The Logic of Modality (2016), p. 354
by Strobino, Riccardo; Thom, Paul
Copyright according to our policy
Caption
- Basic inferential relations holding among the fifteen modalised propositions
- Aristotelian family
- Non-Sigma
- Number of labels per vertex (at most)
- 1
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Heptagon (irregular)
- Colinearity range
- 0
- Coplanarity range
- 8
- Cospatiality range
- 0
- Representation of contradiction
- N.A.
Logic
Geometry
- Conceptual info
- No
- Mnemonic support (AEIO, purpurea ...)
- No
- Form
- circular ,
- none
- Label type
- symbolic
- Symbolic field
- logic
- Contains partial formulas or symbols
- Yes
- Logical system
- modal syllogistics
- Contains definitions of relations
- No
- Form
- solid lines ,
- none
- Has arrowheads
- Yes
- Overlap
- No
- Curved
- No
- Hooked
- No
- As wide as vertices
- No
- Contains text
- No
- Label type
- none
Vertex description
Edge description
- Diagram is colored
- No
- Diagram is embellished
- No
Style
Additional notes
- (i) Alethic modalities:
- $L$: substantial necessity
- $M_1$: substantial one-sided possibility
- $M_2$: substantial two-sided possibility
- $L_{d1}$: descriptional unrestricted necessity
- $M_{d1}$: descriptional one-sided possibility
(ii) Temporal modalities:
- $A$: substantial perpetuity
- $X_1$: substantial one-sided absoluteness
- $X_2$: substantial two-sided absoluteness
- $A_{d1}$: descriptional unrestricted perpetuity
- $X_{d1}$: descriptional one-sided absoluteness
(iii) Mixed alethic and temporal modalities:
- $L_{d2}$: descriptional restricted necessity
- $T$: substantial determinate temporal necessity
- $I$: substantial indeterminate temporal necessity
- $A_{d2}$: descriptional restricted perpetuity
- $X_3$: substantial non-necessary absoluteness
(Cf. p. 353.)