Belief and Degrees of Belief

Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent's degree of belief for a particular proposition, the higher her confidence in the truth of that proposition. For instance, Sophia's degree of belief that it will be sunny in Vienna tomorrow might be .52, whereas her degree of belief that the train will leave on time might be .23. The precise meaning of these statements depends, of course, on the underlying theory of degrees of belief. These theories offer a formal tool to measure degrees of belief, to investigate the relations between various degrees of belief in different propositions, and to normatively evaluate degrees of belief.\ud \ud The purpose of this book is to provide a comprehensive overview and assessment of the currently prevailing theories of degrees of belief. Degrees of belief are primarily studied in formal epistemology, but also in computer science and artificial intelligence, where they find applications in so-called expert systems and elsewhere. In the former case the aim is to adequately describe and, much more importantly, to normatively evaluate the epistemic state of an ideally rational agent. By employing the formal tools of logic and mathematics theories of degrees of belief allow a precise analysis that is hard to come by with traditional philosophical methods.\ud \ud Different theories of degrees of belief postulate different ways in which degrees of beliefs are related to each other and, more generally, how epistemic states should be modeled. After getting a handle on the objects of belief in section 2, we briefly survey the most important accounts in section 3. Section 4 continues this survey by focusing on the relation between belief and degrees of belief. Section 5 concludes this introduction by pointing at some relations to belief revision and nonmonotonic reasoning