Towards Ranking Geometric Automated Theorem Provers

Abstract

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.

Towards a Geometry Automated Provers Competition

“…How to measure the readability of proofs is still a research problem [2,30,31], Chou proposed a way to measure how difficult a formal proof is (using the area method) [9], de Bruijn also proposed a coefficient, the de Bruijn factor, the quotient of the size of corresponding informal proof and the size of the formal proof, could also be used as a measure of readability [37]. This is close to a Turing test for proofs: if a human cannot distinguish the proof generated automatically from a human proof, than it is readable.…”

“…How to make the results and competing tools available so that they can be leveraged in subsequent events? Some partial results are already available: a common language to state the geometric theorems [29], a comprehensive repository of geometric problems [28] and a set of measures of quality capable of assessing the GATPs in different classes [2,31].…”

“…The ideas behind such a competition were presented in [2]. From the subsequent discussion, where a small set of six geometric problems was chosen, we progressed to an actual competition at ThEdu'19, GASC 0.1, run in a local computer, and where a set of GATPs competed over problems in the TGTP database.…”