Knowledge-Based Asynchronous Programming

A knowledge-based program is a high-level description of the behaviour of agents in terms of knowledge that an agent must have before (s)he may perform an action. The definition of the semantics of knowledge-based programs is problematic, since it involves a vicious circle; the knowledge of an agent is defined in terms of the possible behaviours of the program, while the possible behaviours are determined by the actions which depend on knowledge. We define the semantics of knowledge-based programs via an iteration approach generalizing the well-known fixpoint construction. We propose a specific iteration as the semantics of a knowledge-based program, and justify our choice by a number of examples, including the Unexpected Hanging Paradox.