Observational Calculi and Association Rules

1. Front Matter

   Pages 1-20

   PDF

2. Introduction

   • Jan Rauch

   Pages 1-13

3. Logical Calculi of Association Rules

   1. Front Matter

      Pages 15-16

      PDF

   2. Data Matrices

      • Jan Rauch

      Pages 17-20

   3. Logical Calculus of Association Rules

      • Jan Rauch

      Pages 21-26

   4. 4ft-quantifiers

      • Jan Rauch

      Pages 27-38

   5. Useful Results

      • Jan Rauch

      Pages 39-61

4. Classes of Association Rules

   1. Front Matter

      Pages 63-64

      PDF

   2. Overview of Classes

      • Jan Rauch

      Pages 65-79

   3. Implicational Rules

      • Jan Rauch

      Pages 81-97

   4. Double Implicational Rules

      • Jan Rauch

      Pages 99-126

   5. Equivalence Rules

      • Jan Rauch

      Pages 127-147

   6. Rules with F-property

      • Jan Rauch

      Pages 149-154

5. Results on Classes of Association Rules

   1. Front Matter

      Pages 155-156

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   2. Deduction Rules

      • Jan Rauch

      Pages 157-180

   3. Missing Information

      • Jan Rauch

      Pages 181-200

   4. Definability of Association Rules in Classical Predicate Calculi

      • Jan Rauch

      Pages 201-229

6. Applications and Research Challenges

   1. Front Matter

      Pages 231-232

      PDF

   2. GUHA Method and the LISp-Miner System

      • Jan Rauch

      Pages 233-260

   3. Research Projects

      • Jan Rauch

      Pages 261-271

Observational calculi were introduced in the 1960’s as a tool of logic of discovery. Formulas of observational calculi correspond to assertions on analysed data. Truthfulness of suitable assertions can lead to acceptance of new scientific hypotheses. The general goal was to automate the process of discovery of scientific knowledge using mathematical logic and statistics. The GUHA method for producing true formulas of observational calculi relevant to the given problem of scientific discovery was developed. Theoretically interesting and practically important results on observational calculi were achieved. Special attention was paid to formulas - couples of Boolean attributes derived from columns of the analysed data matrix. Association rules introduced in the 1990’s can be seen as a special case of such formulas. New results on logical calculi and association rules were achieved. They can be seen as a logic of association rules. This can contribute to solving contemporary challenging problems of data mining research and practice. The book covers thoroughly the logic of association rules and puts it into the context of current research in data mining. Examples of applications of theoretical results to real problems are presented. New open problems and challenges are listed. Overall, the book is a valuable source of information for researchers as well as for teachers and students interested in data mining.

• Association Rules
• Computational Intelligence
• Data Mining
• Observational calculi

• University of Economics, Prague, Prague, Czech Republic

  Jan Rauch

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