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

Dynamic Graded Epistemic Logic

International audienceGraded epistemic logic is a logic for reasoning about uncertainties. Graded epistemic logic is interpreted on graded models. These models are generalizations of Kripke models. We obtain completeness of some graded epistemic logics. We further develop dynamic extensions of graded epistemic logics, along the framework of dynamic epistemic logic. We give an extension with public announcements, i.e., public events, and an extension with graded event models, a generalization also including nonpublic events. We present complete axiomatizations for both logics

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

Comparing strengths of beliefs explicitly

Inspired by a similar use in provability logic, formulas p > B q and p ≥ B q are introduced in the existing logical framework for discussing beliefs to express that the strength of belief in p is greater than (or equal to) that in q. Besides its usefulness in studying the properties of the concept of greater strength of belief itself this explicit mention of the comparison in the logical language aids in defining several other concepts in a uniform way, namely, older and rather clear concepts like the operators for universality (the totality of possibilities considered by an agent), together with newer notions like plausibility (in the sense of ‘more plausible than not’) and disbelief. Relative expressive powers of the proposed logics are also discussed. A major role is played in our investigations by the relationship between the standard plausibility ordering of the worlds and the strength of belief ordering. If we try to define the strength of belief ordering in terms of the world plausibility ordering we get some undesirable consequences, so we have decided to keep the relation between the two orderings as light as possible to construct a system that allows for widely different interpretations. In fact, we start with considering these orderings to be independent of each other and towards the end we provide a discussion on their possible inter-relationship. Finally, we provide an extension of the framework to the multi-agent setting, and we discuss the possibilities of extending our system to a dynamic one