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Computer Certification of Generalized Rough Sets Based on Relations

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Rough Sets (IJCRS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10313))

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Abstract

The aim of this paper is to describe the issues concerning the full formal translation of a single but important paper devoted to generalized rough sets based on binary relations, authored by William Zhu. Although we started the encoding (using automated proof-assistant Mizar) quite some time ago, we met unexpected difficulties during this task forcing us to refactor the created formal framework. Now, when the work is completed, we can shed some light for lessons learned during the process of encoding of the collection of quite elementary constructions written by means of relatively simple syntactical apparatus.

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Notes

  1. 1.

    http://vsl2014.at/livestream/index.html#Recordings.

  2. 2.

    One exception is described in Sect. 4.

  3. 3.

    The addresses are http://mizar.org/version/current/html/roughs_2.html and http://mizar.org/version/current/html/roughs_3.html.

  4. 4.

    The set of problems extracted from the Mizar Mathematical Library was used for years at yearly CADE (Conferences on Automated Deduction) conferences.

References

  1. Bancerek, G., Byliński, C., Grabowski, A., Korniłowicz, A., Matuszewski, R., Naumowicz, A., Pa̧k, K., Urban, J.: Mizar: state-of-the-art and beyond. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds.) CICM 2015. LNCS, vol. 9150, pp. 261–279. Springer, Cham (2015). doi:10.1007/978-3-319-20615-8_17

    Chapter  Google Scholar 

  2. Blanchette, J.C., Haslbeck, M., Matichuk, D., Nipkow, T.: Mining the archive of formal proofs. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds.) CICM 2015. LNCS, vol. 9150, pp. 3–17. Springer, Cham (2015). doi:10.1007/978-3-319-20615-8_1

    Chapter  Google Scholar 

  3. Bonikowski, Z.: Unit operations in approximation spaces. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.) RSCTC 2010. LNCS, vol. 6086, pp. 337–346. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13529-3_36

    Chapter  Google Scholar 

  4. Bryniarski, E.: Formal conception of rough sets. Fundam. Informaticae 27(2/3), 109–136 (1996). doi:10.3233/FI-1996-272302

    Article  MathSciNet  MATH  Google Scholar 

  5. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen Syst 17(2–3), 191–209 (1990). doi:10.1080/03081079008935107

    Article  MATH  Google Scholar 

  6. Grabowski, A.: Mechanizing complemented lattices within Mizar type system. J. Autom. Reason. 55(3), 211–221 (2015). doi:10.1007/s10817-015-9333-5

    Article  MathSciNet  MATH  Google Scholar 

  7. Grabowski, A.: Binary relations-based rough sets - an automated approach. Formaliz. Math. 24(2), 143–155 (2016). doi:10.1515/forma-2016-0011

    Article  MATH  Google Scholar 

  8. Grabowski, A.: On the computer certification of fuzzy numbers, In: Ganzha, M., Maciaszek, L., Paprzycki, M. (eds.) Proceedings of Federated Conference on Computer Science and Information Systems, FedCSIS 2013, pp. 51–54 (2013)

    Google Scholar 

  9. Grabowski, A.: Automated discovery of properties of rough sets. Fundam. Informaticae 128(1–2), 65–79 (2013). doi:10.3233/FI-2013-933

    Article  MathSciNet  MATH  Google Scholar 

  10. Grabowski, A.: Efficient rough set theory merging. Fundam. Informaticae 135(4), 371–385 (2014). doi:10.3233/FI-2014-1129

    Article  MathSciNet  MATH  Google Scholar 

  11. Grabowski, A.: Lattice theory for rough sets - a case study with Mizar. Fundam. Informaticae 147(2–3), 223–240 (2016). doi:10.3233/FI-2016-1406

    Article  MathSciNet  MATH  Google Scholar 

  12. Grabowski, A.: On the computer-assisted reasoning about rough sets. In: Dunin-Kȩplicz, B., Jankowski, A., Szczuka, M. (eds.) Monitoring, Security and Rescue Techniques in Multiagent Systems. Advances in Soft Computing, vol. 28, pp. 215–226. Springer, Heidelberg (2005). doi:10.1007/3-540-32370-8_15

    Chapter  Google Scholar 

  13. Grabowski, A., Jastrzȩbska, M.: Rough set theory from a math-assistant perspective. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS, vol. 4585, pp. 152–161. Springer, Heidelberg (2007). doi:10.1007/978-3-540-73451-2_17

    Chapter  Google Scholar 

  14. Järvinen, J.: Lattice theory for rough sets. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 400–498. Springer, Heidelberg (2007). doi:10.1007/978-3-540-71200-8_22

    Chapter  MATH  Google Scholar 

  15. Korniłowicz, A.: Flexary connectives in Mizar. Comput. Lang. Syst. Struct. 44(Part C), 238–250 (2015). doi:10.1016/j.cl.2015.07.002

    Article  MATH  Google Scholar 

  16. Naumowicz, A.: Automating boolean set operations in Mizar proof checking with the aid of an external SAT solver. J. Autom. Reason. 55(3), 285–294 (2015). doi:10.1007/s10817-015-9332-6

    Article  MathSciNet  MATH  Google Scholar 

  17. Pawlak, Z.: On conflicts. Int. J. Man-Mach. Stud. 21, 127–134 (1984). doi:10.1016/S0020-7373(84)80062-0

    Article  MATH  Google Scholar 

  18. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991). doi:10.1007/978-94-011-3534-4

    Book  MATH  Google Scholar 

  19. Pa̧k, K.: Improving legibility of formal proofs based on the close reference principle is NP-hard. J. Autom. Reason. 55(3), 295–306 (2015). doi:10.1007/s10817-015-9337-1

    Article  MathSciNet  MATH  Google Scholar 

  20. Rudnicki, P.: Obvious inferences. J. Autom. Reason. 3(4), 383–393 (1987). doi:10.1007/BF00247436

    Article  MathSciNet  MATH  Google Scholar 

  21. Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundam. Informaticae 27(2–3), 245–253 (1996). doi:10.3233/FI-1996-272311

    Article  MathSciNet  MATH  Google Scholar 

  22. Urban, J., Sutcliffe, G.: Automated reasoning and presentation support for formalizing mathematics in Mizar. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.) CICM 2010. LNCS, vol. 6167, pp. 132–146. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14128-7_12

    Chapter  MATH  Google Scholar 

  23. Wiedijk, F.: Formal proof - getting started. Not. AMS 55(11), 1408–1414 (2008)

    MathSciNet  MATH  Google Scholar 

  24. Yao, Y.Y.: Two views of the rough set theory in finite universes. Int. J. Approx. Reason. 15(4), 291–317 (1996). doi:10.1016/S0888-613X(96)00071-0

    Article  MATH  Google Scholar 

  25. Yao, Y., Yao, B.: Covering based rough set approximations. Inf. Sci. 200, 91–107 (2012). doi:10.1016/j.ins.2012.02.065

    Article  MathSciNet  MATH  Google Scholar 

  26. Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965). doi:10.1016/S0019-9958(65)90241-X

    Article  MATH  Google Scholar 

  27. Zhu, W.: Generalized rough sets based on relations. Inf. Sci. 177(22), 4997–5011 (2007). doi:10.1016/j.ins.2007.05.037

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhu, W.: Topological approaches to covering rough sets. Inf. Sci. 177(6), 1499–1508 (2007). doi:10.1016/j.ins.2006.06.009

    Article  MathSciNet  MATH  Google Scholar 

  29. Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 11, 39–59 (1993). doi:10.1016/0022-0000(93)90048-2

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Informatics, University of Białystok, Konstantego Ciołkowskiego 1M, 15-245, Białystok, Poland

    Adam Grabowski

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  1. Adam Grabowski
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Correspondence to Adam Grabowski .

Editor information

Editors and Affiliations

  1. Polish-Japanese Academy of Information Technology, Warsaw, Poland

    Lech Polkowski

  2. University of Regina, Regina, SK, Canada

    Yiyu Yao

  3. University of Warmia and Mazury, Olsztyn, Poland

    Piotr Artiemjew

  4. University of Milano-Bicocca, Milano, Italy

    Davide Ciucci

  5. Southwest Jiaotong University, Chengdu, China

    Dun Liu

  6. Warsaw University, Warszawa, Poland

    Dominik Ślęzak

  7. Silesian University, Sosnowiec, Poland

    Beata Zielosko

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Grabowski, A. (2017). Computer Certification of Generalized Rough Sets Based on Relations. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10313. Springer, Cham. https://doi.org/10.1007/978-3-319-60837-2_7

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  • DOI: https://doi.org/10.1007/978-3-319-60837-2_7

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  • Online ISBN: 978-3-319-60837-2

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