Incomplete Information: Structure, Inference, Complexity

1. Representability and Duality

   1. Information Algebras

      • Stéphane P. Demri, Ewa S. Orłowska

      Pages 355-377

2. Back Matter

   Pages 379-408

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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.

• complexity
• data analysis
• deduction
• incomplete information
• information system
• knowledge
• rough set
• algorithm analysis and problem complexity

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)

• Laboratoire Spécification et Vérification, CNRS UMR 8643, ENS de Cachan, Cachan Cedex, France

  Stéphane P. Demri

• Laboratoire Leibniz, Grenoble, France

  Stéphane P. Demri

• National Institute of Telecommunications, Warszawa, Poland

  Ewa S. Orłowska

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