Philosophical Logic and Formal Epistemology</p> <h2>Philosophical Logic and Formal Epistemology</h2> <p>One of the central problems in formal epistemology is to develop exact formalisms capable of representing knowledge, belief, conditional belief, and belief change.</p> <p>We will start with the modal approach to represent knowledge and belief, which derives from the early work of Hintikka, Kripke and Aumann. This approach has been quite influential and has been applied in many areas like computer science and game theory. Nonetheless, we will see that this approach is limited in many ways. Among other things, we will see that it cannot accommodate influential philosophical accounts of knowledge (like Nozick's) and that many interesting doxastic operators (like "it is highly probable that...") cannot be adequately formalized with the traditional tools of epistemic logic.</p> <p>We will consider a semantic alternative to Kripke models deriving from the work of D. Scott and R. Montague in the 60's: neighborhood models. The alternative approach to epistemic semantics is quite flexible and general. We will consider various applications, and we will extend the usual presentation of neighborhood semantics to the first order case, proving a general completeness result capable of unifying the entire class of classical modal logics.</p> <p>The second influential formal model of belief and belief change is probabilistic in nature. We will review some of the basic building blocks of contemporary Bayesian epistemology, focusing on the following problems: <ul> <li>Is it possible to offer a unified Bayesian account of qualitative belief circumventing the usual paradoxes (like the paradox of the lottery and the paradox of the preface)? <li>Is it possible to use conditionlization as a learning rule? <li>Is it possible to extend the Bayesian account to represent cases of belief revision and contraction? </ul></p> <p>The last problem will lead us to recent work in the field of belief revision. We will consider recent work on belief change focusing on the applications of techniques from rational choice to characterize belief change operators. We will conclude by considering a family of open problems and philosophical puzzles inspired by recent work in formal epistemology.</p>