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},
}