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Leonardi.DB
a logical geometry project

The Interaction Between Logic and Geometry in Aristotelian Diagrams (2016), p. 78
by Demey, Lorenz; Smessaert, Hans

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.

Logic

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

Geometry

Shape
Octahedron (regular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
Representation of contradiction
By central symmetry

Vertex description

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

Edge description

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

Style

Diagram is colored
No
Diagram is embellished
No
Tags
Leuven
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