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We explore an interpretation of FVEL, a four-valued logic of evidence, where states represent agents, the propositional layer corresponds to the evidence available to these agents, and the relation corresponds to peerhood connections between them. Belief is determined based on the agent's evidence, but also on her peers' evidence. Consolidation functions are proposed, which map evidence situations to belief attitudes. We adapt some postulates of Social Choice Theory to our belief formation setting and, with them, we separate rational from irrational consolidations. We define a dynamic operator for addition and removal of evidence, which serves as a basis for some essential dynamic postulates and also for future developments on consolidations that take amounts of evidence into account. Our main technical result is a characterisation of a class of consolidations satisfying most of our rationality postulates.

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My experience in the Master's was pleasing for the most part, and as such I think I owe some people their credit.In first place, I must say that I am very grateful to my advisor, professor Renata, who has guided me with all support needed to complete this Master's. She has a remarkable combination of wisdom and kindness which are unparalleled. Likewise, I need to thank my co-advisor, professor Márcio, whose ideas and insights have been always appropriate and who has helped me with important suggestions and corrections. I also want to express my gratitude to professors Marcelo Finger, Flávio Soares, Leliane de Barros and Eduardo Fermé, who have given me relevant advice. I also would like to thank Glauber de Bona, who participated in some discussions with us and found an application in his work for the theory developed here.Next, I want to thank my friends and colleagues from LIAMF, who have helped me to enjoy a good time these two years, and have also discussed with me some matters about my project, without which the quality of this work would not be the same. I am glad to have had the opportunity to meet such awesome friends. I must thank CNPq for the financial support and USP for the opportunity, and all the people who pay their taxes and believe in public education.Last, I want to thank my family, for, despite having not much to do directly with this project, without them I would not even be here to start it.iii iv Abstract Belief Revision addresses the problem of how to change epistemic states, usually represented in the literature by sets of logical sentences. Solid theoretical results were consolidated with the AGM paradigm, which deals with theories (logically closed sets of sentences). After that, the theory was extended to belief bases, that is, arbitrary sets of sentences. Besides all this theoretical framework, AI researchers face serious difficulties when trying to implement belief revision systems. One of the major complications is the closure required by AGM theory, which cannot be easily computed.Even belief bases, which do not require closure, seem to be improper for practical purposes, since their changes are usually very rigid (syntax dependent).Some operations, known as pseudo-contractions, are in the middle ground between belief set change and belief base change. In the present work we have proposed a new pseudo-contraction operation, studied its properties and characterized it. We have also found connections between this operator and some other pseudo-contractions.Keywords: belief revision, pseudo-contractions. v vi ResumoRevisão de Crenças aborda o problema de como alterar estados epistêmicos, normalmente representados na literatura como conjuntos de sentenças lógicas. Resultados teóricos sólidos foram consolidados com o paradigma AGM, que lida com teorias (conjuntos de sentenças logicamente fechados). Depois disso, a teoria foi estendida para bases de crenças, isto é, conjuntos arbitrários de sentenças. Apesar de todo esse arcabouço teórico, pesquisadores de IA enfrentam sérias dificuldades ...

Epistemic logic is usually employed to model two aspects of a situation: the factual and the epistemic aspects. Truth, however, is not always attainable, and in many cases we are forced to reason only with whatever information is available to us. In this paper, we will explore a four-valued epistemic logic designed to deal with these situations, where agents have only knowledge about the available information (or evidence), which can be incomplete or conflicting, but not explicitly about facts. This layer of available information or evidence, which is the object of the agents' knowledge, can be seen as a database. By adopting this sceptical posture in our semantics, we prepare the ground for logics where the notion of knowledge-or more appropriately, belief-is entirely based on evidence. The technical results include a set of reduction axioms for public announcements, correspondence proofs, and a complete tableau system. In summary, our contributions are twofold: on the one hand we present an intuition and possible application for many-valued modal logics, and on the other hand we develop a logic that models the dynamics of evidence in a simple and intuitively clear fashion. Keywords Many-valued logics • Epistemic logic • Paraconsistent logics • Public announcements • Multi-agent systems • Evidence ments that greatly improved this work. I am very grateful to the anonymous reviewers as well, who gave me very detailed and useful feedback. I would also like to thank my colleagues from the RUG who participated in a discussion of a preliminary version of this paper, and all those present at the LIRa seminar in the ILLC/UvA who gave me very relevant suggestions. Research supported by Ammodo KNAW project "Rational Dynamics and Reasoning".