A crucial problem of conflict management is that whatever happens in negotiations will be interpreted and framed by stakeholders based on their different belief-value systems and world views. This problem will be discussed in the first part of this article as the main cognitive problem of conflict management. The second part develops a general semiotic solution of this problem, based on Charles Peirce's concept of "diagrammatic reasoning." The basic idea is that by representing one 's thought in diagrams, the conditions that determine interpretations can become visible, we can "experiment" with them, and we can change them eventually. The third part, finally, focuses on a concrete tool, called Logical Argument Mapping (LAM), that can be used in conflict management to perform such diagrammatic reasoning and to cope with the cognitive problems discussed in the first part. The Israeli-Palestinian conflict on the sovereignty over Jerusalem will be used as an example to show how LAM could work in practice.