Consolidation of Belief in Two Logics of Evidence

Recently, several logics have emerged with the goal of modelling evidence in a more relaxed sense than that of justifications. Here, we explore two of these logics, one based on neighborhood models and the other being a four-valued modal logic. We establish grounds for comparing these logics, finding, for any model, a counterpart in the other logic which represents roughly the same evidential situation. Then we propose operations for consolidation, answering our central question: What should the doxastic state of a rational agent be in a given evidential situation? These operations map evidence models to Kripke models. We then compare the consolidations in the two logics, finding conditions under which they are isomorphic. By taking this dynamic perspective on belief formation we pave the way for, among other things, a study of the complexity, and an AGM-style analysis of rationality of these belief-forming processes

Iterative social consolidations:Forming beliefs from many-valued evidence and peers' opinions

Recently, several logics modelling evidence have been proposed in the literature. These logics often also feature beliefs. We call the process or function that maps evidence to beliefs consolidation. In this paper, we use a four-valued modal logic of evidence as a basis. In the models for this logic, agents are represented by nodes, peer connections by edges and the private evidence that each agent has by a four-valued valuation. From this basis, we propose methods of consolidating the beliefs of the agents, taking into account both their private evidence as well as their peers' opinions. To this end, beliefs are computed iteratively. The final consolidated beliefs are the ones in the point of stabilization of the model. However, it turns out that some consolidation policies will not stabilize for certain models. Finding the conditions for stabilization is one of the main problems studied here, along with other properties of such consolidations. Our main contributions are twofold: we offer a new dynamic perspective on the process of forming evidence-based beliefs, in the context of evidence logics, and we set up and address some mathematically challenging problems, which are related to graph theory and practical subject areas such as belief/opinion diffusion and contagion in multi-agent networks.</p

A Four-Valued Dynamic Epistemic Logic

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

Evidence-Based Beliefs in Many-Valued Modal Logics

Rational agents, humans or otherwise, build their beliefs from evidence – a process which we call consolidation. But how should this process be carried out? In this thesis, we study a multi-agent logic of evidence and the question how agents should form beliefs in this logic. The main contributions of this thesis are twofold. First, we present and study a many-valued modal logic, and show how it can be suitable for modelling multi-agent scenarios where each agent has access to some evidence, which in turn can be processed into beliefs. This is a technical and practical contribution to many-valued modal logics. Second, we open new paths for research in the field of evidence logics: we show a new approach based on many-valued logics, we highlight the concept of consolidations and the importance of looking at their dynamic nature, and build a methodology based on rationality postulates to evaluate them