Abstract
The MML is one of the largest collection of formalized mathematical knowledge that has been developed with various interactive proof assistants. It comprises more than 1100 “articles” summing to nearly 2.5 million lines of text, each consisting of a unified collection of mathematical definitions and proofs. Semantically, it contains more than 50000 theorems and more than 10000 definitions expressed using more than 7000 symbols. It thus offers a fascinating corpus on which one could carry out a number of experiments. This note discusses a system for computing fine-grained dependencies among the contents of the MML. For an overview of Mizar, see [3]; for a discussion of some successful initial experiments carried out with the help of mizar-items, see [1,2].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alama, J., Kuehlwein, D., Tsivtsivadze, E., Urban, J., Heskes, T.: Premise selection for mathematics by corpus analysis and kernel methods (preprint, submitted)
Alama, J., Mamane, L., Urban, J.: Dependencies in formal mathematics (preprint, submitted)
Grabowski, A., Kornilowicz, A., Naumowicz, A.: Mizar in a nutshell. Journal of Formalized Reasoning 3(2), 153–245 (2010), http://jfr.cib.unibo.it/article/view/1980/1356
Lakatos, I.: Proofs and Refutations. Cambridge University Press, Cambridge (1976)
Simpson, S.G.: Subsystems of Second Order Arithmetic, 2nd edn. Perspectives in Mathematical Logic. Springer, Heidelberg (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alama, J. (2011). mizar-items: Exploring Fine-Grained Dependencies in the Mizar Mathematical Library. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds) Intelligent Computer Mathematics. CICM 2011. Lecture Notes in Computer Science(), vol 6824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22673-1_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-22673-1_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22672-4
Online ISBN: 978-3-642-22673-1
eBook Packages: Computer ScienceComputer Science (R0)