An artificial social system is a set of restrictions of agents' behaviors in a multi-agent environment. Its role is to allow agents to coexist in a shared environment and pursue their respective goals in the presence of other agents. This paper argues that artificial social systems exist in practically every multi-agent system, and play a major role in the performance and effectiveness of the agents. We propose artificial social systems as an explicit and formal object of study, and investigate several basic issues that arise in their design.