Principles of Knowledge, Belief and Conditional Belief

International audienceWe review and examine in this paper the validity of the different axioms (and inference rules) of knowledge and belief and relating knowledge to belief which have been proposed in the epistemic !epistemic logic literature. In doing so, we encounter many of the problems that epistemic !epistemic logic has had to face in its relatively short (modern) history and provide relevant pointers for more details. We also contribute to this area by providing conditions under which the notion of belief can be formally defined in terms of knowledge , and vice versa. We also prove that certain convoluted axioms dealing only with the notion of knowledge can be derived from understandable interaction axioms relating knowledge and conditional belief