On the Expressivity of Byzantine Diagrams in Logic

‘Byzantine logic diagrams’ have been used since at least late antiquity, and became popular in Europe in the 16th century. However, since the criticism of W. Hamilton and J. Venn in the 19th century, Byzantine diagrams have been largely dismissed as obsolete. This paper challenges this prevailing view. Initially, we provide a comprehensive overview of the current state of research pertaining to these diagrams, illustrating their applicability in analyzing assertoric syllogisms. Subsequently, we propose that the expressive capacity of these diagrams extends far beyond their traditional use. In particular, we demonstrate that the expressivity of these diagrams is not limited to checking the validity of syllogisms. Rather, we show that there are various extensions of Byzantine diagrams, including opposition relations, modal logic, particular instances, n-term diagrams and logical connectives. These extensions are compositional and can therefore be combined to create very complex Byzantine diagrams that go far beyond what has been commonly believed since Hamilton and Venn.