Underlying mathematical structures in Aristotelian Diagrams
Corine Nijhof · 2018
In a recent paper, Lorenz Demey presents an algorithm to compute the maximal Boolean complexity of a family of Aristotelian diagrams. However, the underlying mathematical notions, involving partial orders extended with an involutive negation function, are hardly worked out. The purpose of this thesis is to provide a critical analysis of Demey’s paper and related work from a mathematical viewpoint. In a clear and understandable way, the theory of Aristotelian diagrams is connected to the mathematical notions of Hasse diagrams and Boolean algebras. Demey’s algorithm is rewritten and applied in several examples of Aristotelian families.