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Leonardi.DB
a logical geometry project

Aristotelian Logic (1991), p. 165
by Parry, William T.; Hacker, Edward A.

Caption

The Aristotelian Square of Opposition with Entailments and Non-Entailments

Logic

Aristotelian family
Classical Sigma-2
Boolean complexity
3
Number of labels per vertex (at most)
3
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
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 ...)
Yes
Form
none
Label type
linguistic
,
symbolic
Language
English
Lexical field
categorical
Contains partial sentences or single words
No
Contains abbreviations
Yes
Symbolic field
logic
Contains partial formulas or symbols
Yes
Logical system
syllogistics

Edge description

Contains definitions of relations
No
Form
solid lines
Has arrowheads
Yes
Overlap
No
Curved
No
Hooked
No
As wide as vertices
No
Contains text
Yes
Label type
linguistic
Language
English
Contains partial sentences or single words
Yes
Contain abbreviations
No

Style

Diagram is colored
No
Diagram is embellished
No

Additional notes

The F-superscript stands for 'is false'; e.g. A $\leftrightarrow$ O$^\text{F}$ means that A is equivalent to $\neg$O.
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