Geometric and cognitive differences between logical diagrams for the Boolean algebra $\mathbb {B}_{4}$

Aristotelian diagrams are used extensively in contemporary research in artificial intelligence. The present paper investigates the geometric and cognitive differences between two types of Aristotelian diagrams for the Boolean algebra \(\mathbb {B}_{4}\). Within the class of 3D visualizations, the main geometric distinction is that between the cube-based diagrams (such as the rhombic dodecahedron) and the tetrahedron-based diagrams. Geometric properties such as collinearity, central symmetry and distance are examined from a cognitive perspective, focusing on diagram design principles such as congruence/isomorphism and apprehension. The cognitive effectiveness of the different visualizations is compared for the representation of implication versus opposition relations, and for subdiagram embeddings.