# Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics (2021), p. 11

by Demey, Lorenz

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### Caption

- Aristotelian diagrams for $\mathcal{F}_{1b} := \{\Box(p \wedge q), \Box p\wedge \Box q, \Diamond\neg p \vee\Diamond\neg q, \Diamond(\neg p\vee\neg q)\}$ in any normal modal logic and in three non-normal modal logics. (a) PCD for $\mathcal{F}_{1b}$ in any normal modal logic.

- Aristotelian family
- A Single PCD
- Boolean complexity
- 2
- Number of labels per vertex (at most)
- 2
- Equivalence between (some) labels of the same vertex
- No
- Analogy between (some) labels of the same vertex
- No
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Digon (regular)
- 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
- bitstrings ,
- logic
- Contains partial formulas or symbols
- No
- Contains protobitstrings
- No
- Bitstring length
- 2
- Logical system
- modal logic
- Contains definitions of relations
- No
- Form
- solid lines
- Has arrowheads
- No
- 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
- Boolean closed ;
- Leuven