Classification of Alignments Between Concepts of Formal Mathematical Systems

Dennis Müller, Thibault Gauthier, Cezary Kaliszyk, Michael Kohlhase, Florian Rabe
10th International Conference on Intelligent Computer Mathematics, LNCS 10383, pp. 83-98, 2017.

pdf   doi:10.1007/978-3-319-62075-6_7

Abstract

Mathematical knowledge is publicly available in dozens of different formats and languages, ranging from informal (e.g. Wikipedia) to formal corpora (e.g., Mizar). Despite an enormous amount of overlap between these corpora, only few machine-actionable connections exist. We speak of alignment if the same concept occurs in different libraries, possibly with slightly different names, notations, or formal definitions. Leveraging these alignments creates a huge
potential for knowledge sharing and transfer, e.g., integrating theorem provers or reusing services across systems. Notably, even imperfect alignments, i.e. concepts that are very similar rather than identical, can often play very important roles. Specifically, in machine learning techniques for theorem proving and in automation techniques that use these, they allow learning-reasoning based automation for theorem provers to take inspiration from proofs from different formal proof libraries or semi-formal libraries even if the latter is based on a different mathematical foundation. We present a classification of alignments and design a simple format for describing alignments, as well as an infrastructure for sharing them. We propose these as a centralized standard for the community. Finally, we present an initial collection of ≈12000 alignments from the different kinds of mathematical corpora, including proof assistant libraries and semi-formal corpora as a public resource.

BibTex

@inproceedings{dmtgckmkfrcicm17,
author = {Dennis M{\"{u}}ller and
Thibault Gauthier and
Cezary Kaliszyk and
Michael Kohlhase and
Florian Rabe},
title = {Classification of Alignments Between Concepts of Formal
Mathematical
Systems},
booktitle = {10th International Conference on Intelligent Computer
Mathematics (CICM'17)},
pages = {83--98},
year = {2017},
doi = {10.1007/978-3-319-62075-6_7},
editor = {Herman Geuvers and
Matthew England and
Osman Hasan and
Florian Rabe and
Olaf Teschke},
series = {LNCS},
volume = {10383},
publisher = {Springer},
}