Translational embeddings in modal logic

Often when we do philosophy we want to define less well understood notions with which we are concerned in terms of those which we have a much firmer grasp on. Hence, to take a classical example, we often try to define knowledge in terms of belief (and some auxiliary notions such as truth, justification and so on). Such definitions give rise to translations, functions which map the terms to be explained to their intended (simpler) explanation, and it is these which are our objects of study. In particular we will be focused on providing a systematic study of the formal uses of translations between logics, and what they can tell us about the logics involved. Our focus will be on propositional modal logics, both for reasons of explanatory simplicity, and also as modal logic remains one of the best formal tools we have for explicating a wide variety of live philosophical problems.