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Leonardi.DB
a logical geometry project

# Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics (2021), p. 22 by Demey, Lorenz

### Caption

Aristotelian diagrams for $f_3(\mathcal{F}_{1b}) = \{\Box(p\wedge q)\wedge\Box p\wedge\Box q, \Box p\wedge\Box q\wedge\Diamond(\neg p\vee\neg q), (\Diamond\neg p\vee\Diamond\neg q)\wedge\Diamond(\neg p\vee\neg q), \Box(p\wedge q)\vee(\Box p\wedge\Box q), \Box(p\wedge q) \vee\Diamond\neg p\vee\Diamond\neg q, \Diamond\neg p\vee\Diamond\neg q\vee\Diamond(\neg p\vee\neg q)\}$ in two non-normal modal logics. (b) Strong JSB hexagon for $f_3(\mathcal{F}_{1b})$ in EM.

### Logic

Aristotelian family
Boolean complexity
3
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

### Geometry

Shape
Hexagon (irregular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
By central symmetry

### Vertex description

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
3
Logical system
modal logic

### Edge description

Contains definitions of relations
No
Form
dotted lines
,
solid lines
,
dashed lines
Yes
Overlap
No
Curved
No
Hooked
No
As wide as vertices
No
Contains text
No
Label type
none

### Style

Diagram is colored
No
Diagram is embellished
No
Tags
Boolean closed
;
Leuven