# A Geometry of ApproximationLogic and Rough Sets: An Overview

A Geometry of Approximation: Logic and Rough Sets: An Overview Chapter 5 Logic and Rough Sets: An Overview “Any speciﬁc object has a speciﬁc logic” K. Marx. Since the present Part has a certain complexity, it is worth introduc- ing, with some details, the intuitive motivations of the entire picture and their connections with the mathematical machinery which will be used. 5.1 Foreword Thus, let us sum up what we have discussed and discovered as far as now. In Rough Set Theory, the starting point is a collection of observa- tions which are stored in an Information System I and which induces an indiscernibility space U, E. We denote the family of all basic cate- gories by IN D(I). We have seen that from any Information System I one can compute the extension D on the universe U of a basic property D which we call a I-basic property, because it can be formulated using the linguistic material from I. I-basic properties make it possible to classify the objects from U into diﬀerent disjoint equivalence classes which are to be intended as For instance, if I is an Attribute Systems, a deterministic property is a conjunc- tion of sentences of the form “ai = vj ”, where ai ranges http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Geometry of ApproximationLogic and Rough Sets: An Overview

Part of the Trends in Logic Book Series (volume 27)
Editors: Pagliani, Piero; Chakraborty, Mihir
Springer Journals — Jan 1, 2008
23 pages

/lp/springer-journals/a-geometry-of-approximation-logic-and-rough-sets-an-overview-SbKAsGXr4B
Publisher
Springer Netherlands
ISBN
978-1-4020-8621-2
Pages
169 –191
DOI
10.1007/978-1-4020-8622-9_5
Publisher site
See Chapter on Publisher Site

### Abstract

Chapter 5 Logic and Rough Sets: An Overview “Any speciﬁc object has a speciﬁc logic” K. Marx. Since the present Part has a certain complexity, it is worth introduc- ing, with some details, the intuitive motivations of the entire picture and their connections with the mathematical machinery which will be used. 5.1 Foreword Thus, let us sum up what we have discussed and discovered as far as now. In Rough Set Theory, the starting point is a collection of observa- tions which are stored in an Information System I and which induces an indiscernibility space U, E. We denote the family of all basic cate- gories by IN D(I). We have seen that from any Information System I one can compute the extension D on the universe U of a basic property D which we call a I-basic property, because it can be formulated using the linguistic material from I. I-basic properties make it possible to classify the objects from U into diﬀerent disjoint equivalence classes which are to be intended as For instance, if I is an Attribute Systems, a deterministic property is a conjunc- tion of sentences of the form “ai = vj ”, where ai ranges

Published: Jan 1, 2008

Keywords: Boolean Algebra; Approximation Space; Strong Negation; Stone Algebra; Constructive System