Structures for Epistemic Logic

Epistemic modal logic in a narrow sense studies and formalises reasoning about knowledge. In a wider sense, it gives a formal account of the informational attitude that agents may have, and covers notions like knowledge, belief, uncertainty, and hence incomplete or partial information. As is so often the case in modal logic, such formalised notions become really interesting when studied in a broader context. When doing so, epistemic logic in a wider sense in fact relates to most of the other chapters in this book. What if we add a notion of time or action (Chapter 21): how does an agent revise its beliefs (cf. Chapter 8), or update its knowledge (Chapter 7)? And even if we fix one of the notions of interest, say knowledge, if there are many agents, how can we ascribe some level of knowledge to the group, and how do we represent knowledge of one agent about the knowledge (or ignorance, for that matter) of another (cf. Section 2.1)? What are reasonable requirements on the interaction between knowledge and strategic action (Chapter 15), and how is uncertainty dealt with in more general, qualitative models of agency (Chapter 12)? Hintikka, notably through [66], is broadly acknowledged as the father of modern epistemic modal logic. Indeed, [66] gives an account of knowledge and belief based on Kripke models. In a nutshell, crucial for this semantics is the notion of a set of states or worlds, together with a binary relation for each agent, determining which worlds ‘look the same’, for the agent, or ‘carry the same information’. Many disciplines realised the importance of the formalisation of knowledge, using Kripke semantics (or a close relative of it)