logical relations

This page provides the definitions of the various geometries (i.e. sets of logical relations) that we are investigating:

• Aristotelian Geometry,
• Opposition Geometry,
• Implication Geometry,
• Duality Geometry.

Aristotelian Geometry (AG)

The classical, informal definitions of the Aristotelian relations look as follows:

The contemporary, logic-dependent definitions of the Aristotelian relations look as follows:

The contemporary, algebraic definitions of the Aristotelian relations look as follows:

Opposition Geometry (OG)

The contemporary, logic-dependent definitions of the opposition relations look as follows:

Implication Geometry (IG)

The contemporary, logic-dependent definitions of the implication relations look as follows:

Duality Geometry (DG)

The contemporary, algebraic definitions of the duality relations look as follows: