Modeling Relations

In ordinary representations of relations the order of the relata plays a structural role, but in the states of affairs or the facts themselves such an order often does not seem to be intrinsically present. An alternative way to represent relations makes use of positions for the arguments. This is no problem for the love relation, but for relations like the adjacency relation and cyclic relations, different assignments of objects to the positions can give exactly the same states. This is a puzzling situation. The question is, what is the ontological status of the positions, and, more generally, what is the internal structure of relations? In this thesis mathematical models for relations are developed, which provide more insight into the structure of relations “out there” in the real world.