Diagrams are widely used in reasoning about problems in physics,
mathematics and logic, but have traditionally been considered to be
only heuristic tools and not valid elements of mathematical proofs.
This book challenges this prejudice against visualisation in the
history of logic and mathematics and provides a formal foundation
for work on natural reasoning in a visual mode. The author presents
Venn diagrams as a formal system of representation equipped with
its own syntax and semantics and specifies rules of transformation
that make this system sound and complete. The system is then
extended to the equivalent of a first-order monadic language. The
soundness of these diagrammatic systems refutes the contention that
graphical representation is misleading in reasoning. The validity
of the transformation rules ensures that the correct application of
the rules will not lead to fallacies. The book concludes with a
discussion of some fundamental differences between graphical
systems and linguistic systems. This groundbreaking work will have
important influence on research in logic, philosophy and knowledge
representation.
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