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From informal to formal proofs in Euclidean geometry

From informal to formal proofs in Euclidean geometry In this paper, we propose a new approach for automated verification of informal proofs in Euclidean geometry using a fragment of first-order logic called coherent logic and a corresponding proof representation. We use a TPTP inspired language to write a semi-formal proof of a theorem, that fairly accurately depicts a proof that can be found in mathematical textbooks. The semi-formal proof is verified by generating more detailed proof objects expressed in the coherent logic vernacular. Those proof objects can be easily transformed to Isabelle and Coq proof objects, and also in natural language proofs written in English and Serbian. This approach is tested on two sets of theorem proofs using classical axiomatic system for Euclidean geometry created by David Hilbert, and a modern axiomatic system E created by Jeremy Avigad, Edward Dean, and John Mumma. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

From informal to formal proofs in Euclidean geometry

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References (70)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Nature Switzerland AG
Subject
Computer Science; Artificial Intelligence; Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-018-9597-7
Publisher site
See Article on Publisher Site

Abstract

In this paper, we propose a new approach for automated verification of informal proofs in Euclidean geometry using a fragment of first-order logic called coherent logic and a corresponding proof representation. We use a TPTP inspired language to write a semi-formal proof of a theorem, that fairly accurately depicts a proof that can be found in mathematical textbooks. The semi-formal proof is verified by generating more detailed proof objects expressed in the coherent logic vernacular. Those proof objects can be easily transformed to Isabelle and Coq proof objects, and also in natural language proofs written in English and Serbian. This approach is tested on two sets of theorem proofs using classical axiomatic system for Euclidean geometry created by David Hilbert, and a modern axiomatic system E created by Jeremy Avigad, Edward Dean, and John Mumma.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: Aug 29, 2018

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