Source: Notre Dame J. Formal Logic Volume 53, Number 1
(2012), 27-52.
In several articles, Mumma has presented a formal diagrammatic system Eu
meant to give an account of one way in which Euclid's use of diagrams in the
Elements could be formalized. However, largely because of the way in
which it tries to limit case analysis, this system ends up being inconsistent,
as shown here. Eu also suffers from several other problems: it is unable
to prove several wide classes of correct geometric claims and contains a
construction rule that is probably computationally intractable and that may not
even be decidable.
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References
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