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Full Description
This book summarizes the methods and concepts of Statistical Implicative Analysis (SIA), created by Régis Gras in the 1980s to study, in a new way, the behavioural responses of French pupils to mathematics tests. Using a multidimensional, non-symmetrical data analysis method, SIA crosses a set of subjects or objects with a set of variables. It effectively complements traditional correlational and psychometric methods.
SIA, through its various extensions, is today presented as a broad Artificial Intelligence method aimed at extracting trends and possible causalities in the form of rules, from a set of variables. It is based on the unlikeliness of the existence of these relationships, i.e. on the relative weakness of their counter-examples compared to what chance alone would produce. It establishes a dual topological relationship between the set of subjects and the set of variables. Many applications of this approach, driving forces or crucibles for the development of SIA, have concerned and still concern various fields such as didactics, evaluation and assessment, psychology, sociology, medicine, biology, economics, art history, and others.
Key Features:
Presents the foundations and representations of SIA
Provides extensions of variable sets and subjects
Includes a bonus exercise
Contents
1. Paradigmatic overview of Implicative Statistical Analysis. When? Why? How? 2. From the founding situations of the SIA to its formalization 3. Extension of the Statistical Implicative Analysis to rule hierarchies 4. Dual relationships between subject and space of variables in Implicative Statistical Analysis Part 1: Extension of sets of variables and subjects 5. Multivariate variables with Statistical Implicative Analysis 6. Superfluous or redundant rules in SIA 7. Rule Extraction on Fuzzy Sets 8. Extension of Statistical Implicative Analysis to a continuous population space 9. Extension of SIA to the case of continuous variables Rev1: Pablo (FINIE) Rev2: Antoine (FINIE) Part 2: The SIA and the cognitive development 10. Hierarchies of rules and conceptualization 11. SIA, Analyzer and Revealer of Taxonomic Complexity Part 3: D-Slanted views: fractal geometry, formal logic, rational mechanics 12. Fractal dimension of an implicative graph 13. The paraconsistent logic of Implicative Statistical Analysis 14. A mechanical metaphor of the implicative graph of Implicative Statistical Analysis Part 4. Bonus Question 15. Exercise: a numerical example for didactic purposes
