Ebook: Incomplete Information: Structure, Inference, Complexity
- Genre: Mathematics // Logic
- Tags: Mathematical Logic and Formal Languages, Models and Principles, Information Storage and Retrieval, Artificial Intelligence (incl. Robotics), Algorithm Analysis and Problem Complexity
- Series: Monographs in Theoretical Computer Science An EATCS Series
- Year: 2002
- Publisher: Springer
- Language: English
- pdf
The construction of any broadly understood theory of information or infor mation processing system involves two major methodological processes: (1) abstraction and analysis, (2) reasoning and computing. This monograph is a realisation of these two processes in relation to the study of incompleteness of information. The paradigm we are working with is inspired by a rough-set approach to data analysis: the formalisms we develop enable the use of a non invasive data representation. This means that the only information which is and must be used in the process of analysis is the actual information that is to be analysed; we do not require any additional sources of information. An abstraction is formed in the process of conception, design, and develop ment of structures. Then analysis leads to a selection of a class of structures. In this book we delineate a class of informational structures that enable us to represent both numerical and non-numerical information and we analyse var ious manifestations of its incompleteness. We discuss several general types of incompleteness of information which are grounded in a rough-set-style view of imprecision and uncertainty. Manifestations of these types of incompleteness in information systems are investigated.
This monograph presents a systematic, exhaustive and up-to-date overview of formal methods and theories for data analysis and inference inspired by the concept of rough set. The book studies structures with incomplete information from the logical, algebraic and computational perspective. The formalisms developed are non-invasive in that only the actual information is needed in the process of analysis without external sources of information being required.
The book is intended for researchers, lecturers and graduate students who wish to get acquainted with the rough set style approach to information systems with incomplete information.
This monograph presents a systematic, exhaustive and up-to-date overview of formal methods and theories for data analysis and inference inspired by the concept of rough set. The book studies structures with incomplete information from the logical, algebraic and computational perspective. The formalisms developed are non-invasive in that only the actual information is needed in the process of analysis without external sources of information being required.
The book is intended for researchers, lecturers and graduate students who wish to get acquainted with the rough set style approach to information systems with incomplete information.
Content:
Front Matter....Pages I-XVIII
Mathematical Prerequisites....Pages 1-12
Front Matter....Pages 13-13
Structures of Information....Pages 15-36
Information Relations Derived from Information Systems....Pages 37-69
Information Operators Derived from Information Systems....Pages 71-90
Front Matter....Pages 91-91
Towards Information Logics....Pages 93-116
Techniques for Information Logics....Pages 117-136
Front Matter....Pages 137-137
Reasoning About Similarity....Pages 139-170
Reasoning About Indiscernibility....Pages 171-192
Reasoning About Knowledge....Pages 193-216
Front Matter....Pages 217-217
Information Logics Versus Standard Modal Logics....Pages 219-241
Decidability of Information Logics....Pages 243-266
Complexity of Information Logics....Pages 267-293
Front Matter....Pages 295-295
Informational Representability....Pages 297-320
Informational Interpretation of Standard Algebraic Structures....Pages 321-354
Information Algebras....Pages 355-377
Back Matter....Pages 379-408
This monograph presents a systematic, exhaustive and up-to-date overview of formal methods and theories for data analysis and inference inspired by the concept of rough set. The book studies structures with incomplete information from the logical, algebraic and computational perspective. The formalisms developed are non-invasive in that only the actual information is needed in the process of analysis without external sources of information being required.
The book is intended for researchers, lecturers and graduate students who wish to get acquainted with the rough set style approach to information systems with incomplete information.
Content:
Front Matter....Pages I-XVIII
Mathematical Prerequisites....Pages 1-12
Front Matter....Pages 13-13
Structures of Information....Pages 15-36
Information Relations Derived from Information Systems....Pages 37-69
Information Operators Derived from Information Systems....Pages 71-90
Front Matter....Pages 91-91
Towards Information Logics....Pages 93-116
Techniques for Information Logics....Pages 117-136
Front Matter....Pages 137-137
Reasoning About Similarity....Pages 139-170
Reasoning About Indiscernibility....Pages 171-192
Reasoning About Knowledge....Pages 193-216
Front Matter....Pages 217-217
Information Logics Versus Standard Modal Logics....Pages 219-241
Decidability of Information Logics....Pages 243-266
Complexity of Information Logics....Pages 267-293
Front Matter....Pages 295-295
Informational Representability....Pages 297-320
Informational Interpretation of Standard Algebraic Structures....Pages 321-354
Information Algebras....Pages 355-377
Back Matter....Pages 379-408
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