Towards Ranking Geometric Automated Theorem Provers (original) (raw)

Towards a Geometry Automated Provers Competition

Electronic Proceedings in Theoretical Computer Science

The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in the area of artificial intelligence to applications in education). Apart from the usual measures of efficiency (e.g. CPU time), the possibility of visual and/or readable proofs is also an expected output against which the geometry automated theorem provers (GATP) should be measured. The implementation of a competition between GATP would allow to create a test bench for GATP developers to improve the existing ones and to propose new ones. It would also allow to establish a ranking for GATP that could be used by "clients" (e.g. developers of educational e-learning systems) to choose the best implementation for a given intended use.

Combining Dynamic Geometry, Automated Geometry Theorem Proving and Diagrammatic Proofs

2005

This paper outlines Geometry Explorer, a prototype system that allows users to create Euclidean geometry constructions using a dynamic geometry interface, specify conjectures about them and then use a full-angle method prover to automatically produce diagram independent, human-readable proofs to theorems. Our system can then automatically generate novel diagrammatic proofs of the forward-chaining and backward-chaining reasoning used by the geometry theorem prover, as well as visualise multiple proofs to single theorems. We discuss the features of our system, how they were implemented and the issues encountered when trying to create diagrammatic full-angle method proofs.

The moment of truth in automatic theorem proving in elementary geometry

While still being an active field of research, automatic theorem proving in elementary geometry has reached a certain status of maturity. Software and hardware requirements to successfully (and quickly) perform hundreds of interesting examples are now widespread available (such as GEX, Geother, GDI, etc.) Yet, in recent years, a few papers ([BDR],[BFS], [CT1], [CT2]) have repeatedly expressed the need for reviewing some foundational aspects of the algebraic geometry via to automatic geometry theorem proving. Among these papers we will like to highlight the one by P. Conti and C. Traverso ([CT2]), devoted to unveil truth's inherent manifold structure in this context. Actually, unraveling the notion of truth has always been a recurrent task in the realm of automatic proving of geometry theorems by algebraic geometry means. Practically all major contributors to this topic have felt obliged to devote quite a few lines to discuss on what (and, then, why) should be a correct definition for a "true theorem", we refer to the classic articles and books by D. Kapur ([Ka86], [Ka88]), by W.-T. Wu ([Wu78], [Wu82], [Wu84]), by D. Wang ([Wa98]) and by S.-C Chou ([Ch88]). In fact, what is at stake is not a mere scholastic digression, but a crucial issue: after all, automatic proving is expected to deal with proving true statements (and disproving false ones). Roughly speaking, the algebraic geometry method towards theorem proving, proceeds translating thesis and hypothesis about geometric entities into systems of equations, say H = {h 1 = 0,. .. , h r = 0} and T = {t 1 = 0,. .. , t s = 0}. Solutions (in a suitable field: there will be different interpretations for different choices of this field) for H (respectively, for T), can be interpreted as geometric Last author supported by grant "Geometría Algebraica Real y Algoritmos para Curvas y Superficies" (MTM2005-08690-C02-02) from the Spanish MEC.

GraATP: A graph theoretic approach for Automated Theorem Proving in plane geometry

The 8th International Conference on Software, Knowledge, Information Management and Applications (SKIMA 2014), 2014

Automated Theorem Proving (ATP) is an established branch of Artificial Intelligence. The purpose of ATP is to design a system which can automatically figure out an algorithm either to prove or disprove a mathematical claim, on the basis of a set of given premises, using a set of fundamental postulates and following the method of logical inference. In this paper, we propose GraATP, a generalized framework for automated theorem proving in plane geometry. Our proposed method translates the geometric entities into nodes of a graph and the relations between them as edges of that graph. The automated system searches for different ways to reach the conclusion for a claim via graph traversal by which the validity of the geometric theorem is examined.

GEOM-a prolog geometry theorem prover

1979

This paper describes automated reasoning m a PROLOG Euclidean geometry theorem-prover. It brings into focus general topics in automated reasoning and the ability of Prolog in coping with them.

Automatic Deduction in an AI Geometry Book

Artificial Intelligence and Symbolic Computation

The pursuit of an AI Geometry Book should involve the study of how currently developing methodologies and technologies of geometry knowledge representation, management, deduction and discovery can be incorporated effectively into a computational application, a "book" of the future. In the geometry book of the future statements and proofs should be en-lighted by dynamic geometry sketches and diagrams, and the correctness of the proofs should be ensured by computer checking. The book will be intelligent, the reader should be able to ask closed or open questions, and can also ask for proof hints. The book should also provide interactive exercises with automatic correction. To fulfil such a goal the development of an open library of geometry automated theorem provers with a carefully design application interface protocol, must be considered. This would allow to link computer platforms for geometry with theorem provers, providing the automatic deduction capabilities for the AI Geometry Book.

Open Geometry Prover Community Project

Electronic Proceedings in Theoretical Computer Science, 2021

Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely. To avoid disparate efforts, the Open Geometry Prover Community Project aims at the integration of the different efforts for the development of geometry automated theorem provers, under a common "umbrella". In this article the necessary steps to such integration are specified and the current implementation of some of those steps is described.

Design of an intelligent system for the automatic demonstration of geometry theorems

International Conference on Telecommunications, 2010

In this work will be presented the design of an intelligent system destined for development process of demonstrating abilities for geometry theorems. This system will make available to user a proof assistant which will allow interactive vizualization of several demonstrations for the same theorem, demonstrations that have been generated by using three specific methods for automatic demonstration of theorems: area method, full-angle method and inferences accomplishment. For the implementation of the component used to represent knowledge and proof mechanisms will be used Prolog language and for the achievement of geometric construction associated to the theorem will be used Java language.