Agents Homogeneous: A Procedurally Anonymous Semantics Characterizing the Homogeneous Fragment of ATL

Abstract

In many multi-agent scenarios we encounter homogeneous groups of agents; agents that have the same actions available, and for which the system does not care who performs a given action, but only cares about how many agents perform it. Sometimes homogeneity is a descriptive fact, arising from a lack of interest in agents’ identity, or the fact that we are simply unable to distinguish between them. Other times, it is a normative requirement, for instance in the context of voting, where we do not want the outcome to depend on who voted for what, only on how many votes each candidate receives. Another important notion is anonymity, which also often arise in multi-agent scenarios, either because we do not know an agent’s identity, or else because the systems comes with an explicit commitment to ensure that this information is kept secret. Clearly, the two notions are closely related, and in this paper we explore the relationship that exists between them within the framework of Alternating-time Temporal Logic. We add an homogeneity axiom to this logic, and proceed to show that the resulting logic, which we dub hatl, is sound and complete with respect to a class of structures that are both homogeneous and procedurally anonymous, meaning that no information whatsoever needs to be maintained about the actions of individual agents.