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Leonardi.DB
a logical geometry project

Logical Squares for Classical Logic Sentences (2016), p. 309
by Wybraniec-Skardowska, Urszula

Caption

Squares for verum and falsum.

Logic

Aristotelian family
A Single PCD
Boolean complexity
2
Number of labels per vertex (at most)
1
Uniqueness of the vertices up to logical equivalence
Yes
Errors in the diagram
Yes

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
none
Label type
symbolic
Symbolic field
logic
Contains partial formulas or symbols
No
Logical system
propositional logic

Edge description

Contains definitions of relations
No
Form
dotted lines
,
solid lines
Has arrowheads
No
Overlap
Yes
Curved
No
Hooked
No
As wide as vertices
No
Contains text
No
Label type
symbolic
Symbolic field
logic
Contains partial formulas or symbols
Yes
Logical system
propositional logic

Style

Diagram is colored
No
Diagram is embellished
No
Tags
Boolean closed
;
non-contingent formulas

Additional notes

T is the tautological binary connective (1111); F is the contradictory binary connective (0000); $c$ can be any of the 14 other binary truth-functional connectives.

The edges are labeled with propositional connectives corresponding to the Aristotelian relations (cf. Theorem 1 of Smessaert & Demey, 2014, Logical Geometries and Information in the Square of Oppositions, Journal of Logic, Language and Information 23 : 527 - 565).
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