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A Review of Mathematical Knowledge Management

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Intelligent Computer Mathematics (CICM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5625))

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Abstract

Mathematical Knowledge Management (MKM), as a field, has seen tremendous growth in the last few years. This period was one where many research threads were started and the field was defining itself. We believe that we are now in a position to use the MKM body of knowledge as a means to define what MKM is, what it worries about, etc. In this paper, we review the literature of MKM and gather various metadata from these papers. After offering some definitions surrounding MKM, we analyze the metadata we have gathered from these papers, in an effort to cast more light on the field of MKM and its evolution.

This research was supported by NSERC.

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References

  1. Adams, A.A.: Digitisation, representation, and formalisation. In: Asperti, et al. (eds.) [4], pp. 1–16

    Google Scholar 

  2. Adams, A.A., Davenport, J.H.: Copyright issues for MKM. In: Asperti, et al. (eds.) [3], pp. 1–16

    Google Scholar 

  3. Asperti, A., Bancerek, G., Trybulec, A. (eds.): MKM 2004. LNCS, vol. 3119. Springer, Heidelberg (2004)

    Google Scholar 

  4. Asperti, A., Buchberger, B., Davenport, J.H. (eds.): MKM 2003. LNCS, vol. 2594. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  5. Aspinall, D., Lüth, C., Winterstein, D.: A framework for interactive proof. In: Kauers, et al. (eds.) [27], pp. 161–175

    Google Scholar 

  6. Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds.): AISC 2008, Calculemus 2008, and MKM 2008. LNCS, vol. 5144. Springer, Heidelberg (2008)

    Google Scholar 

  7. Borwein, J.M., Farmer, W.M. (eds.): MKM 2006. LNCS, vol. 4108. Springer, Heidelberg (2006)

    Google Scholar 

  8. Borwein, J.M., Stanway, T.: Managing digital mathematical discourse. In: Asperti, et al. (eds.) [4], pp. 45–55

    Google Scholar 

  9. Boyer, R.: The QED Manifesto. In: Bundy, A. (ed.) Proceedings CADE 12, pp. 238–251 (1994)

    Google Scholar 

  10. Buchberger, B., Caprotti, O. (eds.): Electronic Proceedings of the First International Workshop on Mathematical Knowledge Management: MKM 2001. RISC-Linz (2001), http://www.risc.uni-linz.ac.at/about/conferences/MKM2001/Proceedings

  11. Buchberger, B., Gonnet, G.H., Hazewinkel, M. (eds.): Mathematical Knowledge Management. Ann. Math. Artif. Intell, vol. 38. Kluwer, Dordrecht (2003)

    MATH  Google Scholar 

  12. Bundy, A.: Automating signature evolution in logical theories. In: Autexier, et al. (eds.) [6], pp. 333–338

    Google Scholar 

  13. Cairns, P.A., Gow, J., Collins, P.: On dynamically presenting a topology course. Ann. Math. Artif. Intell. 38(1-3), 91–104 (2003)

    Article  MATH  Google Scholar 

  14. Cajori, F.: A History of Mathematical Notations. Dover, New York (reprint) (1929)

    Google Scholar 

  15. Coen, C.S.: From proof-assistants to distributed libraries of mathematics: Tips and pitfalls. In: Asperti, et al. (eds.) [4], pp. 30–44

    Google Scholar 

  16. Davis, M.: The Universal Computer: The Road from Leibniz to Turing. W. W. Norton & Co., Inc., New York (2000)

    MATH  Google Scholar 

  17. de Bruijn, N.G.: A Survey of the Project Automath. To H.B. Curry: Essays on Combinatory Logic, 579–606 (1980)

    Google Scholar 

  18. Encyclopédie ou dictionnaire raisonné des sciences, des arts et des métiers, pp. 1751–1772

    Google Scholar 

  19. Engelbart, D.: A research center for augmenting human intellect (demo) (December 1968), http://en.wikipedia.org/wiki/The_Mother_of_All_Demos

  20. Farmer, W.M.: MKM: A new interdisciplinary field of research. ACM SIGSAM Bulletin 38, 47–52 (2004)

    Article  MATH  Google Scholar 

  21. Farmer, W.M.: Mathematical knowledge management. In: Schwartz, D.G. (ed.) Encyclopedia of Knowledge Management. Information Science Reference, pp. 599–604 (2005)

    Google Scholar 

  22. Frege, G.: Begriffsschrift: eine der arithmetische nachgebildete Formelsprache des reinen Denkens. L. Nebert, Halle a/S (1879/1997)

    Google Scholar 

  23. Gödel, K.: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. Monatshefte für Mathematik und Physik 38(1), 173–198 (1931)

    Article  MathSciNet  MATH  Google Scholar 

  24. Guidi, F., Schena, I.: A query language for a metadata framework about mathematical resources. In: Asperti, et al. (eds.) [4], pp. 105–118

    Google Scholar 

  25. Heeren, B., Jeuring, J., van Leeuwen, A., Gerdes, A.: Specifying strategies for exercises. In: Autexier, et al. (eds.) [6], pp. 430–445

    Google Scholar 

  26. Horozal, F.F., Brown, C.E.: Formal representation of mathematics in a dependently typed set theory. In: Kauers, et al. (eds.) [27], pp. 265–279

    Google Scholar 

  27. Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.): MKM/CALCULEMUS 2007. LNCS, vol. 4573. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  28. Kohlhase, A., Kohlhase, M.: An exploration in the space of mathematical knowledge. In: Kohlhase (ed.) [29], pp. 17–32

    Google Scholar 

  29. Kohlhase, M. (ed.): MKM 2005. LNCS, vol. 3863. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  30. Libbrecht, P., Desmoulins, C., Mercat, C., Laborde, C., Dietrich, M., Hendriks, M.: Cross-curriculum search for Intergeo. In: Autexier, et al. (eds.) [6], pp. 520–535

    Google Scholar 

  31. Mathematical Knowledge Management Symposium, http://www.macs.hw.ac.uk/~fairouz/mkm-symposium03/

  32. Melis, E., Büdenbender, J., Goguadze, G., Libbrecht, P., Ullrich, C.: Knowledge representation and management in activemath. Ann. Math. Artif. Intell. 38(1-3), 47–64 (2003)

    MATH  Google Scholar 

  33. A North American Workshop on Mathematical Knowledge Management (NA-MKM 2002) (2002), http://imps.mcmaster.ca/na-mkm-2002/

  34. Second North American Workshop on Mathematical Knowledge Management (NA-MKM 2004) (2004), http://imps.mcmaster.ca/na-mkm-2004/

  35. Workshop on Mathematical Knowledge Management: Sustainability, Scalability and Interoperability, http://projects.cs.dal.ca/ddrive/seminars/mkm.shtml

  36. Nederpelt, R., Geuvers, J., de Vrijer, R.: Selected Papers on Automath. Studies in Logic and the Foundations of Mathematics 133 (1994)

    Google Scholar 

  37. Padovani, L.: On the roles of LaTeX and MathML in encoding and processing mathematical expressions. In: Asperti, et al. (eds.) [4], pp. 66–79

    Google Scholar 

  38. Parnas, D.L.: On a ”buzzword”: hierarchical structure, pp. 429–440. Springer, Heidelberg (2002)

    Google Scholar 

  39. Turing, A.M.: Practical forms of type theory. Journal of Symbolic Logic 13, 80–94 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  40. Urban, J.: XML-izing Mizar: Making semantic processing and presentation of mml easy. In: Kohlhase (ed.) [29], pp. 346–360

    Google Scholar 

  41. Verchinine, K., Lyaletski, A.V., Paskevich, A., Anisimov, A.: On correctness of mathematical texts from a logical and practical point of view. In: Autexier, et al. (eds.) [6], pp. 583–598

    Google Scholar 

  42. Whitehead, A.N., Russell, B.: Principia Mathematica. Cambridge University Press, Cambridge (1910)

    MATH  Google Scholar 

  43. Wiedijk, F.: The QED manifesto revisited. Studies in Logic, Grammar and Rhetoric 10(23), 121–133 (2007)

    Google Scholar 

  44. Youssef, A.: Roles of math search in mathematics. In: Borwein, Farmer (eds.) [7], pp. 2–16

    Google Scholar 

  45. Youssef, A.: Methods of relevance ranking and hit-content generation in math search. In: Kauers, et al. (eds.) [27], pp. 393–406

    Google Scholar 

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Carette, J., Farmer, W.M. (2009). A Review of Mathematical Knowledge Management. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds) Intelligent Computer Mathematics. CICM 2009. Lecture Notes in Computer Science(), vol 5625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02614-0_21

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  • DOI: https://doi.org/10.1007/978-3-642-02614-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02613-3

  • Online ISBN: 978-3-642-02614-0

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