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Towards MKM in the Large: Modular Representation and Scalable Software Architecture

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Intelligent Computer Mathematics (CICM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6167))

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Abstract

MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM “in the small” is well-studied, so the real problem is to scale up to large, highly interconnected corpora: “MKM in the large”. We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases.

We present instances of both in this paper: the Mmt framework for modular theory-graphs that integrates meta-logical foundations, which forms the base of the next OMDoc version; and TNTBase, a versioned storage system for XML-based document formats. TNTBase becomes an Mmt database by instantiating it with special MKM operations for Mmt.

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References

  1. Autexier, S., Hutter, D., Mantel, H., Schairer, A.: Towards an Evolutionary Formal Software-Development Using CASL. In: Bert, D., Choppy, C., Mosses, P.D. (eds.) WADT 1999. LNCS, vol. 1827, pp. 73–88. Springer, Heidelberg (2000)

    Google Scholar 

  2. Berners-Lee, T., Fielding, R., Masinter, L.: Uniform Resource Identifier (URI): Generic Syntax, RFC 3986, Internet Engineering Task Force (2005)

    Google Scholar 

  3. Bertot, Y., Castéran, P.: Coq’Art: The Calculus of Inductive Constructions. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  4. Bourbaki, N.: Theory of Sets. In: Elements of Mathematics, Springer, Heidelberg (1968)

    Google Scholar 

  5. Bourbaki, N.: Algebra I. In: Elements of Mathematics, Springer, Heidelberg (1974)

    Google Scholar 

  6. Buswell, S., Caprotti, O., Carlisle, D., Dewar, M., Gaetano, M., Kohlhase, M.: The Open Math Standard, Version 2.0. Technical report, The Open Math Society (2004), http://www.openmath.org/standard/om20

  7. CoFI, The Common Framework Initiative. In: CASL Reference Manual. LNCS, vol. 2960. Springer, Heidelberg (2004)

    Google Scholar 

  8. Curry, H., Feys, R.: Combinatory Logic. North-Holland, Amsterdam (1958)

    MATH  Google Scholar 

  9. Dumbrava, S., Horozal, F., Sojakova, K.: A Case Study on Formalizing Algebra in a Module System. In: Rabe, F., Schürmann, C. (eds.) Workshop on Modules and Libraries for Proof Assistants. ACM International Conference Proceeding Series, vol. 429, pp. 11–18 (2009)

    Google Scholar 

  10. Farmer, W.: An Infrastructure for Intertheory Reasoning. In: McAllester, D. (ed.) Conference on Automated Deduction, pp. 115–131. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  11. Farmer, W., Guttman, J., Thayer, F.: Little Theories. In: Kapur, D. (ed.) Conference on Automated Deduction, pp. 467–581 (1992)

    Google Scholar 

  12. Farmer, W.M.: Mathematical Knowledge Management. In: Schwartz, D.G. (ed.) Mathematical Knowledge Management, pp. 599–604. Idea Group Reference (2005)

    Google Scholar 

  13. Giceva, J., Lange, C., Rabe, F.: Integrating Web Services into Active Mathematical Documents. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds.) Calculemus 2009. LNCS, vol. 5625, pp. 279–293. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Goguen, J., Winkler, T., Meseguer, J., Futatsugi, K., Jouannaud, J.: Introducing OBJ. In: Goguen, J., Coleman, D., Gallimore, R. (eds.) Applications of Algebraic Specification using OBJ, Cambridge (1993)

    Google Scholar 

  15. Horozal, F., Rabe, F.: Representing Model Theory in a Type-Theoretical Logical Framework. In: Fourth Workshop on Logical and Semantic Frameworks, with Applications. Electronic Notes in Theoretical Computer Science, vol. 256, pp. 49–65 (2009)

    Google Scholar 

  16. Horozal, F., Rabe, F.: Representing Model Theory in a Type-Theoretical Logical Framework. Under review (2010), http://kwarc.info/frabe/Research/EArabe_folsound_10.pdf

  17. Howard, W.: The formulas-as-types notion of construction. In: To H.B. Curry: Essays on Combinatory Logic, Lambda-Calculus and Formalism, pp. 479–490. Academic Press, London (1980)

    Google Scholar 

  18. Kohlhase, M., Mossakowski, T., Rabe, F.: The LATIN Project (2009), https://trac.omdoc.org/LATIN/

  19. Kohlhase, M., Müller, C., Rabe, F.: Notations for Living Mathematical Documents. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds.) AISC 2008, Calculemus 2008, and MKM 2008. LNCS (LNAI), vol. 5144, pp. 504–519. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  20. Kohlhase, M., Rabe, F., Sacerdoti Coen, C.: A Foundational View on Integration Problems (2010) (Submitted to CALCULEMUS)

    Google Scholar 

  21. Mossakowski, T., Maeder, C., Lüttich, K.: The Heterogeneous Tool Set. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 519–522. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  22. Naumov, P., Stehr, M., Meseguer, J.: The HOL/NuPRL proof translator - a practical approach to formal interoperability. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, p. 329. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  23. Nipkow, T., Paulson, L., Wenzel, M.: Isabelle/HOL — A Proof Assistant for Higher-Order Logic. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  24. Odersky, M., Spoon, L., Venners, B.: Programming in Scala. artima (2007)

    Google Scholar 

  25. Owre, S., Rushby, J., Shankar, N.: PVS: A Prototype Verification System. In: Kapur, D. (ed.) 11th International Conference on Automated Deduction (CADE), pp. 748–752. Springer, Heidelberg (1992)

    Google Scholar 

  26. Paulson, L.C.: Isabelle: A Generic Theorem Prover. LNCS, vol. 828. Springer, Heidelberg (1994)

    MATH  Google Scholar 

  27. Pfenning, F., Schürmann, C.: System description: Twelf - A meta-logical framework for deductive systems. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 202–206. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  28. Poswolsky, A., Schürmann, C.: System Description: Delphin - A Functional Programming Language for Deductive Systems. In: Abel, A., Urban, C. (eds.) International Workshop on Logical Frameworks and Metalanguages: Theory and Practice. ENTCS, pp. 135–141 (2008)

    Google Scholar 

  29. Rabe, F.: Representing Logics and Logic Translations. PhD thesis, Jacobs University Bremen (2008), http://kwarc.info/frabe/Research/phdthesis.pdf

  30. Rabe, F.: The MMT System (2008), https://trac.kwarc.info/MMT/

  31. Rabe, F., Schürmann, C.: A Practical Module System for LF. In: Cheney, J., Felty, A. (eds.) Proceedings of the Workshop on Logical Frameworks: Meta-Theory and Practice (LFMTP), pp. 40–48. ACM Press, New York (2009)

    Chapter  Google Scholar 

  32. Sannella, D., Wirsing, M.: A Kernel Language for Algebraic Specification and Implementation. In: Karpinski, M. (ed.) Fundamentals of Computation Theory, pp. 413–427. Springer, Heidelberg (1983)

    Google Scholar 

  33. Trybulec, A., Blair, H.: Computer Assisted Reasoning with MIZAR. In: Joshi, A. (ed.) Proceedings of the 9th International Joint Conference on Artificial Intelligence, pp. 26–28 (1985)

    Google Scholar 

  34. Zholudev, V., Kohlhase, M.: TNTBase: a Versioned Storage for XML. In: Proceedings of Balisage: The Markup Conference 2009, vol. 3, Mulberry Technologies, Inc. (2009)

    Google Scholar 

  35. Zholudev, V., Kohlhase, M., Rabe, F.: A (insert XML Format) Database for (insert cool application). In: Proceedings of XMLPrague, XMPPrague.cz (2010)

    Google Scholar 

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Kohlhase, M., Rabe, F., Zholudev, V. (2010). Towards MKM in the Large: Modular Representation and Scalable Software Architecture. In: Autexier, S., et al. Intelligent Computer Mathematics. CICM 2010. Lecture Notes in Computer Science(), vol 6167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14128-7_32

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  • DOI: https://doi.org/10.1007/978-3-642-14128-7_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14127-0

  • Online ISBN: 978-3-642-14128-7

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