Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/499
Title: Automated generation of machine verifiable and readable proofs: A case study of tarski’s geometry
Authors: Stojanović-Đurđević. Sana 
Narboux, Julien
Janičić, Predrag 
Affiliations: Informatics and Computer Science 
Keywords: Automated theorem proving;Interactive theorem proving;Tarski’s geometry
Issue Date: 1-Aug-2015
Journal: Annals of Mathematics and Artificial Intelligence
Abstract: 
The power of state-of-the-art automated and interactive theorem provers has reached the level at which a significant portion of non-trivial mathematical contents can be formalized almost fully automatically. In this paper we present our framework for the formalization of mathematical knowledge that can produce machine verifiable proofs (for different proof assistants) but also human-readable (nearly textbook-like) proofs. As a case study, we focus on one of the twentieth century classics-a book on Tarski’s geometry. We tried to automatically generate such proofs for the theorems from this book using resolution theorem provers and a coherent logic theorem prover. In the first experiment, we used only theorems from the book, in the second we used additional lemmas from the existing Coq formalization of the book, and in the third we used specific dependency lists from the Coq formalization for each theorem. The results show that 37 % of the theorems from the book can be automatically proven (with readable and machine verifiable proofs generated) without any guidance, and with additional lemmas this percentage rises to 42 %. These results give hope that the described framework and other forms of automation can significantly aid mathematicians in developing formal and informal mathematical knowledge.
URI: https://research.matf.bg.ac.rs/handle/123456789/499
ISSN: 10122443
DOI: 10.1007/s10472-014-9443-5
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