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Mereological Theories of Concepts in Granular Computing

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Transactions on Computational Science II

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 5150))

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Abstract

This article is conceived as a homage to mathematicians and computer theorists working on basic concepts concerning knowledge and their usage in application contexts. Due to their work, we now have in our possession very impressive tools for analysis of uncertainty like rough set theory and fuzzy set theory along with hybrid ramifications between the two and with other areas of research in the realm of cognitive technologies in particular a very promising area of cognitive informatics.

In this work, we strive at presenting basic issues in granular theory of knowledge emphasizing formal aspects of our approach. This approach can be seen as a continuation of the line of analysis initiated by Gottlob Frege with his idea of exact and inexact concepts through analysis of the idea of knowledge by Popper, Lesniewski, Łukasiewicz and others, to the implementation of the Fregean idea in the theory of knowledge known as rough set theory initiated by Pawlak and pursued by many followers.

The basic tool in our analysis of the idea of a concept and a fortiori of knowledge is mereological theory of concepts (Lesniewski): we try to convince the reader that ideas of that theory suit well needs of analysis of knowledge and granulation of it.

This work arises from some previous attempts at developing this ideas in a wider context of ontological discussion; the author is indebted to the colloquia series SEFIR at Lateran University in Rome, where he was able to present the basic ideas in a lecture in January 2005; for this opportunity he is grateful to Professors Giandomenico Boffi and Alberto Pettorossi.

The author wishes to dedicate this work to the memory of Professors Helena Rasiowa and Zdzisław Pawlak who influenced very much his research interests in this area.

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Authors and Affiliations

  1. Polish-Japanese Institute of Information Technology Warsaw, Poland Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

    Lech Polkowski

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  1. Lech Polkowski
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Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W., Calgary, T2N 1N4, AB, Canada

    Marina L. Gavrilova

  2. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  3. Schulich School of Engineering, Department of Electrical and Computer Engineering, University of Calgary, 2500 University Drive, T2N 1N4, NW Calgary, AB, Canada

    Yingxu Wang

  4. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Yiyu Yao

  5. School of Information Science & Technology, Southwest Jiaotong University, 610031, Chengdu, China

    Guoyin Wang

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Polkowski, L. (2008). Mereological Theories of Concepts in Granular Computing. In: Gavrilova, M.L., Tan, C.J.K., Wang, Y., Yao, Y., Wang, G. (eds) Transactions on Computational Science II. Lecture Notes in Computer Science, vol 5150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87563-5_3

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  • DOI: https://doi.org/10.1007/978-3-540-87563-5_3

  • Publisher Name: Springer, Berlin, Heidelberg

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  • Online ISBN: 978-3-540-87563-5

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