## A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns'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. |

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### Contents

3 | |

Concrete and Formal Information Constructions | 43 |

PreTopological and Topological Approximation Operators | 73 |

Frames Part I | 107 |

Logic and Rough Sets An Overview | 169 |

Basic LogicoAlgebraic Structures | 193 |

Local Validity Grothendieck Topologies and Rough Sets | 211 |

Approximation and Algebraic Logic | 237 |

Modality and Knowledge | 363 |

Modalities and Relations | 389 |

Modalities Topologies and Algebras | 471 |

The Propositional Modal Logic of Rough Sets | 479 |

Frames Part III | 505 |

Mathematical Toolkits | 615 |

631 | |

681 | |

### Other editions - View all

A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology ... Piero Pagliani,Mihir Chakraborty No preview available - 2010 |

A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology ... Piero Pagliani,Mihir Chakraborty No preview available - 2008 |