Algebraic Aspects of Duality Diagrams (2012), p. 301
by Demey, Lorenz

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Caption

Duality squares for (a) universal and existential quantification, (b) conjunction and disjunction, and (c) the natural language expressions ‘already’ and ‘still’

Logic

Aristotelian family

Classical Sigma-2

Boolean complexity

3

Number of labels per vertex (at most)

1

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

By some other geometric feature

Vertex description

Conceptual info

No

Mnemonic support (AEIO, purpurea ...)

No

Form

none

Label type

symbolic

Symbolic field

logic

Contains partial formulas or symbols

No

Logical system

predicate logic

Edge description

Contains definitions of relations

No

Form

solid lines

Has arrowheads

No

Overlap

No

Curved

No

Hooked

No

As wide as vertices

No

Contains text

Yes

Label type

linguistic

Language

English

Contains partial sentences or single words

Yes

Contain abbreviations

Yes

Style

Diagram is colored

No

Diagram is embellished

No

Tags

Leuven

;

duality

Additional notes

'L' and 'R' stand for left (= external) and right (= internal) negation, respectively.