Algebraic Aspects of Duality Diagrams

Duality phenomena are widespread in logic and language; their behavior is visualized using square diagrams. This paper shows how our recent algebraic account of duality can be fruitfully used to study these diagrams. A duality cube is constructed, and it is shown that 14 duality squares can be embedded into this cube (two of which were hitherto unknown). This number is also an upper bound.