You're using an ancient browser to surf the modern web. Please update to the latest version (and don't use Internet Explorer!).

Leonardi.DB
a logical geometry project

From Analogical Proportion to Logical Proportions (2013), p. 476
by Prade, Henri; Richard, Gilles

Caption

Square of homogeneous logical proportions

Logic

Aristotelian family
Non-Sigma
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
Rectangle (irregular)
Colinearity range
0
Coplanarity range
0
Cospatiality range
0
Representation of contradiction
N.A.

Vertex description

Conceptual info
No
Mnemonic support (AEIO, purpurea ...)
No
Form
none
Label type
symbolic
,
generic placeholders
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
,
double solid lines
Has arrowheads
No
Overlap
No
Curved
No
Hooked
No
As wide as vertices
No
Contains text
No
Label type
none

Style

Diagram is colored
No
Diagram is embellished
No

Additional notes

$S_{a,b}$ is defined as $a \wedge b$.
$S'_{a,b}$ is defined as $\overline{a} \wedge \overline{b}$.
$D_{a,b}$ is defined as $a \wedge \overline{b}$.
$D'_{a,b}$ is defined as $\overline{a} \wedge b$.

(Cf. p. 476.)
↑ Back to top ↑