Probabilistic squares and hexagons of opposition under coherence (2017), p. 283
by Pfeifer, Niki; Sanfilippo, Giuseppe
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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.
- 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
- Shape
- Hexagon (regular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By central symmetry
Logic
Geometry
- 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
Vertex description
Edge description
- Diagram is colored
- Yes
- Diagram is embellished
- No
- Tags
- Boolean closed