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Leonardi.DB
a logical geometry project

"Logical Lantern": Analogue of the Square of Opposition for Propositions in V.I. Markin’s Universal Language for Traditional Positive Syllogistic Theories (2024), p. 38
by Cherkashina, Oksana

Caption

“Logical lantern”. Basic scheme for logical relations among propositions about relations between two nonempty sets

Logic

Number of labels per vertex (at most)
1
Errors in the diagram
No

Geometry

Shape
Decagon (irregular)
Colinearity range
0
Coplanarity range
22
Cospatiality range
0
Representation of contradiction
By central symmetry

Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
circular
,
none
Label type
linguistic
,
symbolic
Language
English
Contains partial sentences or single words
Yes
Contains abbreviations
No
Symbolic field
mathematics
Mathematical branch
set theory

Edge description

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

Style

Diagram is colored
No
Diagram is embellished
No

Additional notes

This diagram is decorated with Pellissier's "setting" technique, which is equivalent to bitstring semantics. In particular, $\wp(\{1,2,3,4,5\})$ corresponds to bitstrings of length 5.
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