 A search for the distinct role of diagrams has led researchers to explore the differences among different forms of external or internal representations, and mainly between diagrammatic and sentential representations. Many important results have been produced in cognitive science. Starting from Larkin and Simon’s classic case study  (1987)  to illustrate a difference between informational and computational equivalence among representation systems, Lindsay’s work locates where this computational difference lies, which he calls a ‘non-deductive’ method. As briefly pointed out above, this inference process is called ‘free ride’ by Barwise and Shimojiima  (1995),  i.e., the kind of an inference in which the conclusion seems to be read off automatically from the representation of premises. In Gurr, Lee, and Stenning  (1998)  and Stenning and Lemon  (2001),  there is an explanation of the uniqueness of diagrammatic inference in terms of a degree of ‘directness’ of interpretation, and it is argued that this property is relative, and hence that “some rides are cheaper than others”. Having the role of graphs in mind, Wang and Lee  (1993)  present a formal framework as a guideline for correct visual languages. At this point, we are very close to applied aspects of research in multi-modal reasoning—design theory and AI research—by providing these disciplines with computational support for visual reasoning.