Knowledge Representation and Rough Sets

Acknowledgements The present work was done under the pleasant supervision of Professor Magnus Steinby to whom I owe my warmest thanks. The support and expert guidance he has given made it possible for me to accomplish this work. I am very grateful to Professor Ewa Orłowska for the opportunity to visit her institute and for the stimulating discussions. I thank the Preliminary Referees of my thesis, Professors Miroslav Novotn´y and Ivo Düntsch, for their many valuable comments and suggestions. My special thanks are also due to Professor Tero Harju for the careful reading of the manuscript and for his helpful remarks. I would like to thank everyone in the Department of Mathematical Sciences for the excellent and friendly working atmosphere. The financial support, the computer facilities and office space provided by the Turku Centre for Computer Science (TUCS) are gratefully acknowledged. Finally, I want to express my gratitude to my parents, friends and teachers for their support.

[1]  Zdzislaw Pawlak,et al.  On a problem concerning dependence spaces , 1992, Fundam. Informaticae.

[2]  G. Grätzer,et al.  Lattice Theory: First Concepts and Distributive Lattices , 1971 .

[3]  C. J. Everett.  Closure operators and Galois theory in lattices , 1944 .

[4]  Ewa Orlowska,et al.  Introduction: What You Always Wanted to Know about Rough Sets , 1998 .

[5]  Ewa Orlowska.  Information Algebras , 1995, AMAST.

[6]  G. Grätzer.  General Lattice Theory , 1978 .

[7]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[8]  J. A. Pomykala,et al.  On definability in the nondeterministic information system , 1988 .

[9]  R. Słowiński,et al.  Learning Decision Rules from Similarity Based Rough Approximations , 1998 .

[10]  Ramez Elmasri,et al.  Fundamentals of Database Systems, 5th Edition , 2006 .

[11]  Mathieu Koppen,et al.  How to build a knowledge space by querying an expert , 1990 .

[12]  W. Zakowski.  APPROXIMATIONS IN THE SPACE (U,π) , 1983 .

[13]  J. A. Pomykala.  SOME REMARKS ON APPROXIMATION , 1991 .

[14]  Miroslav Novotný,et al.  Applications of Dependence Spaces , 1998 .

[15]  Zahava Shmuely,et al.  The structure of Galois connections. , 1974 .

[16]  Miroslav Novotný,et al.  Dependence Spaces of Information Systems , 1998 .

[17]  Yiyu Yao,et al.  Rough Sets and Current Trends in Computing , 2001, Lecture Notes in Computer Science.

[18]  H. Priestley,et al.  Distributive Lattices , 2004 .

[19]  Miroslav Novotný,et al.  Notes on the algebraic approach to dependence in information systems , 1992, Fundam. Informaticae.

[20]  Magnus Steinby.  On pair algebras and state-information in automata , 1973 .

[21]  Ewa Orlowska,et al.  Representation of Nondeterministic Information , 1984, Theor. Comput. Sci..

[22]  Beata Konikowska,et al.  A Logic for Reasoning about Relative Similarity , 1997, Stud Logica.

[23]  J. A. Pomykala,et al.  The stone algebra of rough sets , 1988 .

[24]  I. Düntsch.  Rough Sets and Algebras of Relations , 1998 .

[25]  Beata Konikowska,et al.  A Logic for Reasoning about Similarity , 1998 .

[26]  Ewa Orłowska,et al.  Studying Incompleteness of Information: A Class of Information Logics , 1998 .

[27]  Alan Day,et al.  The Lattice Theory of Functional Dependencies and Normal Decompositions , 1992, Int. J. Algebra Comput..

[28]  Cecylia Rauszer.  Reducts in information systems , 1991, Fundam. Informaticae.

[29]  Stanley Burris,et al.  A course in universal algebra , 1981, Graduate texts in mathematics.

[30]  Z..  INFORMATION SYSTEMS THEORETICAL FOUNDATIONS , 2022 .

[31]  George Gratzer,et al.  Universal Algebra , 1979 .

[32]  Ivo Düntsch,et al.  On query procedures to build knowledge structures , 1996 .

[33]  T. Iwiński.  Algebraic approach to rough sets , 1987 .

[34]  Emil Popescu,et al.  On Galois Connexions , 1994 .

[35]  Zdzislaw Pawlak,et al.  Algebraic theory of independence in information systems , 1991, Fundam. Informaticae.

[37]  Petra Himmel.  Algebraic Methodology and Software Technology , 1999, Lecture Notes in Computer Science.

[38]  Jouni Järvinen,et al.  A Representation of Dependence Spaces and Some Basic Algorithms , 1997, Fundam. Informaticae.

[39]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[40]  Sadaaki Miyamoto,et al.  Rough Sets and Current Trends in Computing , 2012, Lecture Notes in Computer Science.

[41]  Miroslav Novotný,et al.  On Dependence in Wille's Contexts , 1993, Fundam. Informaticae.

[42]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[43]  Zdzisław Pawlak,et al.  On rough equalities , 1985 .

[44]  Ivo Düntsch,et al.  Algebraic Aspects of Attribute Dependencies in Information Systems , 1997, Fundam. Informaticae.

[45]  Andrzej Skowron,et al.  The Discernibility Matrices and Functions in Information Systems , 1992, Intelligent Decision Support.

[46]  Miroslav NOVOTNÝ.  Reducts versus Reducing Operators , 1994, Mathematical Aspects of Natural and Formal Languages.

[47]  Ramez Elmasri,et al.  Fundamentals of Database Systems , 1989 .

[48]  J. A. Pomykala,et al.  ON SIMILARITY BASED APPROXIMATION OF INFORMATION , 1994 .

[49]  Ivo Düntsch.  Rough Relation Algebras , 1994, Fundam. Informaticae.

[50]  Z. Pawlak,et al.  Independence of attributes , 1988 .

[51]  Desmond Fearnley-Sander,et al.  Universal Algebra , 1982 .

[52]  Zdzisław Pawlak,et al.  Dependency of attributes in information systems , 1985 .

[53]  Rudolf Wille,et al.  Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts , 2009, ICFCA.

[54]  Jouni Järvinen.  Preimage Relations and Their Matrices , 1998, Rough Sets and Current Trends in Computing.

[55]  S. L. Édel'man.  Closure operators on a lattice , 1980 .

[56]  A. Tarski,et al.  The Algebra of Topology , 1944 .

[57]  Takuya Kon-no,et al.  Transactions of the American Mathematical Society , 1996 .

[58]  Kazimierz Głazek.  Some old and new problems in the independence theory , 1979 .