Naming and identity in epistemic logic part II: a first-order logic for naming

Modal epistemic logics for many agents sometimes ignore or simplify the distinction between the agents themselves, and the names these agents use when reasoning about each other. We consider problems motivated by practical computer science applications, and show that the simplest theories of naming are often inadequate. The issues we raise are related to some well-known philosophical concerns, such as indexical descriptions, de re knowledge, and the problem of referring to nonexistent objects. However, our emphasis is on epistemic logic as a descriptive tool for distributed systems and artificial intelligence applications, which leads to some nonstandard solutions. The main technical result of this paper is a first-order modal logic, specified both axiomatically and semantically (by a variant of possible-worlds semantics), that is expressive enough to cope with all the difficulties we discuss.