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The semiotic square, also known as the Greimas square, is a tool used in structural analysis of the relationships between semiotic signs through the opposition of concepts, such as feminine-masculine or beautiful-ugly, and of extending the relevant ontology.

The semiotic square, derived from Aristotle's logical square of opposition, was developed by Algirdas J. Greimas, a Lithuanian-French linguist and semiotician, who considered the semiotic square to be the elementary structure of meaning.

Greimas first presented the square in Semantique Structurale (1966), a book which was later published as Structural Semantics: An Attempt at a Method (1983). He further developed the semiotic square with Francois Rastier in "The Interaction of Semiotic Constraints" (1968).

Basic structure

The Greimas square is a model based on relationships:

Structure	Relationship Type	Relationship Elements
Complex	Contrary	S₁ + S₂
Neutral	Contrary	~S₂ + ~S₁
Schema 1	Contradiction	S₁ + ~S₁
Schema 2	Contradiction	S₂ + ~S₂
Deixes 1	Implication	~S₂ + S₁
Deixes 2	Implication	~S₁ + S₂

S₁ = positive seme
S₂ = negative seme
S = complex axis (S₁ + S₂)
~S = neutral axis (neither S₁ nor S₂)

The semiotic square is formed by an initial binary relationship between two contrary signs. S₁is considered to be the assertion/positive element and S₂ is the negation/negative element in the binary pair:
The second binary relationship is now created on the ~S axis. ~S₁ is considered to be the complex term, and ~S₂ is the neutral term. This is where the principle of difference is brought into play: every element in a system is defined by its differences from the other elements.
In most modes of interpretation, the S-axis is a hyponym of the ~S-axis. The ~S₁ element combines aspects of S₁ and S₂ and is also contradictory to S₁ . The ~S₂ element contains aspects of neither S₁ nor S₂ .
Finally, the ~S₂ element can be identified. Considered to be "always the most critical position and the one that remains open or empty the longest time, for its identification completes the process and in that sense constitutes the most creative act of the construction.".^[1]

Example

Starting from a given opposition of concepts S1 and S2, the semiotic square entails first the existence of two other concepts, namely ~S1 and ~S2, which are in the following relationships:

S1 and S2: opposition
S1 and ~S1, S2 and ~S2: contradiction
S1 and ~S2, S2 and ~S1: complementarity

The semiotic square also produces, second, so-called meta-concepts, which are compound ones, the most important of which are:

both S1 and S2
neither S1 nor S2

For example, from the pair of opposite concepts masculine-feminine, we get:

S1: masculine
S2: feminine
~S1: not-masculine
~S2: not-feminine
both S1 and S2: masculine and feminine
neither S1 nor S2: neither masculine nor feminine

Styles of interpretation

The Greimas square is a tool used within the system of semiotics.

As such, one form of interpretation is to look at each of the elements: S1, S2, ~S1, and ~S2 as either developed by Ferdinand de Saussure (bi-modal) or Charles Sanders Peirce (tripartite) sign.
In the Peircean system of semiotics, the interpretant becomes the representamen for another, interrelated sign. In this same way, each of the elements of the semiotic square (S1, S2, ~S1, and ~S2) can become an element in a new, interrelated square.
Finally, Greimas suggests placing semiotic squares of associated meaning on top of one another to create a layered effect and another form of analysis and interpretation.

Examples of interpretation

The semiotic square has been used to analyze and interpret a variety of topics, including corporate language,^[2] the discourse of science studies as cultural studies,^[3] the fable of Little Red Riding Hood,^[4] narration,^[5] and print advertising.^[6]

References

^ Jameson, Fredric. 1987. "Foreword." On Meaning: Selected Writings. Algirdas Julien Greimas. Minneapolis: University of Minnesota Press. pg. xvi.
^ Fiol, C. Marlene. 1989. "A Semiotic Analysis of Corporate Language: Organizational Boundaries and Joint Venturing." Administrative Science Quarterly 34(2): 277-303.
^ Haraway, Donna J. (1992). "The Promises of Monsters: A Regenerative Politics for Inappropriate/d Others." The Haraway Reader (2004). New York: Routledge.
^ Laruccia, Victor. 1975. "Little Red Riding Hood's Metacommentary: Paradoxical Injunction, Semiotics and Behavior." Modern Language Notes 90(4): 517-534.
^ Meister, Jan Christoph. 2003. Computing action: a narratological approach. Berlin: Walter de Gruyter GmbH & Co.
^ Cian, Luca. 2012. "A comparative analysis of print advertising applying the two main plastic semiotics schools: Barthes' and Greimas'." Semiotica, 190: 57–79.