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A tabletop storytelling interface called a Narration Negotiation and Reconciliation Table allows disagreements to be visually represented:

Points of Disagreement… can be dragged onto any part of a story to explicitly denote disagreement without preventing the story from continuing.

From A Reflection on Using Technology for Reconciliation through Co-Narration (PDF) by Oliviero Stock, Massimo Zancanaro of FBK-irst, Italy and Chaya Koren, Zvi Eisikovitz, Patrice L. (Tamar) Weiss of University of Haifa, Israel. In the CHI2012 HCI for Peace workshop.
The mutltitouch table interface was tested for peace reconciliation work with Israeli-Jewish and Palestinian-Arab teen boys.

I’d love a screenshot. Quick searching turned up a project description and an (unrelated) discussion of the role of narrative in reconciliation. I excerpt:

The textbooks juxtaposed both historical narratives on the same page: on the right side of the page, the Israeli narrative began with the birth of Zionism in the 19th century; on the left, the Palestinian narrative commenced with Napolean’s plans to establish a Jewish state in Palestine. Historical events faced off like soldiers in trenches; and while students were scrutinizing their positions, they were simultaneously recongnizing their own involvement in the conflict. This, of course, was an intended pedagogical tool carefully thought out by the authors of the book.

From Political Reconciliation and Narrative Negotiation (PDF): by Nadim Khoury of the Department of Politics at the University of Virginia.

This points out the obvious: reconciliation first requires understanding and externally representing the disagreements. Rooting out the disagreement in mundane situations discussed online, and providing representations for them, are a big part of my current work.