From if to iff: Conditional perfection as pragmatic strengthening (2000), p. 307
by Horn, Laurence

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Caption

The extended standard square of opposition (Horn, 1990: 464, after Czezowski, 1955 and Fogelin, 1967)

Logic

Aristotelian family

Sherwood-Czeżowski Sigma-3

Boolean complexity

4

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

Hexagon (irregular)

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

propositional connectives

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