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Fundamental concepts of SIA: statistical modelling, types of
variables, principal and additional variables;
- New advances in progress, stability of indices, entropic implication
intensity, extension to new types of variables, rules of exception,
duality (space of subject- space of rules), metrical structure and
topology of space led by their contribution to the subjects or their
typicality, vector analysis, etc ...);
- Comparison of critical processes, models, representations and
the results of SIA with other methods of data analysis (Galois lattices,
Bayesian networks, trees induction, factorial analysis, etc ...);
- Use of the CHIC software, current and expected developments;
- Applications processed by SIA and comparison with other methods,
in the areas of didactics, sciences of education, psychology, sociology,
economics, art history, biology, medicine, archaeology, etc., ...;
- Graphical presentation of results and numerical applications,
aid for the interpretation of these results, respective roles and
critics of the types of variables, the principal variables and supplementary
choices;
- Specificity of training with the SIA: use of the CHIC software,
interpretation of graphical representations (implicative graph, cohesive
hierarchy tree)
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Challenge 1:
- Implicative cone: how to qualify and quantify the global qualities
of the father variables, and also the son variables, in relation to
the top of the implicative cone. Identify the most coherent liaisons
via the top of the cone.
Challenge 2:
- We have a network of curves from an implicative graph originating
from A. This graph represents a dynamic character of which the curves
are weighted by rule-abiding occurrences. It might be possible to
create a mechanic metaphor illustrating such a graph.
Challenge 3:
- Enrich the extension to continuous variables by authentic examples,
then treat and analyse them.
Challenge 4:
- Do a double analysis of a file with binary data, one-part implicative
analysis and the other using Bayesian-style data
Challenge 5:
- The research and treatment of the internal degree of homogeneity/heterogeneity
of a general population presenting a general sequencing of data compatible
with an implicative and particularly cohesive structure
Challenge 6:
- Establishing variable A and the consequences B, C and D, and knowing
that A = >B, A = >C, and A = >D, is it possible to define
an implication for A on the conjunction of B, C, or D- meaning A =
> (B and C and D ) ?
Challenge 7:
- Establish how the logic that is underlying SIA, the implicative
statistical logic (ISL), where we control contradictions under a certain
dialectic, is a paraconsistent logic.
Challenge 8:
- The cohesive hierarchy seems to be a metaphor of the cognitive development
of humans. Could it not also be a metaphor of Darwinian evolution?
Challenge 9:
- Define for a given analysis the notion of density of the group of
implicative relations (rules). Study it in terms of the retained threshold
(ex. 0.95, 0.8 etc.) et qualify the compacity of an implicative graph
by a relation between the number of represented rules and the threshold.
This study invokes the notion of fractal dimensions of a curve.
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