Naming and Identity in Epistemic Logics Part I: The Propositional Case

Modal epistemic logics for many agents often assume a fixed one-to-one correspondence between agents and the names for agents that occur in the language. This assumption restricts the applicability of any logic because it prohibits, for instance, anonymous agents, agents with many names, named groups of agents, and relative (indexical) reference. Here we examine the principles involved in such cases, and give simple propositional logics that are expressive enough to cope with them all.