Abstract
With more than 120.000 articles published annually in mathematical journals alone, mathematical search has often been touted as a killer application of computer-supported mathematics. But the artefacts of mathematics – e.g. mathematical documents, formulas, examples, algorithms, concrete data sets, or semantic web-style graph abstractions – that should be searched cover a variety of aspects. All are organized in complex ways and offer distinct challenges and techniques for search. Existing representation languages, the corresponding query languages and search systems usually concentrate on only one of these aspects. As a consequence, each system only partially covers the information retrieval needs of mathematical practitioners, and integrated solutions allowing multi-aspect queries are rare and basic.
We present an architecture for a generic multi-aspect search system and analyze the requirements on paradigmatic practical information retrieval needs.
The authors were supported by DFG grant RA-1872/3-1, KO 2428/13-1 OAF and EU grant Horizon 2020 ERI 676541 OpenDreamKit.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Apache Drill - Schema-free SQL Query Engine for Hadoop, NoSQL and Cloud Storage. https://drill.apache.org. Accessed 03 Feb 2020
Aizawa, A., et al.: NTCIR-12 MathIR task overview. In: Kando, N., Sakai, T., Sanderson, M. (ed.) Proceedings of the 12th NTCIR Conference on Evaluation of Information Access Technologies, Tokyo, Japan: NII, Tokyo, pp. 299–308 (2016). https://tinyurl.com/sofcxjs
Berčič, K., Kohlhase, M., Rabe, F.: Towards a Heterogeneous Query Language for Mathematical Knowledge - Extended Report (2020). http://kwarc.info/kohlhase/papers/tetrasearch.pdf. Accessed 27 Mar 2020
Carette, J., et al.: Big math and the one-brain barrier - the tetrapod model of mathematical knowledge. In: Mathematical Intelligencer (2020, in press). https://arxiv.org/abs/1904.10405
Carette, J., et al.: The space of mathematical software systems - a survey of paradigmatic systems. preprint; http://arxiv.org/abs/2002.04955 (2020)
Chong, E.I., et al.: An efficient SQL-based RDF querying scheme. In: Proceedings of the 31st VLDB Conference (2005)
Doan, A.H., Halevy, A., Ives, Z.: Principles of Data Integration. Elsevier, Amsterdam (2012)
Datasets on MathHub.info. https://data.mathhub.info. Accessed 24 Sept 2019
Eick, B., Besche, H.U., O’Brien, E.: SmallGrp - The GAP Small Groups Library. https://www.gap-system.org/Manuals/pkg/SmallGrp-1.3/doc/chap1.html. Accessed 13 Oct 2018
Wilson, S., Potočnik, P.: A Census of edge-transitive tetravalent graphs. https://jan.ucc.nau.edu/~swilson/C4FullSite/index.html. Accessed 23 Jan 2019
Elastic Search, 20 February 2014. http://www.elasticsearch.org/. Accessed 20 Feb 2014
Kohonen, J.: Lists of finite lattices (modular, semimodular, graded and geometric). https://www.shsu.edu/mem037/Lattices.html. Accessed 25 Jan 2019
Guidi, F., Sacerdoti Coen, C.: A survey on retrieval of mathematical knowledge. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds.) CICM 2015. LNCS (LNAI), vol. 9150, pp. 296–315. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20615-8_20
Hambasan, R., Kohlhase, M., Prodescu, C.: MathWeb-search at NTCIR-11. In: Kando, N., Joho, H., Kishida, K. (ed.) NTCIR 11 Conference, Tokyo, Japan: NII, Tokyo, pp. 114–119 (2014). https://tinyurl.com/wzj7mcg
Iancu, M., Kohlhase, M., Prodescu, C.: Representing, archiving, and searching the space of mathematical knowledge. In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 26–30. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44199-2_5
The L-functions and Modular Forms Database. http://www.lmfdb.org. Accessed 27 Aug 2016
McKay, B.: Description of graph6, sparse6 and digraph6 encodings. http://users.cecs.anu.edu.au/~bdm/data/formats.txt. Accessed 22 Mar 2019
Berčič, K.: Math Databases Table. https://mathdb.mathhub.info/. Accessed 15 Jan 2020
The On-Line Encyclopedia of Integer Sequences. http://oeis.org. Accessed 28 May 2017
Rabe, F.: A query language for formal mathematical libraries. In: Jeuring, J., et al. (eds.) CICM 2012. LNCS (LNAI), vol. 7362, pp. 143–158. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31374-5_10
Stamerjohanns, H., Kohlhase, M.: Transforming the arXiv to XML. In: Autexier, S., et al. (eds.) CICM 2008. LNCS (LNAI), vol. 5144, pp. 574–582. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85110-3_46
Sloane, N.J.A.: The on-line encyclopedia of integer sequences. In: Notices of the AMS, vol. 50, no. 8, p. 912 (2003)
Stathopoulos, Y., Teufel, S.: Mathematical information retrieval based on type embeddings and query expansion. In: Proceedings of COLING 2016, ACL, pp. 2344–2355 (2016). https://www.aclweb.org/anthology/C16-1221
Stathopoulos, Y., et al.: Variable typing: assigning meaning to variables in mathematical text. In: NAACL 2018 Proceedings, ACL, pp. 303–312 (2018). https://doi.org/10.18653/v1/N18-1028
T. Wiesing, M. Kohlhase, and F. Rabe. "Virtual Theories - A Uniform Interface to Mathematical Knowledge Bases". In: Mathematical Aspects of Computer and Information Sciences. Ed. by J. Blömer et al. Springer, 2017, pp. 243–257
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Berčič, K., Kohlhase, M., Rabe, F. (2020). Towards a Heterogeneous Query Language for Mathematical Knowledge. In: Benzmüller, C., Miller, B. (eds) Intelligent Computer Mathematics. CICM 2020. Lecture Notes in Computer Science(), vol 12236. Springer, Cham. https://doi.org/10.1007/978-3-030-53518-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-53518-6_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-53517-9
Online ISBN: 978-3-030-53518-6
eBook Packages: Computer ScienceComputer Science (R0)