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Approaching the Standard of Knowledge Representation in the Web by Algebraic Means

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Abstract

Modern systems of open linked data, including Wikidata, are built on ontology representation standards such as RDF, RDFstar, RDFa, OWL, and query language standards such as SPARQL, GraphQL, etc. At the same time, the standards for the representation of axioms such as SWRL, RIF, and even OWL are little used, as calculations in ontologies presented on the Web based on axioms and rewriting rules are not widely used. In this regard, the article proposes to use the rich experience of the theory of algebraic calculations and algebraic representation of knowledge to create a convenient universal tool for constructing ontologies focused on computing answers to queries using axioms and rewriting rules to build answers to queries, and not just facts. The possibility of building a standard for the Algebraic Web Ontology Language (Algebraic OWL) is considered. Some elements of such standard is considered. The experience and methodologies of the approaches of the Common Algebraic Specification Language (CASL), the Mathematica system, and the Haskell and Prolog programming languages are used.

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Notes

  1. In this article, relationships and predicates are distinguished. So, type is a relation (a subset in the set of pairs of elements and classes). Expression type(e, A) specifies the element (e,A) in a relationship type. On the other hand, hasType—predicate. Expression hasType(e, A) takes a Boolean value.

REFERENCES

  1. RDF 1.1 Concepts and Abstract Syntax, W3C Recommendation 25 February 2014. https://www.w3.org/TR/ 2014/REC-rdf11-concepts-20140225/Overview.html. Cited July 30, 2022.

  2. RDF Schema 1.1, W3C Recommendation 25 February 2014. https://www.w3.org/TR/rdf-schema/. Cited July 30, 2022.

  3. OWL 2 Web Ontology Language, Structural Specification and Functional-Style Syntax (Second Edition), W3C Recommendation 11 December 2012. https:// www.w3.org/TR/owl-syntax/. Cited July 30, 2022.

  4. OWL 2 Web Ontology Language, New Features and Rationale (Second Edition), W3C Recommendation 11 December 2012. https://www.w3.org/TR/2012/REC-owl2-new-features-20121211/. Cited July 30, 2022.

  5. RDF-star and SPARQL-star, Final Community Group Report 17 December 2021. https://www.w3.org/ 2021/12/rdf-star.html. Cited July 30, 2022.

  6. www.wikidata.org/wiki/Wikidata:SPARQL_tutorial Cited July 30, 2022.

  7. Bidoit, M. and Mosses, P.D., CASL User Manual: Introduction to Using the Common Algebraic Specification Language, Lecture Notes in Computer Science, vol. 2900, Berlin: Springer, 2004.  https://doi.org/10.1007/b11968

    Book  MATH  Google Scholar 

  8. Mena, A., Izuchaem Haskell (Studying Haskell), Programmer’s Library, St. Petersburg: Piter, 2015.

  9. Durán, F., Eker, S., Escobar, S., Martí-Oliet, N., Meseguer, J., Rubio, R., and Talcott, C.L., Programming and symbolic computation in Maude, J. Logical Algebraic Methods Programm., 2020, vol. 110, p. 100497. https://doi.org/10.1016/j.jlamp.2019.100497

    Article  MathSciNet  MATH  Google Scholar 

  10. Clavel, M., Duran, F., Eker, S., Escobar, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Rubio, R., and Talcott, C., Maude Manual (Version 3.2.1), 2022. http://maude. cs.illinois.edu/w/images/6/65/Maude-3.2.1-manual. pdf. Cited July 30, 2022.

  11. Beniaminov, E.M. and Lapshin, V.A., Levels of presenting ontologies, languages, mathematical models, and ontology web-server project in Web 2.0, Autom. Doc. Math. Linguist., 2012, vol. 46, no. 2, pp. 59–67.  https://doi.org/10.3103/S0005105512020021

    Article  Google Scholar 

  12. Beniaminov, E.M., Working in the system of collective ontology library formation EZOP (user’s manual), Moscow: Russian State University for the Humanities, 2015. http://beniaminov.rsuh.ru/User_guideEzop.pdf. Cited July 30, 2022.

  13. SWRL: A Semantic Web Rule Language, Combining OWL and RuleML. W3C Member Submission 21 May 2004. https://www.w3.org/Submission/SWRL/. Cited July 30, 2022.

  14. RIF Overview (Second Edition). W3C Working Group Note 5 February 2013. https://www.w3.org/TR/rif-overview/. Cited July 30, 2022.

  15. Church, A. and Rosser, J.B., Some properties of conversion, Trans. Am. Math. Soc., 1936, vol. 39, no. 3, pp. 472–482.  https://doi.org/10.2307/1989762

    Article  MathSciNet  MATH  Google Scholar 

  16. Ontology Engineering with Ontology Design Patterns: Foundations and Applications (Studies on the Semantic Web), Hitzler, P., Gangemi, A., Janowicz, K., Krisnadhi, A., and Presutti, V., Eds., IOS Press, 2016, vol. 25.

    Google Scholar 

  17. Ontology design pattern. http://ontologydesignpatterns.org/wiki/. Cited July 30, 2022.

  18. Shimizu, C., Hammar, K., and Hitzler, P., Modular ontology modeling, Semantic Web, 2022.  https://doi.org/10.3233/SW-222886

  19. Modular Knowledge 2022, 1st Workshop on Modular Knowledge, ESWC 2022, Hersonissos, Greece, 2022. https://mk2022.fbk.eu/home. Cited July 30, 2022.

  20. Goguen, J., (home page), https://cseweb.ucsd.edu/ ~goguen/. Cited July 30, 2022.

  21. Goguen, J., Information integration, databases and ontologies. https://cseweb.ucsd.edu/~goguen/projs/data. html. Cited July 30, 2022.

  22. CoFI: The Common Framework Initiative for algebraic specification and development of software. https:// homepages.inf.ed.ac.uk/dts/cofi/. Cited July 30, 2022.

  23. Mossakowski, T., Codescu, M., Neuhaus, F., and Kutz, O., The distributed ontology, modelling and specification language—DOL, The Road to Universal Logic—Festschrift for 50th Birthday of Jean-Yves Beziau, vol. 2, Koslow, A. and Buchsbaum, A., Eds., Studies in Universal Logic, Birkhäuser, 2015.

  24. Object Management Group. http://www.omg.org/ spec/DOL. Cited July 30, 2022.

  25. Stephen Wolfram. https://www.stephenwolfram.com/. Cited July 30, 2022.

  26. Wolfram. https://www.wolfram.com/. Cited July 30, 2022.

  27. Wolfram Mathematica. https://www.wolfram.com/ mathematica/. Cited July 30, 2022.

  28. WolframAlpha. https://www.wolframalpha.com/. Cited July 30, 2022.

  29. Wikidata. https://www.wikidata.org/wiki/Wikidata: Main_Page. Cited July 30, 2022.

  30. Hernandez, D., Hogan, A., Riveros, C., Rojas, C., and Zerega, E., Querying Wikidata: Comparing SPARQL, relational and graph databases, The Semantic Web—ISWC 2016, Groth, P., Simperl, E., Gray, A., Sabou, M., Krötzsch, M., Lecue, F., Flöck, F., and Gil, Yo., Eds., Lecture Notes in Computer Science, vol. 9982, Cham: Springer, pp. 88–103.  https://doi.org/10.1007/978-3-319-46547-0_10

  31. Project: Abstract Wikipedia. https://meta.wikimedia.org/ wiki/Special:MyLanguage/Abstract_Wikipedia. Cited July 30, 2022.

  32. Vrandečić, D., Building a multilingual Wikipedia, Commun. ACM, 2021, vol. 64, no. 4, pp. 38–41. https://doi.org/10.1145/3425778

    Article  Google Scholar 

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  1. Russian State University for the Humanities, Moscow, Russia

    E. M. Beniaminov

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Beniaminov, E.M. Approaching the Standard of Knowledge Representation in the Web by Algebraic Means. Autom. Doc. Math. Linguist. 56, 265–273 (2022). https://doi.org/10.3103/S0005105522050065

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