Diagrams have been widely used in reasoning, for example, in solving problems in physics, mathematics, and logic. Mathematicians, psychologists, philosophers, and logicians have been aware of the value of diagrams and, moreover, there has been an increase in the research on visual representation. Many interesting and important issues have been discussed: the distinction, if any, between linguistic symbols and diagrams, the advantages of diagrams over linguistic symbols, the importance of imagery to human reasoning, diagrammatic knowledge representation (especially in artificial intelligence systems), and so on.

The work presented in this book was mainly motivated by the fact that we use diagrams in our reasoning. Despite the great interest shown in diagrams, nevertheless a negative attitude toward diagrams has been prevalent among logicians and mathematicians. They consider any nonlinguistic form of representation to be a heuristic tool only. No diagram or collection of diagrams is considered a valid proof at all. It is more interesting to note that nobody has shown any legitimate justification for this attitude toward diagrams. Let me call this traditional attitude, that is, that diagrams can be only heuristic tools but not valid proofs, the general prejudice against diagrams. This prejudice has been unquestioned even when proponents of diagrams have worked on the applications of diagrams in many areas and argued for the advantages of diagrams over linguistic symbols. This is why it is quite worthwhile to question the legitimacy of this prejudice, that is, whether this prejudice is well grounded or not.