# Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics (2021), p. 2

by Demey, Lorenz

Copyright according to our policy

### Caption

- Aristotelian diagrams for $\{\Box p, \Diamond p, \Box \neg p, \Diamond\neg p\}$ with respect to two systems of modal logic. Full, dashed, and dotted lines visualize contradiction, contrariety, and subcontrariety, respectively; arrows visualize subalternations. (a) Classical square of opposition in the modal logic KD.

- Aristotelian family
- Classical Sigma-2
- Boolean complexity
- 3
- Number of labels per vertex (at most)
- 1
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Rectangle (irregular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By central symmetry

### Logic

### Geometry

- Conceptual info
- No
- Mnemonic support (AEIO, purpurea ...)
- No
- Form
- none
- Label type
- symbolic
- Symbolic field
- logic
- Contains partial formulas or symbols
- No
- Logical system
- modal logic
- Contains definitions of relations
- No
- Form
- dotted lines ,
- solid lines ,
- dashed lines
- 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
- Tags
- Leuven