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Leonardi.DB
a logical geometry project

A Précis of Mathematical Logic (1959), p. 14
by Bocheński, Jozef; Bird, Otto (trans.)

Logic

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

Geometry

Shape
Rectangle (irregular)
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
solid lines
Has arrowheads
Yes
Overlap
No
Curved
No
Hooked
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

Additional notes

Each vertex contains a formula from propositional logic, both in Peano-Russell notation and in Polish notation.

The edges are labeled with propositional connectives in Polish notation.

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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