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

Probabilistic squares and hexagons of opposition under coherence (2017), p. 283
by Pfeifer, Niki; Sanfilippo, Giuseppe

Caption

Probabilistic hexagon of opposition on the six sentence types $A$, $E$, $I$, $O$, $U$, $Y$, where $A$, $E$, $I$, $O$ is a square of opposition, $ U=A \vee E$ and $Y = I \wedge O$. The arrows indicate subalternation, dashed lines indicate contraries, and dotted lines indicate sub-contraries. Contradictories are indicated by combined dotted and dashed lines.

Logic

Aristotelian family
Jacoby-Sesmat-Blanché Sigma-3
Boolean complexity
3
Number of labels per vertex (at most)
3
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
Hexagon (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
syllogistics
Contains partial sentences or single words
No
Contains abbreviations
Yes
Symbolic field
mathematics
,
logic
Contains partial formulas or symbols
Yes
Logical system
syllogistics
Mathematical branch
probability theory

Edge description

Style

Diagram is colored
Yes
Diagram is embellished
No
Tags
Boolean closed
↑ Back to top ↑