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Philosophy - Logic & Philosophy of Language | A Geometry of Approximation - Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns

A Geometry of Approximation

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

Series: Trends in Logic, Vol. 27

Pagliani, Piero, Chakraborty, Mihir

2008, LXXXII, 704 p.

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  • Provides a full and detailed overview of all aspects of Rough Set Theory
  • The first book to place Rough Set Theory in a broad historical and applied setting
  • Provides the theoretical basis and strong examples of the value of Rough Sets for datamining and machine learning

'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.

Content Level » Research

Keywords » Algebraic logic - Approximation - Conceptual patterns - Data mining - Incomplete information - Rough Sets - Topology - logic - modal logic

Related subjects » Algebra - Database Management & Information Retrieval - Logic & Philosophy of Language - Mathematics - Philosophy - Theoretical Computer Science

Table of contents 

Perception and Concepts: A Phenomenological.- Observations, Noumena and Phenomena.- Concrete and Formal Information Constructions.- Pre-Topological and Topological Approximation Operators.- Frames (Part I).- The Logico-Algebraic Theory of Rough Sets.- Logic and Rough Sets: An Overview.- Basic Logico-Algebraic Structures.- Local Validity, Grothendieck Topologies and Rough Sets.- Approximation and Algebraic Logic.- A Logico-Philosophic Excursus.- Frames (Part II).- The Modal Logic of Rough Sets.- Modality and Knowledge.- Modalities and Relations.- Modalities, Topologies and Algebras.- The Propositional Modal Logic of Rough Sets.- Frames (Part III).- Mathematical Toolkits.

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