Dans ce mémoire, on s’inspire des sciences cognitives pour aborder la question de la modélisation logique du raisonnement et de l’apprentissage. Notre principale conviction est qu’il faudrait, pour traiter ce problème, prendre modèle sur la manière dont les agents naturels (c’est à dire les humains et les animaux) procèdent lorsqu’ils raisonnent ou apprennent. Considérant que le raisonnement fait appel à un grand nombre de facultés cognitives distinctes, et qu’il ne serait donc pas raisonnable d’espérer modéliser d’un seul coup l’ensemble du raisonnement humain, on se concentre ici sur un type d’inférences très simples dont on soutient qu’elles constituent le coeur du raisonnement chez tous les animaux à cerveau. On identifie un processus sous-jacent plausible pour ces inférences, d’abord au niveau mental de description, puis au niveau neuronal, et on développe une famille de modèles logiques permettant de le simuler. On s’attache ensuite à produire un ensemble de règles d’inférence caractérisant les relations d’inférence induites par ces modèles. Ces règles résultent du processus suggéré, et doivent donc être vues comme des règles qui, d’après le modèle, émergent fonctionnement des cerveaux. Enfin, on analyse les processus d’apprentissage attachés aux inférences considérées, et on montre comment le formalisme proposé permet de les modéliser. Pour conclure on évoque brièvement les possibles développements futurs du modèle, et notamment on donne quelques indications quant à la manière dont la modélisation d’un certain nombre de facultés additionnelles pourrait être envisagée. / In this dissertation, we take inspiration in cognitive sciences to address the issue of the logical modelling of reasoning and learning. Our main thrust is that to address these issues one should take inspiration in the way natural agents (i.e., humans and animals) actually proceed when they draw inferences and learn. Considering that reasoning incorporates a wide range of cognitive abilities, and that it would thus be unreasonable to hope to model the whole of human’s reasoning all at once, we focus here on a very basic kind of inferences that, we argue, can be considered as the primary core of reasoning in all brained animals. We identify a plausible underlying process for these inferences, first at the mental level of description and then at the neural level, and we develop a family of logical models that allow to simulate it. Then we tackle the issue of providing sets of rules to characterise the inference relations induced by these models. These rules are a by-product of the posited process, and should thus be seen as rules that, according to the model, result from the very functioning of brains. Finally we examine the learning processes attached to the considered inferences, and we show how to they can be modelled within our framework. To conclude we briefly discuss possible further developments of the framework, and in particular we give indications about how the modelling of some other cognitive abilities might be envisioned.

Operators which map subsets of a given set to the set of their minimal elements with respect to some relation R form the basis of a semantic approach in non-monotonic logic, belief revision, conditional logic and updating. In this paper we investigate operators of this type from an algebraic viewpoint. A representation theorem is proved and various properties of the resulting algebras are investigated. It is shown that they behave quite differently from known algebras related to logics, e.g. modal algebras and Heyting algebras.

We show how the non-monotonic nature of common-sense reasoning can be formalised by circumscription. Various forms of circumscription are discussed. A new form of circumscription, namely naive circumscription, is introduced in order to facilitate the comparison of the various forms. Finally, some issues connected with the automation of circumscriptive reasoning are examined. / Computing / M. Sc. (Computer Science)

Este trabalho procura utilizar algumas das idéias de J. Piaget, em especial a "Lógica Operatória Intraproposicional", para uma análise das relações de herança entre classes empregadas em sistemas de representação de conhecimento. Procura-se sistematizar a noção de taxonomias do conhecimento "científico", ou "classificações sistemáticas". Estas estruturas foram utilizadas por Piaget como ponto de partida para a descoberta de estruturas cognitivas do conhecimento científico. Em especial, define-se a relação CS, que determina quais quais relações de herança seguem de uma taxonomia do conhecimento científico. A noção de classificação do conhecimento científico é comparada com a de "classificação do senso comum". São mostradas as diferenças entre estes conceitos. Determina-se a semântica das classificag6es do senso comum nas estruturas de agrupamentos de Piaget, via uma extensão epistêmica da lógica de classes. É estudada a relação de herança do senso comum que admite exceções. É também apresentada a formulação usual em lógica de predicados, e é proposta uma formulação em lógica de classes estendida. Conclui-se que a definição intuitiva da relação de herança empregada em uma formulação em lógica de classes pode ser diferente daquela que é empregada em uma formulação em lógica do proposições. Observa-se, em especial na formulação em lógica de classes, que as relações de herança não-estrita não se adaptam A estrutura de grafo direcionado acíclico. Na verdade, a relação de herança não-estrita não estabelece uma ordenação entre as classes (no sentido de conjunto parcialmente ordenado, ou CPO), mas uma possível simetria entre estas classes. Esta observação não aparece tão claramente na formulação proposicional, já que a relação de herança é mascarada pelo uso da implicação lógica (->), o que dá uma aparência de ordenação parcial. Verifica-se o que ocorre quando são combinadas relações de herança com ou sem exceções em uma única teoria de herança. É feita ainda alguma sistematização da lógica operatória intraproposicional de Piaget. Esta sistematização não prima pelo rigor, mas em fornecer algum entendimento básico para os não iniciados em Piaget. O trabalho abrange a sistematização dos quatro agrupamento de classes da lógica intraproposicional, e relega o estudo dos quatro agrupamentos de relações para um trabalho posterior. / This work use some ideas of Jean Piaget, mainly the Operating Logic, for an analysis of inheritance relationships used in knowledge representation systems. The notion of "scientific" knowledge classifications as defined by Piaget is shown. These structures were used by Piaget as a starting point to find the cognitive structures of scientific knowledge. It is also defined a relation CS. This relation tells whether an inheritance relationship follows from a scientific knowledge taxonomy or not. The notion of scientific knowledge classification is compared with that of "commonsense classification". The differences between these concepts are shown. The semantics of common sense classifications is determined in terms of Piaget's "groupments", through an epistemic extension of the logic of classes. The common sense inheritance relationship with exceptions is studied. The usual formulation of inheritance in propositional logic is presented, and a formulation in the extended logic of classes is proposed. The conclusion is that the intuitive definition of inheritance relationship in one formulation may be different of that in the other. It is observed in the formulation in logic of classes that non-strict inheritance relationships don't adapt to the structure of an acyclic directed graph. In fact, the non-strict inheritance relation doesn't stablish an ordering between classes (in the sense of a partially ordered set, or POSET), but it stablishes a possible simmetry between these classes. This is not so clear in the propositional formulation, because the inheritance relation is masked by using logic implication (->), what gives an appearance of partial ordering. It is verified what occurs when inheritance relations with or without exceptions are mixed in one single theory. It is made some sistematization of the Piaget's intrapropositional operating logic. This sistematization doesn't try to be rigorous, but gives some basic understanding on this theme. The work involves the sistematization of the four groupmonts of classes of the intrapropositional logic, and leaves the study of the four groupments of relations for a future work.

We show how the non-monotonic nature of common-sense reasoning can be formalised by circumscription. Various forms of circumscription are discussed. A new form of circumscription, namely naive circumscription, is introduced in order to facilitate the comparison of the various forms. Finally, some issues connected with the automation of circumscriptive reasoning are examined. / Computing / M. Sc. (Computer Science)

Este trabalho procura utilizar algumas das idéias de J. Piaget, em especial a "Lógica Operatória Intraproposicional", para uma análise das relações de herança entre classes empregadas em sistemas de representação de conhecimento. Procura-se sistematizar a noção de taxonomias do conhecimento "científico", ou "classificações sistemáticas". Estas estruturas foram utilizadas por Piaget como ponto de partida para a descoberta de estruturas cognitivas do conhecimento científico. Em especial, define-se a relação CS, que determina quais quais relações de herança seguem de uma taxonomia do conhecimento científico. A noção de classificação do conhecimento científico é comparada com a de "classificação do senso comum". São mostradas as diferenças entre estes conceitos. Determina-se a semântica das classificag6es do senso comum nas estruturas de agrupamentos de Piaget, via uma extensão epistêmica da lógica de classes. É estudada a relação de herança do senso comum que admite exceções. É também apresentada a formulação usual em lógica de predicados, e é proposta uma formulação em lógica de classes estendida. Conclui-se que a definição intuitiva da relação de herança empregada em uma formulação em lógica de classes pode ser diferente daquela que é empregada em uma formulação em lógica do proposições. Observa-se, em especial na formulação em lógica de classes, que as relações de herança não-estrita não se adaptam A estrutura de grafo direcionado acíclico. Na verdade, a relação de herança não-estrita não estabelece uma ordenação entre as classes (no sentido de conjunto parcialmente ordenado, ou CPO), mas uma possível simetria entre estas classes. Esta observação não aparece tão claramente na formulação proposicional, já que a relação de herança é mascarada pelo uso da implicação lógica (->), o que dá uma aparência de ordenação parcial. Verifica-se o que ocorre quando são combinadas relações de herança com ou sem exceções em uma única teoria de herança. É feita ainda alguma sistematização da lógica operatória intraproposicional de Piaget. Esta sistematização não prima pelo rigor, mas em fornecer algum entendimento básico para os não iniciados em Piaget. O trabalho abrange a sistematização dos quatro agrupamento de classes da lógica intraproposicional, e relega o estudo dos quatro agrupamentos de relações para um trabalho posterior. / This work use some ideas of Jean Piaget, mainly the Operating Logic, for an analysis of inheritance relationships used in knowledge representation systems. The notion of "scientific" knowledge classifications as defined by Piaget is shown. These structures were used by Piaget as a starting point to find the cognitive structures of scientific knowledge. It is also defined a relation CS. This relation tells whether an inheritance relationship follows from a scientific knowledge taxonomy or not. The notion of scientific knowledge classification is compared with that of "commonsense classification". The differences between these concepts are shown. The semantics of common sense classifications is determined in terms of Piaget's "groupments", through an epistemic extension of the logic of classes. The common sense inheritance relationship with exceptions is studied. The usual formulation of inheritance in propositional logic is presented, and a formulation in the extended logic of classes is proposed. The conclusion is that the intuitive definition of inheritance relationship in one formulation may be different of that in the other. It is observed in the formulation in logic of classes that non-strict inheritance relationships don't adapt to the structure of an acyclic directed graph. In fact, the non-strict inheritance relation doesn't stablish an ordering between classes (in the sense of a partially ordered set, or POSET), but it stablishes a possible simmetry between these classes. This is not so clear in the propositional formulation, because the inheritance relation is masked by using logic implication (->), what gives an appearance of partial ordering. It is verified what occurs when inheritance relations with or without exceptions are mixed in one single theory. It is made some sistematization of the Piaget's intrapropositional operating logic. This sistematization doesn't try to be rigorous, but gives some basic understanding on this theme. The work involves the sistematization of the four groupmonts of classes of the intrapropositional logic, and leaves the study of the four groupments of relations for a future work.

Este trabalho procura utilizar algumas das idéias de J. Piaget, em especial a "Lógica Operatória Intraproposicional", para uma análise das relações de herança entre classes empregadas em sistemas de representação de conhecimento. Procura-se sistematizar a noção de taxonomias do conhecimento "científico", ou "classificações sistemáticas". Estas estruturas foram utilizadas por Piaget como ponto de partida para a descoberta de estruturas cognitivas do conhecimento científico. Em especial, define-se a relação CS, que determina quais quais relações de herança seguem de uma taxonomia do conhecimento científico. A noção de classificação do conhecimento científico é comparada com a de "classificação do senso comum". São mostradas as diferenças entre estes conceitos. Determina-se a semântica das classificag6es do senso comum nas estruturas de agrupamentos de Piaget, via uma extensão epistêmica da lógica de classes. É estudada a relação de herança do senso comum que admite exceções. É também apresentada a formulação usual em lógica de predicados, e é proposta uma formulação em lógica de classes estendida. Conclui-se que a definição intuitiva da relação de herança empregada em uma formulação em lógica de classes pode ser diferente daquela que é empregada em uma formulação em lógica do proposições. Observa-se, em especial na formulação em lógica de classes, que as relações de herança não-estrita não se adaptam A estrutura de grafo direcionado acíclico. Na verdade, a relação de herança não-estrita não estabelece uma ordenação entre as classes (no sentido de conjunto parcialmente ordenado, ou CPO), mas uma possível simetria entre estas classes. Esta observação não aparece tão claramente na formulação proposicional, já que a relação de herança é mascarada pelo uso da implicação lógica (->), o que dá uma aparência de ordenação parcial. Verifica-se o que ocorre quando são combinadas relações de herança com ou sem exceções em uma única teoria de herança. É feita ainda alguma sistematização da lógica operatória intraproposicional de Piaget. Esta sistematização não prima pelo rigor, mas em fornecer algum entendimento básico para os não iniciados em Piaget. O trabalho abrange a sistematização dos quatro agrupamento de classes da lógica intraproposicional, e relega o estudo dos quatro agrupamentos de relações para um trabalho posterior. / This work use some ideas of Jean Piaget, mainly the Operating Logic, for an analysis of inheritance relationships used in knowledge representation systems. The notion of "scientific" knowledge classifications as defined by Piaget is shown. These structures were used by Piaget as a starting point to find the cognitive structures of scientific knowledge. It is also defined a relation CS. This relation tells whether an inheritance relationship follows from a scientific knowledge taxonomy or not. The notion of scientific knowledge classification is compared with that of "commonsense classification". The differences between these concepts are shown. The semantics of common sense classifications is determined in terms of Piaget's "groupments", through an epistemic extension of the logic of classes. The common sense inheritance relationship with exceptions is studied. The usual formulation of inheritance in propositional logic is presented, and a formulation in the extended logic of classes is proposed. The conclusion is that the intuitive definition of inheritance relationship in one formulation may be different of that in the other. It is observed in the formulation in logic of classes that non-strict inheritance relationships don't adapt to the structure of an acyclic directed graph. In fact, the non-strict inheritance relation doesn't stablish an ordering between classes (in the sense of a partially ordered set, or POSET), but it stablishes a possible simmetry between these classes. This is not so clear in the propositional formulation, because the inheritance relation is masked by using logic implication (->), what gives an appearance of partial ordering. It is verified what occurs when inheritance relations with or without exceptions are mixed in one single theory. It is made some sistematization of the Piaget's intrapropositional operating logic. This sistematization doesn't try to be rigorous, but gives some basic understanding on this theme. The work involves the sistematization of the four groupmonts of classes of the intrapropositional logic, and leaves the study of the four groupments of relations for a future work.

In this dissertation a formalisation of nonmonotonic reasoning, namely Default logic, is discussed. A proof theory for default logic and a variant of Default logic - Prioritised Default logic - is presented. We also pursue an investigation into the relationship between default reasoning and making inferences in a neural network. The inference problem shifts from the logical problem in Default logic to the optimisation problem in neural networks, in which maximum consistency is aimed at The inference is realised as an adaptation process that identifies and resolves conflicts between existing knowledge about the relevant world and external information. Knowledge and data are transformed into constraint equations and the nodes in the network represent propositions and constraint equations. The violation of constraints is formulated in terms of an energy function. The Hopfield network is shown to be suitable for modelling optimisation problems and default reasoning. / Computer Science / M.Sc. (Computer Science)

In this dissertation a formalisation of nonmonotonic reasoning, namely Default logic, is discussed. A proof theory for default logic and a variant of Default logic - Prioritised Default logic - is presented. We also pursue an investigation into the relationship between default reasoning and making inferences in a neural network. The inference problem shifts from the logical problem in Default logic to the optimisation problem in neural networks, in which maximum consistency is aimed at The inference is realised as an adaptation process that identifies and resolves conflicts between existing knowledge about the relevant world and external information. Knowledge and data are transformed into constraint equations and the nodes in the network represent propositions and constraint equations. The violation of constraints is formulated in terms of an energy function. The Hopfield network is shown to be suitable for modelling optimisation problems and default reasoning. / Computer Science / M.Sc. (Computer Science)

Thèse par articles. / La présente thèse fait état des avancées en logique déontique et propose des outils formels pertinents à l'analyse de la validité des inférences légales. D'emblée, la logique vise l'abstraction de différentes structures. Lorsqu'appliquée en argumentation, la logique permet de déterminer les conditions de validité des inférences, fournissant ainsi un critère afin de distinguer entre les bons et les mauvais raisonnements. Comme le montre la multitude de paradoxes en logique déontique, la modélisation des inférences normatives fait cependant face à divers problèmes. D'un point de vue historique, ces difficultés ont donné lieu à différents courants au sein de la littérature, dont les plus importants à ce jour sont ceux qui traitent de l'action et ceux qui visent la modélisation des obligations conditionnelles. La présente thèse de doctorat, qui a été rédigée par articles, vise le développement d'outils formels pertinents à l'analyse du discours juridique. En première partie, nous proposons une revue de la littérature complémentaire à ce qui a été entamé dans Peterson (2011). La seconde partie comprend la contribution théorique proposée. Dans un premier temps, il s'agit d'introduire une logique déontique alternative au système standard. Sans prétendre aller au-delà de ses limites, le système standard de logique déontique possède plusieurs lacunes. La première contribution de cette thèse est d'offrir un système comparable répondant au différentes objections pouvant être formulées contre ce dernier. Cela fait l'objet de deux articles, dont le premier introduit le formalisme nécessaire et le second vulgarise les résultats et les adapte aux fins de l'étude des raisonnements normatifs. En second lieu, les différents problèmes auxquels la logique déontique fait face sont abordés selon la perspective de la théorie des catégories. En analysant la syntaxe des différents systèmes à l'aide des catégories monoïdales, il est possible de lier certains de ces problèmes avec des propriétés structurelles spécifiques des logiques utilisées. Ainsi, une lecture catégorique de la logique déontique permet de motiver l'introduction d'une nouvelle approche syntaxique, définie dans le cadre des catégories monoïdales, de façon à pallier les problèmes relatifs à la modélisation des inférences normatives. En plus de proposer une analyse des différentes logiques de l'action selon la théorie des catégories, la présente thèse étudie les problèmes relatifs aux inférences normatives conditionnelles et propose un système déductif typé. / The present thesis develops formal tools relevant to the analysis of legal discourse. When applied to legal reasoning, logic can be used to model the structure of legal inferences and, as such, it provides a criterion to discriminate between good and bad reasonings. But using logic to model normative reasoning comes with some problems, as shown by the various paradoxes one finds within the literature. From a historical point of view, these paradoxes lead to the introduction of different approaches, such as the ones that emphasize the notion of action and those that try to model conditional normative reasoning. In the first part of this thesis, we provide a review of the literature, which is complementary to the one we did in Peterson (2011). The second part of the thesis concerns our theoretical contribution. First, we propose a monadic deontic logic as an alternative to the standard system, answering many objections that can be made against it. This system is then adapted to model unconditional normative inferences and test their validity. Second, we propose to look at deontic logic from the proof-theoretical perspective of category theory. We begin by proposing a categorical analysis of action logics and then we show that many problems that arise when trying to model conditional normative reasoning come from the structural properties of the logic we use. As such, we show that modeling normative reasoning within the framework of monoidal categories enables us to answer many objections in favour of dyadic and non-monotonic foundations for deontic logic. Finally, we propose a proper typed deontic system to model legal inferences.