Deontic modality schematized according to the semiotic square

Actions may be classified according to their deontic modality (using the Greimasian scheme of the semiotic square) as follows:

S₁                                                              S₂

those that we are                those that we are   required to do                      required not to do

those that we are               those that we are    not required not to do           not required to do

~S₂                                                            ~S₁

S₁                                                                S₂

those that we are               those that we are   advised to do                      advised not to do

those that we are               those that we are   not advised not to do          not advised to do

~S₂                                                           ~S₁

S₁                                                               S₂

those that we are                those that we are permitted to do                  permitted not to do

those that we are                those that we are not permitted not to do       not permitted to do

~S₂                                                            ~S₁

S₁ – S₂ is a relation of contrariety, ~S₁ - S₂ is a relation of complementarity, S₁ - ~S₁ is a relation of contradiction, S₂ - ~S₂ is a relation of contradiction, ~S₂ - ~S₁ is a relation of contrariety, and S₁ - ~S₂ is a relation of complementarity.¹

Relations of material equivalence may thus be stated as follows (where "↔" stands for “is materially equivalent to”):

1. Being required to do (having to do) ↔ not being permitted not to do ↔ not being permitted to do otherwise

2. Being required not to do (having not to do) ↔ being required to do otherwise ↔ not being permitted not to do

3. Not being required to do (not having to do) ↔ being permitted not to do ↔ being permitted to do otherwise

4. Not being required not to do (not having not to do) ↔ being permitted to do ↔ not being required to do otherwise.

FOOTNOTES

¹A.J. Greimas and J. Courtés, Semiotics and Language: An Analytical Dictionary, translated by Larry Crist, Daniel Patte, et al. (Bloomington: Indiana University Press, 1979), p. 309.