 Logical reasoning with diagrams is often carried out in virtue of their depiction of all possible models of a situation, up to topological equivalence of the diagrams (this, of course, depends on the particular diagrammatic system in use). A single diagram is often an abstraction over a class of situations, and once a suitable diagram has been constructed, inferences can simply be read off the representation without any further manipulation. In some diagrammatic systems (e.g., Euler Circles) inference is carried out by constructing diagrams correctly and reading information off them. The complexity of using inference rules in a symbolic logic is, in these cases, replaced by the problem of drawing particular diagrams  correctly.[5]  For instance, an Euler Circles diagram ventures to capture relationships between sets using topological relationships between plane regions in such a way that that it depicts all the possible ways that a certain collection of set-theoretic statements could be true. This has two important consequences: (1) if a certain diagram cannot be drawn then the described situation must be impossible (termed “self-consistency”), and (2) if a certain relationship between diagram objects must be drawn, then the corresponding relation can be inferred as logically valid. (See the numerous examples in  Section 2.)  This phenomenon is often termed a “free-ride” (Barwise &amp; Shimojima  1995).  This style of diagrammatic reasoning is thus dependent on a particular representational use of diagrams—that they represent classes of models. If a particular class of models cannot be represented by a diagrammatic system, then those cases will not be taken into account in inferences using the system, and incorrect inferences might be drawn. This fact makes the representational adequacy of diagrammatic systems, restricted by their spatial nature, of paramount importance, as we shall now explore.