 The representational use of the spatial relations in the plane constrains diagrammatic representation, and therefore reasoning with diagrams, in certain important ways. In particular, there are topological and geometrical (let us lump them together as “spatial”) properties of diagrammatic objects and relations which limit the expressive power of diagrammatic systems. For instance, in graph theory it is known that some simple structures cannot be drawn in the plane. For example, the graph K5 is the graph consisting of 5 nodes, each joined to the other by an arc. This graph is non-planar, meaning that it cannot be drawn without at least two of the arcs crossing. This is just the sort of constraint on possible diagrams that limits the expressive power of diagrammatic systems. Now, since diagrammatic reasoning can occur by enumeration of all possible models of a situation, this representational inadequacy (a type of incompleteness) renders many diagrammatic systems incorrect if they are used for logical reasoning (e.g., see the critique of Englebretsen  1992  in Lemon &amp; Pratt  1998).