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.
