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+\chapter{From the founding situations of the SIA to its formalization}
+\label{intro} % Always give a unique label
+% use \chaptermark{}
+% to alter or adjust the chapter heading in the running head
+
+
+
+\abstract{
+Starting from mathematical didactic situations, the implicitative
+statistical analysis method develops as problems are encountered and
+questions are asked.
+Its main objective is to structure data crossing subjects and
+variables, to extract inductive rules between variables and, based on
+the contingency of these rules, to explain and therefore forecast in
+various fields: psychology, sociology, biology, etc.
+It is for this purpose that the concepts of intensity of implication,
+class cohesion, implication-inclusion, significance of hierarchical
+levels, contribution of additional variables, etc., are based.
+Similarly, the processing of binary variables (e.g., descriptors) is
+gradually being supplemented by the processing of modal, frequency
+and, recently, interval and fuzzy variables.
+}
+
+\section{Preamble}
+
+Human operative knowledge is mainly composed of two components: that
+of facts and that of rules between facts or between rules themselves.
+It is his learning that, through his culture and his personal
+experiences, allows him to gradually develop these forms of knowledge,
+despite the regressions, the questioning, the ruptures that arise at
+the turn of decisive information.
+However, we know that these dialectically contribute to ensuring a
+balanced operation.
+However, the rules are inductively formed in a relatively stable way
+as soon as the number of successes, in terms of their explanatory or
+anticipatory quality, reaches a certain level (of confidence) from
+which they are likely to be implemented.
+On the other hand, if this (subjective) level is not reached, the
+individual's economy will make him resist, in the first instance, his
+abandonment or criticism.
+Indeed, it is costly to replace the initial rule with another rule
+when a small number of infirmations appear, since it would have been
+reinforced by a large number of confirmations.
+An increase in this number of negative instances, depending on the
+robustness of the level of confidence in the rule, may lead to its
+readjustment or even abandonment.
+Laurent Fleury~\cite{Fleury}, in his thesis, correctly cites the
+example - which Régis repeats - of the highly admissible rule: "all
+Ferraris are red".
+This very robust rule will not be abandoned when observing a single or
+two counter-examples.
+Especially since it would not fail to be quickly
+re-comforted.
+
+Thus, contrary to what is legitimate in mathematics, where not all
+rules (theorem) suffer from exception, where determinism is total,
+rules in the human sciences, more generally in the so-called "soft"
+sciences, are acceptable and therefore operative as long as the number
+of counter-examples remains "bearable" in view of the frequency of
+situations where they will be positive and effective.
+The problem in data analysis is then to establish a relatively
+consensual numerical criterion to define the notion of a level of
+confidence that can be adjusted to the level of requirement of the
+rule user.
+The fact that it is based on statistics is not surprising.
+That it has a property of non-linear resistance to noise (weakness of
+the first counter-example(s)) may also seem natural, in line with the
+"economic" meaning mentioned above.
+That it collapses if counter-examples are repeated also seems to have
+to guide our choice in the modeling of the desired criterion.
+This text presents the epistemological choice we have made.
+As such it is therefore refutable, but the number of situations and
+applications where it has proved relevant and fruitful leads us to
+reproduce its genesis here.
+
+\section{Introduction}
+
+Different theoretical approaches have been adopted to model the
+extraction and representation of imprecise (or partial) inference
+rules between binary variables (or attributes or characters)
+describing a population of individuals (or subjects or objects).
+But the initial situations and the nature of the data do not change
+the initial problem.
+It is a question of discovering non-symmetrical inductive rules to
+model relationships of the type "if a then almost b".
+This is, for example, the option of Bayesian networks~\cite{Amarger}
+or Galois lattices~\cite{Simon}.
+But more often than not, however, since the correlation and the
+${\chi}^2$ test are unsuitable because of their symmetric nature,
+conditional probability~\cite{Loevinger, Agrawal,Grasn} remains the
+driving force behind the definition of the association, even when the
+index of this selected association is multivariate~\cite{Bernard}.
+
+
+
\bibitem{Agrawal}Agrawal R., Imielinsky T. et Swami A (1993) Mining association rules between sets of items in large databases, Proc. of the ACM SIGMOD'93.
+
+\bibitem{Amarger} Amarger S., Dubois D. and Prade H. (1991) Imprecise quantifiers and conditional probabilities - in Symbolic and quantitative approaches to uncertainty (R. KRUSE, P. SIEGEL), Springer-Verlag, 33-37.
+
\bibitem{Atlana} Atlan H. (1986), A tort et à raison, Seuil.
\bibitem{Atlanb} Atlan H. (2014) Croyances, Paris, Autrement.
\bibitem{Benzecri} Benzecri, J.P. (1973) L’analyse des données (vol 1), Dunod, Paris.
-
+\bibitem{Bernard} Bernard J.-M. and Poitrenaud S. (1999) L'analyse implicative bayesienne d'un questionnaire binaire : quasi-implications et treillis de Galois simplifié", Mathématiques, Informatique et Sciences Humaines, n° 147, 1999, 25-46
\bibitem{Blanchard} Blanchard J., Guillet F. et Gras R. (2009) Analyse Implicative Séquentielle, Analyse Statistique Implicative, Une méthode d’analyse de données pour la recherche de causalités, dir. R.Gras, eds R.Gras, J.-C. Régnier, Guillet F. Cépaduès, Toulouse, p. 183-194.
\bibitem{Espagnat} d’Espagnat B. (1981) A la recherche du réel, Le
regard d’un physicien, Paris.
+
+\bibitem{Fleury} Fleury L. (1996) Extraction de connaissances dasn une base de données pour la gestion de ressources humaines, Thèse d’Université, Université de Nantes, 22 novembre 1996.
+
\bibitem{Foucault} Foucault M. (1966) Les mots et les choses, Éditions
Gallimard, Paris.
\bibitem{Levi-strauss} Lévi-Strauss C. (1967) Structures élémentaires
de la parenté, De Gruyter Mouton.
+\bibitem{Loevinger} Loevinger J. (1947), A systematic approach to the
+ construction and evaluation of tests of abilities, Psychological Monographs, 61, n° 4.
+
\bibitem{Marx} Marx K. (1857-1858) Manuscrits de 1857-1858.
\bibitem{Schelling} Schelling F.-W. (1994) Philosophie de la mythologie, p.361, Paris, J. Millon
\bibitem{Seve} Sève L. (2005) Émergence, complexité et dialectique, Paris.
+
+
+\bibitem{Simon} Simon A. (2001),Outils classificatoires par objets pour l'extraction de connaissances dans des bases de données, Thèse de l'Université de Nancy 1.
\bibitem{Shapin} Shapin S. (2014) Une histoire sociale de la vérité, La Découverte, Paris.
