Structures for epistemic logic

In this chapter we overview the main structures of epistemic and doxastic logic. We start by discussing the most celebrated models for epistemic logic, i.e., epistemic Kripke structures. These structures provide a very intuitive interpretation of the accessibility relation, based on the notion of information. This also naturally extends to the multi-agent case. Based on Kripke models, we then look at systems that add a temporal or a computational component, and those that provide a ‘grounded’ semantics for knowledge. We also pay special attention to ‘non-standard semantics’ for knowledge and belief, i.e., semantics that are not based on an underlying relation on the sets of states. In particular, we discuss here neighbourhood semantics and topological semantics. In all of these approaches, we can clearly point at streams of results that are inspired by work by Johan van Benthem. We are extremely pleased and honoured to be part of this book dedicated to his work and influences.