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Über dieses Buch

This book explores reasoning with rough sets by developing a granularity-based framework. It begins with a brief description of the rough set theory, then examines selected relations between rough set theory and non-classical logics including modal logic. In addition, it develops a granularity-based framework for reasoning in which various types of reasoning can be formalized. The book will be of interest to all researchers whose work involves Artificial Intelligence, databases and/or logic.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
This gives an introductory presentation to motivate our work on rough set theory. Rough set theory is interesting theoretically as well as practically, and a quick survey on the subject, including overview, history and applications, is helpful to the readers.
Seiki Akama, Tetsuya Murai, Yasuo Kudo

Chapter 2. Rough Set Theory

Abstract
This chapter describes the foundations for rough set theory. We outline Pawlak’s motivating idea and give a technical exposition. Basics of Pawlak’s rough set theory and variable precision rough set model are presented with some related topics. We also present variants and related theories.
Seiki Akama, Tetsuya Murai, Yasuo Kudo

Chapter 3. Non-classical Logics

Abstract
This chapter surveys some non-classical logics. They are closely related to the foundations of rough set theory. We provide the basics of modal, many-valued, intuitionistic and paraconsistent logic.
Seiki Akama, Tetsuya Murai, Yasuo Kudo

Chapter 4. Logical Characterizations of Rough Sets

Abstract
This chapter introduces several logical characterizations of rough sets. We outline some approaches in the literature, including double Stone algebras, Nelson algebras and modal logics. We also discuss rough set logics, logics for reasoning about knowledge, and logics for knowledge representation.
Seiki Akama, Tetsuya Murai, Yasuo Kudo

Chapter 5. A Granularity-Based Framework of Reasoning

Abstract
This chapter presents a granularity-based framework of deduction, induction, and abduction using variable precision rough set models proposed by Ziarko and measure-based semantics for modal logic proposed by Murai et al. This is of special importance as a general approach to reasoning based on rough set theory. We also discuss non-monotonic reasoning, association rules in conditional logic, and background knowledge.
Seiki Akama, Tetsuya Murai, Yasuo Kudo

Chapter 6. Conclusions

Abstract
This chapter gives some conclusions with the summary of the book. We evaluate our work in connection with others. We also discuss several issues to be investigated.
Seiki Akama, Tetsuya Murai, Yasuo Kudo

Backmatter

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