Aristotle already observed that logical relations apply between expressions containing adjectives. For instance, the relation of contrariety holds between the sentences in (1): they cannot both be true at the same time, but they can both be false at the same time, namely when (2) is true.
(1) a. Socrates is tall.
(1) b. Socrates is short.
(2) Socrates is neither tall nor short.
In this talk, I will demonstrate that the four Aristotelian relations (contrariety, contradictoriness, subalternation and subcontrariety) are fundamental to adjectival lexical fields. The relations uncover the internal organisation of adjectival fields and provide insights into how they are generated. More specifically, I will first develop a model using standard logic that computes all logically possible concepts in a given field. A second model, involving natural logic, predicts which of these concepts are actually realised in natural language. These models are then visualised using 3D diagrams that give a straightforward representation of the intricate relations inside a lexical field.http://www.krowland.net/diamondstructure