Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This dissertation presents a reconstruction of John Venn s (1834-1923) logical theory in Symbolic Logic (1881; 1894). In his work, Venn presents an algebra of logic, and faces a number of philosophical problems underlying this symbolic logic. Firstly, Venn needs to consider the relation between symbolic logic and traditional logic, i.e., Syllogistic. Secondly, Venn needs to consider the relation between symbolic logic and Mathematics. In treating these issues, Venn will have to reflect upon a number of philosophical notions concerning the nature of symbolic knowledge. The objective of this dissertation is to present Venn s treatment to the concept of symbolic knowledge. Throughout the research, it is shown that according to Venn s point of view the algebra of logic is a formal generalization of Syllogistic. Such formal generalization is possible due to the ecthetic function algebraic symbols perform in logical representation. Furthermore, according to Venn, the logic represented by his algebraic symbolism can be precisely differentiated from Mathematics. Such differencing is possible due to the reflection upon the different modes in which algebraic symbolism performs the subrogative function of symbolic knowledge. This dissertation achieves twofold results. On the one hand, it achieves a historiographically important result, for it permits the determination of the locus of Venn s work among the efforts of logical symbolization in the Nineteenth century. On the other, it achieves a philosophical result insofar it permits, through the analysis of a historical case, to clarify key-notions of symbolic knowledge. Venn is more recognized for the creation of Venn diagrams than for his work in the algebra of logic, however, Venn doesn t elaborate much any systematic reflection upon the nature of graphic knowledge. Nevertheless, the research of Venn s work in the algebra of logic provides results concerning the nature of Venn diagrams, which are here presented as a secondary issue. / Esta dissertação apresenta uma reconstrução da teoria lógica de John Venn (1834- 1923) em Symbolic Logic (1881; 1894). Em sua obra, Venn apresenta uma álgebra da lógica, e enfrenta uma série de problemas filosóficos subjacentes a essa lógica simbólica. Em primeiro lugar, Venn precisa considerar a relação entre a lógica simbólica e a lógica tradicional, i.e., a silogística. Em segundo lugar, Venn precisa considerar a relação entre a lógica simbólica e a matemática. No tratamento dessas questões, Venn precisará refletir sobre uma série de noções filosóficas acerca da natureza do conhecimento simbólico. O objetivo dessa dissertação é apresentar o tratamento oferecido por Venn ao conceito de conhecimento simbólico. No desenvolvimento da pesquisa, verifica-se que, na opinião de Venn, sua álgebra da lógica é uma generalização formal da silogística. Tal processo de generalização formal é possível graças à função ectética que os símbolos algébricos cumprem na representação lógica. Além disso, verifica-se que, de acordo com Venn, a lógica representada pelo seu simbolismo algébrico pode ser precisamente diferenciada da matemática. Tal diferenciação é possível graças à reflexão sobre os diferentes modos em que o simbolismo algébrico cumpre a função subrogativa do conhecimento simbólico. Essa dissertação alcança, por fim, um duplo resultado. Por um lado, obtém-se um resultado de valor historiográfico, pois permite determinar o lugar do trabalho de Venn entre os esforços de simbolização da lógica do século XIX. Além disso, alcança também um resultado filosófico na medida em que permite, através de análise de um caso histórico, clarificar noções-chave do conhecimento simbólico. Venn é mais conhecido pela criação dos diagramas de Venn do que por seu trabalho em álgebra da lógica, contudo Venn pouco oferece em termos de reflexão sistemática sobre o tema filosófico da natureza do conhecimento gráfico. Apesar disso, o estudo do trabalho de Venn em álgebra da lógica oferece resultados sobre a natureza dos diagramas de Venn, resultados esses que são aqui apresentados como produto secundário da investigação.

Le cancer du sein est le cancer le plus répandu chez les femmes de plus de 40 ans. En effet, des études ont montré qu'une détection précoce et un traitement approprié du cancer du sein augmentent de manière significative les chances de survie. La mammographie constitue le moyen d'investigation le plus utilisé dans le diagnostic des lésions mammaires. Cependant, cette technique peut être insuffisante pour montrer les structures du sein et faire apparaître les anomalies présentes et le médecin peut faire appel à d'autres modalités d'imagerie telle que l'imagerie IRM. Ces modalités sont généralement complémentaires. Par conséquent, le médecin procède à une fusion mentale des différentes informations sur les deux images dans le but d'effectuer le diagnostic adéquat. Pour assister le médecin et l'aider dans ce processus, nous proposons une solution permettant de fusionner les deux images. Bien que l'idée de la fusion paraisse simple, sa mise en oeuvre pose de nombreux problèmes liés non seulement au problème de fusion en général mais aussi à la nature des images médicales qui sont généralement des images mal contrastées et présentant des données hétérogènes, imprécises et ambigües. Notons que les images mammographiques et les images IRM présentent des représentations très différentes des informations, étant donnée qu'elles sont prises dans des conditions distinctes. Ce qui nous amène à poser la question suivante: Comment passer de la représentation hétérogène des informations dans l'espace image, à un autre espace de représentation uniforme. Afin de traiter cette problématique, nous optons pour une approche de traitement multi-niveaux : niveau pixel, niveau primitives, niveau objet et niveau scène. Nous modélisons les objets pathologiques extraits des différentes images par des ontologies locales. La fusion est ensuite effectuée sur ces ontologies locales et résulte en une ontologie globale contenant les différentes connaissances sur les objets pathologiques du cas étudié. Cette ontologie globale sert à instancier une ontologie de référence modélisant les connaissances du diagnostic médical des lésions mammaires. Un raisonnement à base de cas est exploité pour fournir les rapports diagnostic des cas les plus similaires pouvant aider le médecin à prendre la meilleure décision. Dans le but de modéliser l'imperfection des informations traitées, nous utilisons la théorie des possibilités avec les différentes ontologies. Le résultat fourni est présenté sous forme de rapports diagnostic comportant les cas les plus similaires au cas étudié avec des degrés de similarité exprimés en mesures de possibilité. Un modèle virtuel 3D complète le rapport diagnostic par un aperçu simplifié de la scène étudiée. / The breast cancer is the most prevalent cancer among women over 40 years old. Indeed, studies evinced that an early detection and an appropriate treatment of breast cancer increases significantly the chances of survival. The mammography is the most tool used in the diagnosis of breast lesions. However, this technique may be insufficient to evince the structures of the breast and reveal the anomalies present. The doctor can use additional imaging modalities such as MRI (Magnetic Reasoning Image). Therefore, the doctor proceeds to a mental fusion of the different information on the two images in order to make the adequate diagnosis. To assist the doctor in this process, we propose a solution to merge the two images. Although the idea of the fusion seems simple, its implementation poses many problems not only related to the paradigm of fusion in general but also to the nature of medical images that are generally poorly contrasted images, and presenting heterogeneous, inaccurate and ambiguous data. Mammography images and IRM images present very different information representations, since they are taken under different conditions. Which leads us to pose the following question: How to pass from the heterogeneous representation of information in the image space, to another space of uniform representation from the two modalities? In order to treat this problem, we opt a multilevel processing approach : the pixel level, the primitive level, the object level and the scene level. We model the pathological objects extracted from the different images by local ontologies. The fusion is then performed on these local ontologies and results in a global ontology containing the different knowledge on the pathological objects of the studied case. This global ontology serves to instantiate a reference ontology modeling knowledge of the medical diagnosis of breast lesions. Case-based reasoning (CBR) is used to provide the diagnostic reports of the most similar cases that can help the doctor to make the best decision. In order to model the imperfection of the treated information, we use the possibility theory with the ontologies. The final result is a diagnostic reports containing the most similar cases to the studied case with similarity degrees expressed with possibility measures. A 3D symbolic model complete the diagnostic report with a simplified overview of the studied scene.