When a set of autonomous agents are going to decide on a global plan, it may be difficult to determine whether the set of common goals is nonempty. Furthermore, even if the combined plan is consistent, it may be hard to determine the set of common goals. We present a formal framework for the analysis of conflicts in sets of autonomous agents restricted in the sense that they can be described by first-order formulae and transaction mechanisms. In this framework, we allow for enrichment of agent systems with correspondence assertions, expressing the relationship between different entities in the formal specifications of the agents. Thereafter the specifications are analysed with respect to conflictfreeness. If two specifications are conflictfree, the formulae of one specification together with the set of correspondence assertions do not restrict the models of the other specification, i.e. the agent system does not restrict the individual agents. The approach takes into account static as well as dynamic aspects of the concept of conflictfreeness.