Towards a Mental Probability Logic (2005), p. 94
by Pfeifer, Niki; Kleiter, Gernot D.

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Caption

Generalized squares of opposition (Adapted from Peterson, 1985: 351ff). The solid lines indicate contradictions, dashed contraries, dotted subcontraries, and arrows subalternations (i.e. immediate entailments), respectively. $\neg$ is the negation.

Logic

Aristotelian family

Non-Sigma

Boolean complexity

9

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

0–5

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

N.A.

Vertex description

Conceptual info

Yes

Mnemonic support (AEIO, purpurea ...)

Yes

Form

none

Label type

linguistic

,

symbolic

Language

English

Lexical field

categorical

,

proportional quantifiers

Contains partial sentences or single words

No

Contains abbreviations

Yes

Symbolic field

logic

Contains partial formulas or symbols

Yes

Logical system

syllogistics

Edge description

Style

Diagram is colored

No

Diagram is embellished

No

Additional notes

The negation closure of this diagram contains the negations of "Most $S$ are $P$" and "Most $S$ are $\neg P$". It is a sigma-8 ladder.