A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns (Trends in Logic Book 27)

'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. "'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."--BOOK JACKET 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 Piero Pagliani, Mihir Chakraborty. Includes Bibliographical References (p. 631-680) And Index.