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Leonardi.DB
a logical geometry project

Data Technology in Materials Modelling (2021), p. 77
by Horsch, Martin Thomas; Chiacchiera, Silvia; Cavalcanti, Welchy Leite; Schembera, Björn

Caption

Selected traditional (top) and generalized (bottom) modal squares of opposition from VIPRS. Here, occ[$I$] stands for "$I$ occurs", and $K_I C I$ stands for "$K_I$ conceptualizes $I$", arrows denote subsumption and solid lines denote complementarity (top) and logical negation with respect to the modal formula (bottom)

Logic

Number of labels per vertex (at most)
1
Uniqueness of the vertices up to logical equivalence
Yes
Errors in the diagram
No

Geometry

Shape
Hexagon (irregular)
Colinearity range
0
Coplanarity range
2
Cospatiality range
0
Representation of contradiction
By central symmetry

Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No

Edge description

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

Style

Diagram is colored
Yes
Diagram is embellished
No
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