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: