 As discussed above, much of the interest in diagrams has been generated by the claim that they are somehow more “effective” than traditional logical representations for certain types of task. Certainly, for example, a map is a greater aid to navigation than a verbal description of a landscape. However, while there are certainly psychological advantages to be gained through the use of diagrams, they are (as in the case of Euler Circles) often ineffective as representations of abstract objects and relationships. Once a purely intuitive notion, non-psychological claims about “efficacy” of diagrammatic systems can be examined in terms of standard formal properties of languages (Lemon et al.  1999).  In particular, many diagrammatic systems are self-consistent, incorrect, and incomplete, and complexity of inference with the diagrams is NP-hard. By way of contrast, most sentential logics, while able to express inconsistencies, are complete and  correct[8]  .