A Common Logic Approach to Data Mining and Pattern Recognition

In this chapter a common logical approach is suggested to solve both data mining and pattern recognition problems. It is based on using finite spaces of Boolean or multi-valued attributes for modeling of the natural subject areas. Inductive inference used for extracting knowledge from data is combined with deductive inference, which solves other pattern recognition problems. A set of efficient algorithms was developed to solve the regarded problems, dealing with Boolean functions and finite predicates represented by logical vectors and matrices.

[1]  George Boolos,et al.  Computability and logic , 1974 .

[2]  Willi Klösgen,et al.  Efficient discovery of interesting statements in databases , 2004, Journal of Intelligent Information Systems.

[3]  William Frawley,et al.  Knowledge Discovery in Databases , 1991 .

[4]  J. Spencer.  Ramsey Theory , 1990 .

[5]  Willard Van Orman Quine,et al.  The Problem of Simplifying Truth Functions , 1952 .

[6]  Richard C. T. Lee,et al.  Symbolic logic and mechanical theorem proving , 1973, Computer science classics.

[7]  Hantao Zhang,et al.  SATO: An Efficient Propositional Prover , 1997, CADE.

[8]  Nils J. Nilsson,et al.  Problem-solving methods in artificial intelligence , 1971, McGraw-Hill computer science series.

[9]  Raymond J. Nelson,et al.  Simplest normal truth functions , 1955, Journal of Symbolic Logic.

[10]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[11]  Gregory Piatetsky-Shapiro,et al.  Discovery, Analysis, and Presentation of Strong Rules , 1991, Knowledge Discovery in Databases.

[12]  Evangelos Triantaphyllou.  Inference of a minimum size boolean function from examples by using a new efficient branch-and-bound approach , 1994, J. Glob. Optim..

[13]  Philip K. Chan,et al.  Systems for Knowledge Discovery in Databases , 1993, IEEE Trans. Knowl. Data Eng..

[14]  Donald A. Waterman,et al.  A Guide to Expert Systems , 1986 .

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

[16]  Rocco H. Urbano,et al.  A Topological Method for the Determination of the Minimal Forms of a Boolean Function , 1956, IRE Trans. Electron. Comput..

[17]  R. Düsing.  Knowledge discovery in data bases , 2000 .

[18]  A. Zakrevsky.  Logical recognition in the space of multivalued attributes , 1994, Comput. Sci. J. Moldova.

[19]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[20]  Gregory Piatetsky-Shapiro,et al.  Knowledge Discovery in Databases: An Overview , 1992, AI Mag..

[21]  E. McCluskey.  Minimization of Boolean functions , 1956 .