Argumentation-based negotiation (ABN) provides agents with an effective means to resolve conflicts within a multi-agent society. However, to engage in such argumentative encounters the agents require the ability to generate arguments, which, in turn, demands four fundamental capabilities: a schema to reason in a social context, a mechanism to identify a suitable set of arguments, a language and a protocol to exchange these arguments, and a decision making functionality to generate such dialogues. This paper focuses on the first two issues and formulates models to capture them. Specifically, we propose a coherent schema, based on social commitments, to capture social influences emanating from the roles and relationships of a multi-agent society. After explaining how agents can use this schema to reason within a society, we then use it to identify two major ways of exploiting social influence within ABN to resolve conflicts. The first of these allows agents to argue about the validity of each other's social reasoning, whereas the second enables agents to exploit social influences by incorporating them as parameters within their negotiation. For each of these, we use our schema to systematically capture a comprehensive set of social arguments that can be used within a multi-agent society.