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Approximate Reasoning by Parts

An Introduction to Rough Mereology

  • Conference proceedings
  • © 2011

Overview

Authors:
  1. Lech Polkowski

    1. Polish-Japanese Institute of Information Technology, University of Warmia and Mazury, Warszawa, Poland

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  • An Introduction to Rough Mereology
  • Recent research on Approximate Reasoning
  • Written by a leading expert in the field

Part of the book series: Intelligent Systems Reference Library (ISRL, volume 20)

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Table of contents (9 papers)

  1. Front Matter

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  2. On Concepts. Aristotelian and Set—Theoretic Approaches

    • Lech Polkowski
    Pages 1-43

  3. Topology of Concepts

    • Lech Polkowski
    Pages 45-78

  4. Reasoning Patterns of Deductive Reasoning

    • Lech Polkowski
    Pages 79-143

  5. Reductive Reasoning Rough and Fuzzy Sets as Frameworks for Reductive Reasoning

    • Lech Polkowski
    Pages 145-190

  6. Mereology

    • Lech Polkowski
    Pages 191-228

  7. Rough Mereology

    • Lech Polkowski
    Pages 229-257

  8. Reasoning with Rough Inclusions: Granular Computing, Granular Logics, Perception Calculus, Cognitive and MAS Reasoning

    • Lech Polkowski
    Pages 259-295

  9. Reasoning by Rough Mereology in Problems of Behavioral Robotics

    • Lech Polkowski
    Pages 297-318

  10. Rough Mereological Calculus of Granules in Decision and Classification Problems

    • Lech Polkowski
    Pages 319-334

  11. Back Matter

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Keywords

About this book

The monograph offers a view on Rough Mereology, a tool for reasoning under uncertainty, which goes back to Mereology, formulated in terms of  parts by Lesniewski, and borrows from Fuzzy Set Theory and Rough Set Theory ideas of the containment to a degree. The result is a theory based on the notion of a part to a degree.

 

One can invoke here a formula Rough: Rough Mereology : Mereology = Fuzzy Set Theory : Set Theory. As with Mereology, Rough Mereology finds important applications in problems of Spatial Reasoning, illustrated in this monograph with examples from Behavioral Robotics. Due to its involvement with concepts, Rough Mereology offers new approaches to Granular Computing, Classifier and Decision Synthesis, Logics for Information Systems, and are--formulation of  well--known ideas of Neural Networks and Many Agent Systems. All these approaches are discussed in this monograph.

 

To make the exposition self--contained,  underlying notions of Set Theory, Topology, and Deductive and Reductive Reasoning with emphasis on Rough and Fuzzy Set Theories along with a thorough exposition of Mereology both in Lesniewski and Whitehead--Leonard--Goodman--Clarke versions are discussed at length.

 

It is hoped that the monograph offers researchers in various areas of Artificial Intelligence a  new tool to deal with analysis of relations among concepts.

Authors and Affiliations

  • Polish-Japanese Institute of Information Technology, University of Warmia and Mazury, Warszawa, Poland

    Lech Polkowski

Bibliographic Information

  • Book Title: Approximate Reasoning by Parts

  • Book Subtitle: An Introduction to Rough Mereology

  • Authors: Lech Polkowski

  • Series Title: Intelligent Systems Reference Library

  • DOI: https://doi.org/10.1007/978-3-642-22279-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer Berlin Heidelberg 2011

  • Hardcover ISBN: 978-3-642-22278-8Published: 16 July 2011

  • Softcover ISBN: 978-3-642-26985-1Published: 27 November 2013

  • eBook ISBN: 978-3-642-22279-5Published: 27 August 2011

  • Series ISSN: 1868-4394

  • Series E-ISSN: 1868-4408

  • Edition Number: 1

  • Number of Pages: XIV, 346

  • Topics: Computational Intelligence, Artificial Intelligence

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