Abstract
The main goal of most systems for formalizing mathematics is creating the database of formalized knowledge. Every system uses its own way of storing that knowledge. Pieces of the information stored in such a database are something more than just elements of that database – we may also look at it from another perspective. Namely, the information is the reflection of some text and that text is the representation of some logical reasoning. Therefore every such piece of information may be treated as an element of some set and then we may analyze the relationships between all these elements. This article describes such an approach to one of the systems for formalizing mathematics.
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References
Bonarska, E.: An Introduction to PC Mizar, Fondation Ph. le Hodey, Brussels (1990)
Milewski, R.: Robustness of Systems for Formalizing Mathematics – Testing Monotonicity and Permutability of References in Mizar, Mechanized Mathematics and Its Applications, vol. 4, pp. 51–58 (2005)
Muzalewski, M.: An Outline of PC Mizar, Fondation Philippe le Hodey, Brussels (1993)
Rudnicki, P.: An Overview of the Mizar Project. In: Proceedings of the 1992 Workshop on Types for Proofs and Programs, Chalmers University of Technology, Bastad (1992)
Rudnicki, P., Trybulec, A.: On Equivalents of Well-foundedness. An experiment in Mizar Journal of Automated Reasoning 23, 197–234 (1999)
Trybulec, A.: Some Features of the Mizar Language. In: ESPRIT Workshop, Torino (1993)
Wiedijk, F.: Comparing Mathematical Provers. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 188–202. Springer, Heidelberg (2003)
Wiedijk, F.: Mizar: An Impression, http://mizar.org/project/mizarintro.ps
Mizar Home Page, http://mizar.org/
Mizar Lecture Notes, 4th Edition, Shinshu University, Nagano (2001), http://markun.cs.shinshu-u.ac.jp/kiso/projects2/proofchecker/mizar/Mi-zar4/index-e.html
Mizar Users Guide in Japanese, Shinshu University, Nagano (1994), English translation http://markun.cs.shinshu-u.ac.jp/kiso/projects2/proofchecker/mizar/Mizar-E/Miz-etit.htm
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© 2006 Springer-Verlag Berlin Heidelberg
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Milewski, R. (2006). Transformations of MML Database’s Elements. In: Kohlhase, M. (eds) Mathematical Knowledge Management. MKM 2005. Lecture Notes in Computer Science(), vol 3863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11618027_25
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DOI: https://doi.org/10.1007/11618027_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31430-1
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