3 research outputs found
Towards Ranking Geometric Automated Theorem Provers
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.Comment: In Proceedings ThEdu'18, arXiv:1903.1240
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.Comment: 14 pages, 5 figures, accepted at CICM 201