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Leonardi.DB
a logical geometry project

Duality Patterns in 2-PCD Fragments (2017), p. 240
by Smessaert, Hans; Demey, Lorenz

Caption

Example of the $\textit{classical}$ (CLCL1) duality pattern: (a) classical square for the fragment $\mathcal{F}$, (b) classical square for $\delta^*(\pi_\alpha)$, (c) classical square for $\delta^*(\pi_\beta)$, (d) octagon for the fragment $\mathcal{F}^*$.

Logic

Aristotelian family
Classical Sigma-2
Boolean complexity
3
Number of labels per vertex (at most)
1
Uniqueness of the vertices up to logical equivalence
Yes
Errors in the diagram
No

Geometry

Shape
Square (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
dots
Label type
symbolic
Symbolic field
logic
Contains partial formulas or symbols
No
Logical system
modal logic

Edge description

Contains definitions of relations
No
Form
dash-double-dotted lines
,
solid lines
,
dash-dotted lines
Has arrowheads
No
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
;
duality
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