Dans le cadre de cette thèse, nous présentons l’extension des résultats sur le raisonnement avec des bases de croyances totalement ordonnées au cas partiellement ordonné. L’idée est de raisonner avec des bases logiques équipées d’un ordre partiel exprimant la certitude relative et de construire une fermeture déductive partiellement ordonnée. Au niveau syntaxique, nous pouvons soit utiliser un langage exprimant des paires de formules et des axiomes décrivant les propriétés de l’ordre, ou utiliser des formules en relation avec des poids symboliques partiellement ordonnés dans l’esprit de la logique possibiliste. Une sémantique possible consiste à supposer que cet ordre provient d’un ordre partiel sur les modèles. Elle exige la capacité d’induire un ordre partiel sur les sous-ensembles d’un ensemble, à partir d’un ordre partiel sur ses éléments. Parmi plusieurs définitions de relations d’ordre partiel ainsi définies, nous sélectionnons la plus pertinente pour représenter la notion de certitude relative, en accord avec la théorie des possibilités. Nous montrons les limites d’une sémantique basée sur un ordre partiel unique sur les modèles et proposons une sémantique plus générale qui utilise une relation d’ordre partiel entre les ensembles de modèles. Nous utilisons un langage de plus haut niveau qui exprime des conjonctions de paires de formules en relation, avec des axiomes qui décrivent les propriétés de la relation. Nous proposons deux approches syntaxiques pour inférer de nouvelles paires de formules à partir d’une base partiellement ordonnée, et compléter ainsi l’ordre sur le langage propositionnel. L’une des inférences est proche des logiques conditionnelles de Lewis (qui traite le cas totalement ordonné) et d’un travail de Halpern. Elle est également proche du Système P. Nous reprenons la logique possibiliste symbolique proposée par Benferhat et Prade et comparons cette approche avec l’approche par certitude relative. Pour cela nous poursuivons l’étude de la logique possibiliste symbolique en démontrant un résultat de complétude. Nous étudions la question de la traduction d’une base partiellement ordonnée en base possibiliste symbolique et inversement. Nous proposons enfin des pistes pour une implémentation du système d’inférence de certitude relative et du système possibiliste symbolique. / In this thesis, we present results on the extension of the existing methods for reasoning with totally ordered belief bases to the partially ordered case. The idea is to reason from logical bases equipped with a partial order expressing relative certainty and to construct a partially ordered deductive closure. The difficult part lies in the fact that equivalent definitions in the totally ordered case are no longer equivalent in the partially ordered case. At the syntactic level we can either use a language expressing pairs of related formulas and axioms describing the properties of the ordering, or use formulas with partially ordered symbolic weights attached to them in the spirit of possibilistic logic. A possible semantics consists in assuming that the partial order on formulas stems from a partial order on interpretations. It requires the capability of inducing a partial order on subsets of a set from a partial order on its elements so as to extend possibility theory functions. Among different possible definitions of induced partial order relations, we select the one generalizing necessity orderings (closely related to epistemic entrenchments). We study such a semantic approach inspired from possibilistic logic, and show its limitations when relying on a unique partial order on interpretations. We propose a more general sound and complete approach to relative certainty, inspired by conditional modal logics, in order to get a partial order on the whole propositional language. Some links between our approach and several inference systems, namely conditional logic, modal epistemic logic and non-monotonic preferential inference are established. Possibilistic logic with partially ordered symbolic weights proposed by Benferhat and Prade is also revisited and we continue the study by proving a completeness result. A comparison with the relative certainty approach is made via mutual translations. We compare this approach with the relative certainty approach.We study the question of the translation of a partially ordered base into a symbolic possibilistic base and vice versa. The results for this translation highlight different assumptions underlying the two logics. We also offer steps toward implementation tools for the inference of relative certainty and for the symbolic possibilistic system.

A área de revisão de crenças estuda a forma como agentes racionais operam sobre seus conhecimentos, permitindo que estes evoluam à vista de novas informações. Muitas das formas de manipulação do conhecimento hoje utilizadas foram desenvolvidas tendo como base o paradigma estabelecido por Alchourrón, Gärdenfors e Makinson em 1985, que evoluiu nas últimas décadas sob influência de diversas correntes de pensamento, dando origem a múltiplas abordagens para a estruturação de operadores sobre crenças. Esta dissertação limita-se à análise das duas principais construções de operadores sobre bases de crenças, bem como suas propriedades e relações. A partir desta análise, foi construído um framework computacional que permitiu a análise empírica do comportamento destas construções em diversos casos gerados, de modo a averiguar a eficiência real dos algoritmos envolvidos. Também são expostos detalhes do framework, construído de forma flexível para permitir sua reutilização em trabalhos futuros. / Belief revision studies the ways rational agents change their beliefs, allowing them to evolve when exposed to new information. Many of the belief change forms currently used were developed based on the paradigm established by Alchourrón, Gärdenfors and Makinson in 1985, which evolved over the last decades under the influence of several distinct fields, originating multiple approaches to implement operators on beliefs. This dissertation is limited to the analysis of the two main constructions of operators on belief bases, including their properties and relations. Based on this analysis, a computational framework was created to allow the empirical analysis of the behavior of these constructions on generated scenarios, in order to measure the real eficiency of the algorithms concerned. It also describes the framework, built aiming for exibility in order to allow it\'s usage in future works.

This thesis consists in six articles and a comprehensive summary. • The pourpose of the summary is to introduce the AGM theory of belief change and to exemplify the diversity and significance of the research that has been inspired by the AGM article in the last 25 years. The research areas associated with AGM was divided in three parts: criticisms, where we discussed some of the more common criticisms of AGM. Extensions where the most common extensions and variations of AGM are presented and applications where we provided an overview of applications and connections with other areas of research. • Article I elaborates on the connection between partial meet contractions [AGM85] and kernel contractions [Han94a] in belief change theory. Also both functions are equivalent in belief sets, there are notequivalent in belief bases. A way to define incision functions (used in kernel contractions) from selection functions (used in partial meet contractions) and vice versa is presented. It is explained under which conditions there are exact correspondences between selection and incision functions so that the same contraction operations can be obtained by using either of them. • Article II proposes an axiomatic characterization for ensconcement-based contraction functions, belief base functions proposed byWilliams and relates this function with other kinds of base contraction functions. • Article III adapts the Fermé and Hansson model of Shielded Contraction [FH01] as well as Hansson et all Credibility-Limited Revision [HFCF01] for belief bases, to join two of the many variations of the AGM model [AGM85], i.e. those in which knowledge is represented through belief bases instead of logic theories, and those in which the object of the epistemic change does not get the priority over the existing information as it is the case in the AGM model. • Article IV introduces revision by comparison a refined method for changing beliefs by specifying constraints on the relative plausibility of propositions. Like the earlier belief revision models, the method proposed is a qualitative one, in the sense that no numbers are needed in order to specify the posterior plausibility of the new information. The method uses reference beliefs in order to determine the degree of entrenchment of the newly accepted piece of information. Two kinds of semantics for this idea are proposed and a logical characterization of the new model is given. • Article V focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. This essay proposes for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction,proposed by Hansson [Han94a] to construct classical AGM contractions and belief base contractions. • Article VI relates AGM model with the DFT model proposed by Carlos Alchourrón [Alc93]. Alchourrón devoted his last years to the analysis of the notion of defeasible conditionalization. His definition of the defeasible conditional is given in terms of strict implication operator and a modal operator f which is interpreted as a revision function at the language level. This essay points out that this underlying revision function is more general than AGM revision. In addition, a complete characterization of that more general kind of revision that permits to unify models of revision given by other authors is given. / QC 20110211

A área de revisão de crenças estuda a forma como agentes racionais operam sobre seus conhecimentos, permitindo que estes evoluam à vista de novas informações. Muitas das formas de manipulação do conhecimento hoje utilizadas foram desenvolvidas tendo como base o paradigma estabelecido por Alchourrón, Gärdenfors e Makinson em 1985, que evoluiu nas últimas décadas sob influência de diversas correntes de pensamento, dando origem a múltiplas abordagens para a estruturação de operadores sobre crenças. Esta dissertação limita-se à análise das duas principais construções de operadores sobre bases de crenças, bem como suas propriedades e relações. A partir desta análise, foi construído um framework computacional que permitiu a análise empírica do comportamento destas construções em diversos casos gerados, de modo a averiguar a eficiência real dos algoritmos envolvidos. Também são expostos detalhes do framework, construído de forma flexível para permitir sua reutilização em trabalhos futuros. / Belief revision studies the ways rational agents change their beliefs, allowing them to evolve when exposed to new information. Many of the belief change forms currently used were developed based on the paradigm established by Alchourrón, Gärdenfors and Makinson in 1985, which evolved over the last decades under the influence of several distinct fields, originating multiple approaches to implement operators on beliefs. This dissertation is limited to the analysis of the two main constructions of operators on belief bases, including their properties and relations. Based on this analysis, a computational framework was created to allow the empirical analysis of the behavior of these constructions on generated scenarios, in order to measure the real eficiency of the algorithms concerned. It also describes the framework, built aiming for exibility in order to allow it\'s usage in future works.