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. Throughout, Demri studies structures with incomplete information from the logical, algebraic and computational perspective. The formalisms developed are non-invasive in that only the actual information that is needed in the process of analysis without external sources of information being required. The book is self-contained to a large degree, providing detailed derivations of most of the technical results, and is intended for researchers, lecturers and graduate students.

Inhalt

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.