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Leonardi.DB
a logical geometry project

# Caramuel's Theory of Opposition (2017), p. 366 by Lenzen, Wolfgang

### Caption

Caramuel's "Cube of opposition"

### Logic

Aristotelian family
Buridan Sigma-4
Boolean complexity
6
Number of labels per vertex (at most)
2
Equivalence between (some) labels of the same vertex
No
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
Cube (regular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
By some other geometric feature

### Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
none
Label type
linguistic
,
symbolic
Language
Latin
Lexical field
syllogistics
Contains partial sentences or single words
No
Contains abbreviations
No
Symbolic field
logic
Contains partial formulas or symbols
No
Logical system
predicate logic

### Edge description

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

### Style

Diagram is colored
Yes
Diagram is embellished
No
Tags
oblique terms
;
composed operator duality

DQ1: $\forall x\forall y E(x,y)$
DQ2: $\exists x\forall y E(x,y)$
DQ3: $\forall x\exists y E(x,y)$
DQ4: $\exists x\exists y E(x,y)$
DQ5: $\exists x\exists y \neg E(x,y)$
DQ6: $\forall x\exists y \neg E(x,y)$
DQ7: $\exists x\forall y \neg E(x,y)$
DQ8: $\forall x\forall y \neg E(x,y)$