Using Multigraphs to Study the Interaction Between Opposition, Implication and Duality Relations in Logical Squares.

This paper uses multigraphs to study the interaction between opposition, implication and duality relations in classical and degenerate logical squares. We show, first of all, that opposition and implication are highly symmetrical in their interaction with each other. Secondly, opposition and implication also display a higher-order symmetry, in the sense that they fulfill highly similar roles in their respective interactions with duality. Thirdly, we show that all these symmetries hold for classical squares as well as for degenerate squares.