Rough sets and rough logic: a KDD perspective

Basic ideas of rough set theory were proposed by Zdzislaw Pawlak [90, 91] in the early 1980’s. In the ensuing years, we have witnessed a systematic, world-wide growth of interest in rough sets and their applications. There are numerous areas of successful applications of rough set software systems [101]. Many interesting case studies are reported (for references see e.g., [100, 101], [87] and the bibliography in these books, in particular [19], [46], [57], [132], [1461).

[1]  George Boole,et al.  An Investigation of the Laws of Thought: Frontmatter , 2009 .

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[3]  E. H. Moore.  ON THE FOUNDATIONS OF MATHEMATICS. , 1903 .

[4]  J. Dewey.  Studies In Logical Theory , 1904 .

[5]  Jan Łukasiewicz,et al.  Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls (micro) , 1930 .

[6]  K. Gödel.  Die Vollständigkeit der Axiome des logischen Funktionenkalküls , 1930 .

[7]  K. Gödel.  Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I , 1931 .

[8]  F. Ramsey.  The foundations of mathematics , 1932 .

[9]  G. Gentzen.  Untersuchungen über das logische Schließen. I , 1935 .

[10]  Alfred Tarski,et al.  Der Wahrheitsbegriff in den formalisierten Sprachen , 1935 .

[11]  Atwell R. Turquette,et al.  On the Many-Valued Logics , 1941 .

[12]  J. Armstrong.  Knowledge and Belief , 1953 .

[13]  G. P. Henderson,et al.  An Essay in Modal Logic. , 1953 .

[14]  A. R. Turquette,et al.  On the Many-Valued Logics , 1941 .

[15]  A. R. Turquette,et al.  Logic, Semantics, Metamathematics , 1957 .

[16]  Martin D. Davis,et al.  Computability and Unsolvability , 1959, McGraw-Hill Series in Information Processing and Computers.

[17]  Aiko M. Hormann,et al.  Programs for Machine Learning. Part I , 1962, Inf. Control..

[18]  D. Prawitz.  Natural Deduction: A Proof-Theoretical Study , 1965 .

[19]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[20]  Max J. Cresswell,et al.  A New Introduction to Modal Logic , 1998 .

[21]  Robert Stalnaker.  A Theory of Conditionals , 2019, Knowledge and Conditionals.

[22]  N. Rescher.  Many Valued Logic , 1969 .

[23]  E. F. Codd,et al.  A Relational Model for Large Shared Data Banks , 1970 .

[24]  Nuel D. Belnap,et al.  Entailment : the logic of relevance and necessity , 1975 .

[25]  H. Keisler,et al.  Handbook of mathematical logic , 1977 .

[26]  A. S. Troelstra,et al.  Aspects of Constructive Mathematics , 1977 .

[27]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[28]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[29]  J. Gibson.  The Ecological Approach to Visual Perception , 1979 .

[30]  Elliott Mendelson,et al.  Introduction to Mathematical Logic , 1979 .

[31]  Lotfi A. Zadeh,et al.  A Theory of Approximate Reasoning , 1979 .

[32]  Zdzislaw Pawlak,et al.  Information systems theoretical foundations , 1981, Inf. Syst..

[33]  E. F. Codd,et al.  A relational model of data for large shared data banks , 1970, CACM.

[34]  J. Etchemendy.  The Concept of Logical Consequence , 1991 .

[35]  Alasdair Urquhart.  Many-valued Logic , 1986 .

[36]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

[37]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[38]  Hector Geffner,et al.  Default reasoning - causal and conditional theories , 1992 .

[39]  Martin Anthony,et al.  Computational Learning Theory , 1992 .

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

[41]  J. Ross Quinlan,et al.  C4.5: Programs for Machine Learning , 1992 .

[42]  R. Słowiński.  Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory , 1992 .

[43]  Dov M. Gabbay,et al.  Handbook of logic in artificial intelligence and logic programming (vol. 1) , 1993 .

[44]  Wilfrid Hodges,et al.  Logical features of Horn Clauses , 1993 .

[45]  Tomasz Imielinski,et al.  Mining association rules between sets of items in large databases , 1993, SIGMOD Conference.

[46]  Norbert Eisinger,et al.  Deduction systems based on resolution , 1993 .

[47]  Edward P. K. Tsang,et al.  Foundations of constraint satisfaction , 1993, Computation in cognitive science.

[48]  Morton Nadler,et al.  Pattern recognition engineering , 1993 .

[49]  Wojciech Ziarko,et al.  Variable Precision Rough Set Model , 1993, J. Comput. Syst. Sci..

[50]  Melvin Fitting,et al.  Basic modal logic , 1993 .

[51]  Avelino J. Gonzalez,et al.  The engineering of knowledge-based systems: theory and practice , 1993 .

[52]  Temporal Logic , 1994, Lecture Notes in Computer Science.

[53]  David Martin,et al.  Book review: The Engineering of Knowledge-based Systems Theory and Practice by Avelino J. Gonzales and Douglas D. Dankel (Prentice Hall, 1993) , 1993, SGAR.

[54]  Frank Klawonn,et al.  Foundations of fuzzy systems , 1994 .

[55]  Kurt Konolige,et al.  Autoepistemic logic , 1994 .

[56]  David Poole,et al.  Default logic , 1994 .

[57]  Wojciech Ziarko.  Rough Sets, Fuzzy Sets and Knowledge Discovery, Proceedings of the International Workshop on Rough Sets and Knowledge Discovery (RSKD'93), Banff, Alberta, Canada, 12-15 October 1993 , 1994, RSKD.

[58]  David J. Spiegelhalter,et al.  Machine Learning, Neural and Statistical Classification , 2009 .

[59]  Dov M. Gabbay,et al.  Handbook of logic in artificial intelligence and logic programming (Vol. 4): epistemic and temporal reasoning , 1995 .

[60]  D. Vanderpooten.  Similarity Relation as a Basis for Rough Approximations , 1995 .

[61]  Peter Gärdenfors,et al.  Belief Revision , 1995 .

[62]  J. van Benthem,et al.  Temporal logic , 1995 .

[63]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[64]  Yoav Shoham,et al.  Non-monotonic temporal reasoning , 1995 .

[65]  Joseph Y. Halpern,et al.  Reasoning about knowledge: a survey , 1995 .

[66]  Andrzej Skowron,et al.  Rough set rudiments , 1995 .

[67]  Ron Kohavi,et al.  Supervised and Unsupervised Discretization of Continuous Features , 1995, ICML.

[68]  K. Upton,et al.  A modern approach , 1995 .

[69]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[70]  Andrzej Skowron,et al.  Synthesis of Adaptive Decision Systems from Experimental Data , 1995, SCAI.

[71]  Andrzej Skowron,et al.  Parallel Communicating Grammar Systems with Negotiation , 1996, Fundam. Informaticae.

[72]  Zbigniew W. Ras,et al.  Cooperative Knowledge-Based Systems , 1996, Intell. Autom. Soft Comput..

[73]  Tsau Young Lin,et al.  Rough Sets and Data Mining: Analysis of Imprecise Data , 1996 .

[74]  Bernhard Ganter,et al.  Formale Begriffsanalyse - mathematische Grundlagen , 1996 .

[75]  Dominik Slezak,et al.  Approximate Reducts in Decision Tables , 1996 .

[76]  Andrzej Skowron,et al.  Rough mereology: A new paradigm for approximate reasoning , 1996, Int. J. Approx. Reason..

[77]  Thomas G. Dietterich.  What is machine learning? , 2020, Archives of Disease in Childhood.

[78]  Andrzej Skowron,et al.  A Rough Set Framework for Data Mining of Propositional Default Rules , 1996, ISMIS.

[79]  Jerzy W. Grzymala-Busse,et al.  Global discretization of continuous attributes as preprocessing for machine learning , 1996, Int. J. Approx. Reason..

[80]  Andrzej Skowron,et al.  Tolerance Approximation Spaces , 1996, Fundam. Informaticae.

[81]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[82]  Heikki Mannila,et al.  Fast Discovery of Association Rules , 1996, Advances in Knowledge Discovery and Data Mining.

[83]  Lotfi A. Zadeh,et al.  Fuzzy logic = computing with words , 1996, IEEE Trans. Fuzzy Syst..

[84]  Ron Kohavi,et al.  Lazy Decision Trees , 1996, AAAI/IAAI, Vol. 1.

[85]  Vijay V. Raghavan,et al.  Data Mining: Trends in Research and Development , 1997 .

[86]  Paul P. Wang.  Advances in machine intelligence & soft-computing , 1997 .

[87]  Shan-Hwei Nienhuys-Cheng,et al.  Foundations of Inductive Logic Programming , 1997, Lecture Notes in Computer Science.

[88]  Marzena Kryszkiewicz,et al.  Generation of Rules from Incomplete Information Systems , 1997, PKDD.

[89]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[90]  T. Y. Lin,et al.  Rough Sets and Data Mining , 1997, Springer US.

[91]  Jennifer Widom,et al.  A First Course in Database Systems , 1997 .

[92]  Ivo Düntsch,et al.  Statistical evaluation of rough set dependency analysis , 1997, Int. J. Hum. Comput. Stud..

[93]  Bart Selman,et al.  Ten Challenges in Propositional Reasoning and Search , 1997, IJCAI.

[94]  J. Kacprzyk,et al.  Incomplete Information: Rough Set Analysis , 1997 .

[95]  Wei Li,et al.  New parallel algorithms for fast discovery of associ-ation rules , 1997 .

[96]  Andrzej Czyzewski,et al.  Soft Processing of Audio Signals , 1998 .

[97]  Salvatore Greco,et al.  Fuzzy Similarity Relation as a Basis for Rough Approximations , 1998, Rough Sets and Current Trends in Computing.

[98]  Dov M. Gabbay,et al.  Handbook of defeasible reasoning and uncertainty management systems: volume 2: reasoning with actual and potential contradictions , 1998 .

[99]  S. Greco,et al.  Rough Approximation of a Preference Relation in a Pairwise Comparison Table , 1998 .

[100]  Lech Polkowski,et al.  Rough Sets in Knowledge Discovery 2 , 1998 .

[101]  Laurent Vigneron,et al.  Rough Algebras & Automated Deduction , 1998 .

[102]  Sinh Hoa Nguyen,et al.  Pattern Extraction from Data , 1998, Fundam. Informaticae.

[103]  Andrzej Skowron,et al.  Discovery of Data Patterns with Applications to Decomposition and Classification Problems , 1998 .

[104]  Andrzej Skowron,et al.  Rough Sets in Knowledge Discovery 2: Applications, Case Studies, and Software Systems , 1998 .

[105]  Andrzej Skowron,et al.  Synthesis of Decision Rules for Object Classification , 1998 .

[106]  Shusaku Tsumoto,et al.  Modelling Medical Diagnostic Rules Based on Rough Sets , 1998, Rough Sets and Current Trends in Computing.

[107]  Max J. Egenhofer,et al.  Spatial and temporal reasoning in geographic information systems , 1998 .

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

[109]  A. Skowron,et al.  Towards adaptive calculus of granules , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[110]  John F. Roddick,et al.  A bibliography of temporal, spatial and spatio-temporal data mining research , 1999, SKDD.

[111]  Andrzej Skowron,et al.  Rough-Fuzzy Hybridization: A New Trend in Decision Making , 1999 .

[112]  Ning Zhong,et al.  Rough Problem Settings for Inductive Logic Programming , 1999, RSFDGrC.

[113]  Janusz Kacprzyk,et al.  Computing with Words in Information/Intelligent Systems 1 , 1999 .

[114]  Hung Son Nguyen,et al.  Efficient SQL-Querying Method for Data Mining in Large Data Bases , 1999, IJCAI.

[115]  Sinh Hoa Nguyen,et al.  Rough Sets and Association Rule Generation , 1999, Fundam. Informaticae.

[116]  Jan Komorowski,et al.  Taming Large Rule Models in Rough Set Approaches , 1999, PKDD.

[117]  Victor W. Marek,et al.  Contributions to the Theory of Rough Sets , 1999, Fundam. Informaticae.

[118]  John F. Roddick,et al.  A bibliography of temporal , 1999 .

[119]  Andrzej Skowron,et al.  Boolean Reasoning Scheme with Some Applications in Data Mining , 1999, PKDD.

[120]  Zdzislaw Pawlak,et al.  Decision Rules, Bayes' Rule and Ruogh Sets , 1999, RSFDGrC.

[121]  Amit Konar,et al.  Artificial Intelligence and Soft Computing: Behavioral and Cognitive Modeling of the Human Brain , 1999 .

[122]  Shusaku Tsumoto,et al.  Information Granules for Spatial Reasoning , 2001, PAKDD.

[123]  Daniel Vanderpooten,et al.  A Generalized Definition of Rough Approximations Based on Similarity , 2000, IEEE Trans. Knowl. Data Eng..

[124]  Lech Polkowski.  On Connection Synthesis via Rough Mereology , 2001, Fundam. Informaticae.

[125]  Tsau Young Lin,et al.  Granular Computing on Binary Relations , 2002, Rough Sets and Current Trends in Computing.