Playing with Knowledge and Belief
Virginie Fiutek

Abstract:
This thesis contributes to the development of Soft
Dynamic Epistemic Logic. Soft Dynamic Epistemic Logic has been introduced
to deal with a number of informational phenomena, including belief
revision. The work in this thesis extends the scope of Soft Dynamic
Epistemic Logic to belief contraction, providing as such a framework which
can now deal with belief change. This study of belief change contributes
also to the study of the notion of knowledge. Nowadays, one of the main
challenges in formal epistemology is to formally capture what is a correct
definition of knowledge. To tackle this issue we need to be able to formally
define the notions of evidence and justified true belief. In this thesis, we
extend Soft Dynamic Epistemic Logic such that it can indeed deal with the
notions of evidence and justification. In this context we provide a game
semantics for “defeasible knowledge”, offering a new formalization of K.
Lehrer’s concept of knowledge in terms of “undefeated justified acceptance”.
This setting provides a new perspective for analysing epistemological
problems such that the Gettier problem. This thesis also connects Soft
Dynamic Epistemic Logic to two different approaches that have been studied
in the literature. One of these other approaches is Dynamic Doxastic Logic,
as introduced by K. Segerberg. An important part of the work we have done,
compares Dynamic Doxastic Logic to Soft Dynamic Epistemic Logic. This
comparison makes it possible to investigate what are the differences and the
similarities between these two approaches. Finally we connect our work to
the argumentative study of belief revision, offering an investigation of
belief dynamics in a dynamic argumentative setting.

Chapter 2 presents a number of different settings of belief change that have
been studied in the literature.

Chapter 3 introduces three notions of belief contraction that we choose
from the literature: severe withdrawal, moderate contraction and
conservative contraction. We define the corresponding belief contracting
operations as operations on total plausibility models and axiomatize each
of them in *DEL* style.

In chapter 4 we introduce the new framework of justification models as a
general setting to model the information and evidence an agent has. We
formally define what is a sound (true) argument and what is a justification.

Chapter 5 introduces the informal theory of knowledge of K. Lehrer as a
solution to the Gettier problem and proposes a game semantics that
formalises the notion of defeasible knowledge of K. Lehrer. Our
ultra-justification game formally determines if an agent defeasibly knows a
proposition (or merely believes but does not know this proposition): an
agent (the Claimant) defeasibly knows a proposition *P* iff she has a
winning strategy in the ultra-justification game corresponding to the claim
*P*.

Chapter 6 compares Dynamic Doxastic Logic and Dynamic Epistemic Logic,
studying *full DDL* from the perspective of *Soft DEL*. We provide several
versions of *DDL* internalizing different belief revision operations, as
well as several operations of expansion and contraction, showing that the
*DDL* approach is at least as powerful as the *DEL* approach.

Chapter 7 introduces the branching-time belief revision logic of G. Bonanno
and provides an argumentative study of this belief revision logic. We use
the dialogical approach to logic and provide the language as well as the
rules of our dialogical system of belief revision. We focus on the
dialogical interpretation of the notions of belief and information.