### Classification of Alignments Between Concepts of Formal Mathematical Systems

Dennis Müller, Thibault Gauthier, Cezary Kaliszyk, Michael Kohlhase, Florian Rabe10th International Conference on Intelligent Computer Mathematics, LNCS 10383, pp. 83-98, 2017.

### 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}, }