The Temporal Mind. Observations on the logic of belief change in interactive systems Cédric Dégremont Abstract: Modeling rational agents' reasoning in interactive contexts and identifying its logic is the general analytic project to which this dissertation contributes. The borders of this project run through economics, computer science and philosophy. It includes several theoretical lines that we are connecting. Interactive epistemology is the study of interactive reasoning: how agents entertain beliefs and reason about the beliefs of other agents. Formal learning theory is the study of the conditions under which agents can reach stable beliefs or identify a correct hypothesis from a stream of data. Epistemic game theory is a theory of how rational agents would make decisions based on their beliefs in strategic interactive situations. In all these systems, beliefs, interactive beliefs, and their evolution as informational processes unfold are at stake. This dissertation connects these themes by developing one single logical framework. For this purpose, we are operating at the interface of two major logics of belief change: the temporal approach and the dynamic approach. Concretely, we connect and merge the two families of logics, first at a structural semantic level and then at a syntactic one. Subsequently, we apply the resulting system to analyze what happens to agents' beliefs over time when agents communicate, learn, interact, and reason interactively, inductively, or strategically. Chapter 2 identifies the main structural properties of belief revising agents over time, and Chapter 3 then formulates their main logical proof principles. This chiefly takes the form of semantic representation theorems, plus a completeness theorem for changing beliefs in a temporal logic that admits protocols. Chapter 4 identifies common belief of posteriors in suitable structures as a key sufficient condition for agents to agree, and iterated announcement of beliefs as a major way of reaching agreement. We also determine the right family of static and dynamic logics to reason about agreement, and find agreement results, invariance results, and concrete syntactic proofs of agreement results. Chapter 5 investigates the logical principles behind inductive learning and in particular behind the key notion of finite identifiability. This takes the form of a reduction of the problem of finite identifiability to a problem of model-checking for an epistemic temporal logic, plus further representation results. Chapter 6 takes the dynamic-temporal logical viewpoint to the building blocks of strategic reasoning: solution algorithms, rationality, equilibrium, and expectations, discussing the importance of belief change for the epistemic foundations of game theory. We are giving many concrete scenarios sketching a bigger picture. Chapter 7 completes the whole approach with two further key aspects of agency: preferences, and coalitional powers. We explore the logical expressive power demanded by notions imported in this area from social choice theory and cooperative and non-cooperative game theory, in terms of modal invariance and definability. Keywords: