Incomplete Information: Structure, Inference, Complexity

by Stephane P. Demri, Ewa Orlowska

Overview

The construction of any broadly understood theory of information or information 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 development 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.

Product Details

ISBN-13:	9783642075407
Publisher:	Springer Berlin Heidelberg
Publication date:	12/08/2010
Series:	Monographs in Theoretical Computer Science. An EATCS Series
Edition description:	Softcover reprint of hardcover 1st ed. 2002
Pages:	408
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1. Mathematical Prerequisites.- I. Structures with Incomplete Information.- 2. Structures of Information.- 3. Information Relations Derived from Information Systems.- 4. Information Operators Derived from Information Systems.- II. Introduction to Information Logics.- 5. Towards Information Logics.- 6. Techniques for Information Logics.- III. Proof Systems for Information Logics.- 7. Reasoning About Similarity.- 8. Reasoning About Indiscernibility.- 9. Reasoning About Knowledge.- IV. Computational Aspects of Information Logics.- 10. Information Logics Versus Standard Modal Logics.- 11. Decidability of Information Logics.- 12. Complexity of Information Logics.- V. Representability and Duality.- 13. Informational Representability.- 14. Informational Interpretation of Standard Algebraic Structures.- 15. Information Algebras.- References.

Editorial Reviews

From the reviews of the first edition:

"This monograph presents a systematic, exhaustive and up to date overview of formal methods and theories related to data analysis and inference using the concept of rough sets. … In a nutshell, it is an interesting book for researchers and scientists in the area of information structure." (Prabhat Kumar Mahanti, Zentralblatt MATH, Vol. 1016, 2003)

"The present monograph gives a systematic presentation of the theory related to the … relation-based knowledge representation and the underlying logics and algebras. … The structure of this book is clear. … The book is written to be self-contained … . The references section of this book is excellent … . The book can be recommended to researchers and graduate students interested in rough-set-style reasoning and knowledge representation. Also for lecturers this provides a great source … ." (Jouni Järvinen, Studia Logica, Vol. 89 (3), 2006)

From the Publisher