A Geometry of Approximation Rough Set Theory: Logic, Algebra and Top
'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that inclu
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Piero Pagliani Mihir Chakraborty
Tre n d s i n Lo g i c 2 7
A Geometry of Approximation Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns
A B3
A Geometry of Approximation
TRENDS IN LOGIC Studia Logica Library VOLUME 27 Managing Editor Ryszard Wójcicki, Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland Editors Vincent F. Hendricks, Department of Philosophy and Science Studies, Roskilde University, Denmark Daniele Mundici, Department of Mathematics “Ulisse Dini”, University of Florence, Italy Ewa Orłowska, National Institute of Telecommunications, Warsaw, Poland Krister Segerberg, Department of Philosophy, Uppsala University, Sweden Heinrich Wansing, Institute of Philosophy, Dresden University of Technology, Germany
SCOPE OF THE SERIES Trends in Logic is a bookseries covering essentially the same area as the journal Studia Logica – that is, contemporary formal logic and its applications and relations to other disciplines. These include artificial intelligence, informatics, cognitive science, philosophy of science, and the philosophy of language. However, this list is not exhaustive, moreover, the range of applications, comparisons and sources of inspiration is open and evolves over time.
Volume Editor Ewa Orłowska
For other titles published in this series, go to www.springer.com/series/6645
Piero Pagliani • Mihir Chakraborty
A Geometry of Approximation Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns
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Piero Pagliani Research Group on Knowledge and Communication Models Rome, Italy [email protected]
ISBN 978-1-4020-8621-2
Mihir Chakraborty University of Calcutta West Bengal, India [email protected]
e-ISBN 978-1-4020-8622-9
Library of Congress Control Number: 2008928689 © 2008 Springer Science+Business Media B.V. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper. 9 8 7 6 5 4 3 2 1 springer.com
Preface Rough Set Theory was proposed by Zdzislaw Pawlak in 1980. Since inception it has generated an increasing interest in different research fields, namely computer science, mathematics and logic. An impressive amount of research-papers have been devoted to this topic. A number of good books have appeared in the recent years, in which Rough Set Theory has been investigated under one or more privileged points of view. We mention Demri & Orlowska [2002] and Polkowski [2002] as two works close to our scientific purpose. Recently in the Transactions on Rough Sets a monograph by J. J¨arvinen has been published, which has close connections with Part II of this book (J¨ arvinen [2007]). An almost complete bibliography on the subject may be found in the web
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