The Aristotelian “square of oppositions” is at the centre of recent developments in the geometry of logic. The image below is a modified representation of the logical tetra-icosahedron defined by Regis Pellisier [2004, 2009]. I have moved the nodes and edges around to better show the standard logical square (depicted in red).
The labels “Immediate”, “Present”, “Real”, “Normal”, “Valid” and “Ideal” correspond to my usage of the six vertices of the logical hexagon built around the standard Aristotelian square. These (provisional) terms apply to my six-level model of decision and action logics.
Each “label” corresponds to one sub-logic or discourse. For example, the “Present” sub-logic corresponds to the “Protect” perspective in the security disciplines. See the four Security Perspectives here:
The Aristotelian Square and the Logical Hexagon: Mapping the Logic of Action