily with the discovery, verification, communication, and application of scientific knowledge. Learning, reusing, inventing, and archiving are the four essential aspects of knowledge accumulation in mankind's civilization process.…”

A Classification of Artificial Intelligence Systems for Mathematics Education

“…In order to apply a post-hoc explainer onto an ATP, it might be necessary to construct an ATP based purely on logic, though, as [38] notes, "while logic methods proposed have always been the dream of mankind, their applications are limited due to the massive search space". One case in point is found in DGS, where geometric automated theorem provers (GATP) are now being integrated [39]. State-of-the-art GATP are based on algebraic methods, and their results cannot be translated into human-readable proofs [39,40].…”

“…One case in point is found in DGS, where geometric automated theorem provers (GATP) are now being integrated [39]. State-of-the-art GATP are based on algebraic methods, and their results cannot be translated into human-readable proofs [39,40]. For this reason, explainability is to be introduced in ATP by designing ATP techniques that are transparent by design [33,34].…”

“…Another type of AI-based calculator is found in DGS with reasoning capabilities, which take geometric constructions as an input. While these tools contain a reasoning engine in the form of their GATP, they do not have explainer capabilities, as mentioned before, since the GATP they include produce proofs that cannot be translated to human-readable reasoning [39,40].…”