Open Geometry Prover Community Project

Abstract

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.

A Rule Based Theorem Prover: an Introduction to Proofs in Secondary Schools

“…The use of a rule-based theorem prover being developed within our research group [1] will allow to implement the set of rules which deem appropriated for the automation for one side and its use with the intended target audience. There are many challenges ahead: the implementation of an efficient prover; the possibility to separate the set of rules from the inference mechanisms, i.e.…”

“…2 Its formalisation in the TPTP FOF-format is presented here 3 . This set of rules is to be added to the set of rules used to implement the deductive database prover [1,4], notice that some of them 1 JGEx: https://github.com/yezheng1981/Java-Geometry-Expert, OGP-GDDM: https://github.com/ opengeometryprover/OpenGeometryProver 2 Only the rules needed in the proofs were chosen. are already taken (coincide) with rules presented in that set of rules.…”

“…In the original implementation [4] and in a new implementation being finished [1], a rule set based on the full-angle method [3] is used. Both implementation are open source software, available in GitHub servers.…”

“…Both implementation are open source software, available in GitHub servers. 1 A different set of rules can be used, keeping the efficient database search strategy. In the following, the application of a set of rules [9,10], more adapted to the 7th year (≈ 12-year-old students) in the Portuguese curricula [5,7,8] is presented and its application to the demonstration of formal proof of some geometric theorems is described.…”

“…are already taken (coincide) with rules presented in that set of rules. The FOF format is chosen because it is the format used in the new implementation of the deductive database method already mentioned above [1]. The geometric predicates 4 are those described in [4], with some additions whose meaning should be clear.…”