Abstract Graph theory proved to be a quite powerful mathematical tool model several problems in discrete setting. In this paper the authors illustrate how general graph framework can used multi-dimensional alternatives decision processes three different contexts: social choice, judgment aggregation and automata decisions.

We explore the social context of mathematical knowledge: Even though, the community of mathematicians may look homogeneous from the outside, it is actually structured into various sub-communities that differ in preferred notations, the choice of basic assumptions, or e.g. in the choice of motivating examples. We contend that we cannot manage mathematical knowledge for human recipients if we do ...