Euclid and beyond: towards a long-term history of deductivity

The deductive organization of Euclid’s Elements serves as a model for mathematical and scientific texts in a variety of subjects from antiquity through the early modern period, not only in the West but also in the Islamic world and beyond. The study of this tradition demands formal methods that will explicitly and unambiguously represent the deductive structures of given texts. This paper explores the creation of an ontology of proposition use within deductive texts and demonstrates graph theoretical models for visualizing and interpreting the structure of this ontology. Since the approach is language-independent, it is broadly applicable to any text in any language that makes use of the explicit deductive form exemplified by the Elements.