Argumentation and problem-solving networks

Mathematical knowledge is not only shared and communicated by passing on proofs, but proofs are also used to convince that a certain theorem is true. To model this aspect, we propose to explore the so-called argumentation networks and problem-solving networks that were mainly developed by researchers in Artificial Intelligence (see Dung (1995)). Groundbreaking work has already been done very recently, see Pease & Aberdein (2011), and it shows clearly that the incorporation of insights from argumentation theory is a natural move, and the adoption of formal models of that allow us to represent and study the interaction between arguments and counter-arguments (arguments can be stronger or weaker, can reinforce each other, or oppose each other) follows immediately.