A Vernacular for Coherent Logic

The power of state-of-the-art automated and interactive the-orem provers has reached the level at which a significant portion of non-trivial mathematical contents can be formalized almost fully automat-ically. 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 auto-matically 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.

S. Stojanovic Durdevic , J. Narboux , M. Bezem , P. Janicic

Conferences on Intelligent Computer Mathematics (CICM 2014) , Volume 8543 , page 388-403 - 2014

International conference with proceedings A Vernacular for Coherent Logic, Conferences on Intelligent Computer Mathematics (CICM 2014), Coimbra, Portugal, pages 388-403, Springer, LNCS, Volume 8543, juillet 2014, doi:10.1007/978-3-319-08434-3_28 Research team : IGG

 author = {Stojanovic Durdevic, S. and Narboux, J. and Bezem, M. and Janicic, P.},
 title = {A Vernacular for Coherent Logic},
 booktitle  = {Conferences on Intelligent Computer Mathematics (CICM 2014)},
 series = {LNCS},
 volume = {8543},
 pages = {388-403},
 month = {Jul},
 year = {2014},
 publisher = {Springer},
 doi = {10.1007/978-3-319-08434-3_28},
 x-international-audience = {Yes},
 x-language = {EN},
 url = {http://icube-publis.unistra.fr/4-SNBJ14}