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Partial First-order Logic with Approximative Functors Based on Properties

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Rough Sets and Knowledge Technology (RSKT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7414))

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Abstract

In the present paper a logically exact way is presented in order to define approximative functors on object level in the partial first-order logic relying on approximation spaces. By the help of defined approximative functors one can determine what kind of approximations has to be taken into consideration in the evaluating process of a formula. The representations of concepts (properties) of our available knowledge can be used to approximate not only any concept (property) but any relation. In the last section lower and upper characteristic matrixes are introduced. These can be very useful in different applications.

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References

  1. Pawlak, Z.: Rough sets. International Journal of Information and Computer Science 11(5), 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  2. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  3. Yao, Y.Y.: On Generalizing Rough Set Theory. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 44–51. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Yao, Y.Y.: Information granulation and rough set approximation. International Journal of Intelligent Systems 16(1), 87–104 (2001)

    Article  MATH  Google Scholar 

  5. Skowron, A., Stepaniuk, J.: Information granules: Towards foundations of granular computing. International Journal of Intelligent Systems 16(1), 57–85 (2001)

    Article  MATH  Google Scholar 

  6. Skowron, A., Świniarski, R., Synak, P.: Approximation Spaces and Information Granulation. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 175–189. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Zadeh, L.A.: Granular Computing and Rough Set Theory. In: Kryszkiewicz, M., Peters, J.F., Rybiński, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 1–4. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Lin, T.Y.: Approximation Theories: Granular Computing vs Rough Sets. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 520–529. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: An approach to vagueness. In: Rivero, L.C., Doorn, J., Ferraggine, V. (eds.) Encyclopedia of Database Technologies and Applications, pp. 575–580. Idea Group Inc., Hershey (2005)

    Chapter  Google Scholar 

  10. Zhu, P.: Covering rough sets based on neighborhoods: An approach without using neighborhoods. International Journal of Approximate Reasoning 52(3), 461–472 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Düntsch, I., Gediga, G.: Approximation Operators in Qualitative Data Analysis. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds.) Theory and Applications of Relational Structures as Knowledge Instruments. LNCS, vol. 2929, pp. 214–230. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177(1), 3–27 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Polkowski, L.: Rough Sets: Mathematical Foundations. AISC. Physica-Verlag, Heidelberg (2002)

    MATH  Google Scholar 

  14. Csajbók, Z., Mihálydeák, T.: Partial approximative set theory: A generalization of the rough set theory. International Journal of Computer Information System and Industrial Management Applications 4, 437–444 (2012)

    Google Scholar 

  15. Csajbók, Z.: Partial approximative set theory: A generalization of the rough set theory. In: Martin, T., Muda, A.K., Abraham, A., Prade, H., Laurent, A., Laurent, D., Sans, V. (eds.) Proceedings of the International Conference of Soft Computing and Pattern Recognition (SoCPaR 2010), Pontoise/Paris, France, December 7-10, pp. 51–56. IEEE (2010)

    Google Scholar 

  16. Mihálydeák, T., Csajbók, Z.: Tool–based partial first–order logic with approximative functors (forthcoming)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Faculty of Informatics, University of Debrecen, Kassai út 26, H-4028, Debrecen, Hungary

    Tamás Mihálydeák

Authors
  1. Tamás Mihálydeák
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Editor information

Editors and Affiliations

  1. School of Information Science and Technology, Southwest Jiaotong University, 610031, Chengdu, P.R. China

    Tianrui Li

  2. Institute of Mathematics, The University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Hung Son Nguyen

  3. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, 400065, Chongqing, China

    Guoyin Wang

  4. Department of Electrical Engineering and Computer Science, University of Kansas, 66045 - 7621, Lawrence, KS, USA

    Jerzy Grzymala-Busse

  5. Department of Computing and Software, McMaster University, L8S 4K1, Hamilton, Ontario, Canada

    Ryszard Janicki

  6. Faculty of Computers and Information, Cairo University, Cairo, Egypt

    Aboul Ella Hassanien

  7. Software School, Dalian University of Technology, Dalian, China

    Hong Yu

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© 2012 Springer-Verlag Berlin Heidelberg

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Mihálydeák, T. (2012). Partial First-order Logic with Approximative Functors Based on Properties. In: Li, T., et al. Rough Sets and Knowledge Technology. RSKT 2012. Lecture Notes in Computer Science(), vol 7414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31900-6_63

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  • DOI: https://doi.org/10.1007/978-3-642-31900-6_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31899-3

  • Online ISBN: 978-3-642-31900-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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