 Challenging a long-standing prejudice against diagrammatic representation, those working on multi-modal reasoning have taken different kinds of approaches which we may categorize into three distinct groups. One branch of research can be found in philosophy of mind and cognitive science. Since the limits of linguistic forms are clear to those who have been working on mental representation and reasoning, some philosophers and cognitive scientists have embraced this new direction of multi-modal reasoning with enthusiasm and have explored human reasoning and mental representation involving non-linguistic forms (Cummins  1996;  Chandrasekaran et al.  1995).  Another strand of work on diagrammatic reasoning shows that there is no intrinsic difference between symbolic and diagrammatic systems as far as their logical status goes. Some logicians have presented case studies to prove that diagrammatic systems can be sound and complete in the same sense as symbolic systems. This type of result directly refuted a widely-held assumption that diagrams are inherently misleading, and abolished theoretical objections to diagrams being used in proofs (Shin  1994;  Hammer  1995a).  A third direction in multi-modal reasoning has been taken by computer scientists, whose interest is much more practical than those of the other groups. Not so surprisingly, those working in many areas in computer science—for example, knowledge representation, systems design, visual programming, GUI design, and so on—found new and exciting opportunities in this new concept of ‘heterogeneous system’ and have implemented diagrammatic representations in their research areas.