A Taxonomy of the Greimas Square

Abstract

In this article I introduce the semiotic square by A.J. Greimas and the notions of negation and opposition that were central to the Paris School of structural semiotics. I trace the connection of the square to both Aristotle’s square of opposition and the Klein four-group as well as propose a formalization of the square. This is first achieved through identifying R-relations on meta-term/seme pairs of the square, then applying lattice theory and formal concept analysis in order to visualize an extended structure. The main result is a protoconcept algebra that generalizes the Greimas square through Boolean operations and provides an ordering of all possible formal concepts, thereby acting as a taxonomy.

Keywords

• semiotic square
• A.J. Greimas
• formal concept analysis
• Boolean concept logic