Playing with knowledge and belief

This thesis contributes to the development of Soft Dynamic Epistemic Logic (Soft DEL). Soft DEL has been introduced to deal with a number of informational phenomena, including belief revision. The work in this thesis extends the scope of Soft DEL 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 DEL 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 as the Gettier problem. This thesis also connects Soft DEL 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 DEL. 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.