The Interaction Between Logic and Geometry in Aristotelian Diagrams (2016), p. 78
by Demey, Lorenz; Smessaert, Hans
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Caption
- (a-c) The three remaining fundamental forms of a hexagon for the U4 fragment of S5-formulas whose first fundamental form was already shown in Fig. 2(c); (d–e) two of the four fundamental forms of a hexagon for the U8 fragment $\{\Box p, \Box\neg p, \Diamond p, \Diamond\neg p, q, \neg q\}$; (f) (the unique fundamental form of) an octahedron for the same fragment.
- Aristotelian family
- Degenerate Sigma-3 with Unconnectedness 8
- Boolean complexity
- 6
- Number of labels per vertex (at most)
- 1
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Octahedron (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
- logic
- Contains partial formulas or symbols
- No
- Logical system
- modal logic
- Contains definitions of relations
- No
- Form
- dotted lines ,
- solid lines ,
- none ,
- 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