A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns

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'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 includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost.

Such an approach endows the present treatise with a unique character. Due to this uniqueness in the treatment of the subject, the book will be useful to researchers, graduate and pre-graduate students from various disciplines, such as computer science, mathematics and philosophy. It features an impressive number of examples supported by about 40 tables and 230 figures. The comprehensive index of concepts turns the book into a sort of encyclopaedia for researchers from a number of fields.

'A Geometry of Approximation' links many areas of academic pursuit without losing track of its focal point, Rough Sets.

Author(s): Piero Pagliani, Mihir Chakraborty
Series: Trends in Logic 27
Publisher: Springer
Year: 2008

Language: English
Pages: 771
Tags: Logic; Order, Lattices, Ordered Algebraic Structures; Data Mining and Knowledge Discovery; Mathematical Logic and Foundations; Discrete Mathematics in Computer Science; Epistemology

Front Matter....Pages i-lxxxii
Observations, Noumena and Phenomena....Pages 3-42
Concrete and Formal Information Constructions....Pages 43-71
Pre-Topological and Topological Approximation Operators....Pages 73-105
Frames (Part I)....Pages 107-166
Logic and Rough Sets: An Overview....Pages 169-191
Basic Logico-Algebraic Structures....Pages 193-210
Local Validity, Grothendieck Topologies and Rough Sets....Pages 211-236
Approximation and Algebraic Logic....Pages 237-254
A Logico-Philosophic Excursus....Pages 255-279
Frames (Part II)....Pages 281-359
Modality and Knowledge....Pages 363-387
Modalities and Relations....Pages 389-469
Modalities, Topologies and Algebras....Pages 471-477
The Propositional Modal Logic of Rough Sets....Pages 479-503
Frames (Part III)....Pages 505-613
Mathematical Toolkits....Pages 615-629
Back Matter....Pages 631-704