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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’
- 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
- Shape
- Rectangle (irregular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By some other geometric feature
Logic
Geometry
- Conceptual info
- No
- Mnemonic support (AEIO, purpurea ...)
- No
- Form
- none
- Label type
- symbolic
- Symbolic field
- logic
- Contains partial formulas or symbols
- No
- Logical system
- propositional logic
- 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
Vertex description
Edge description
- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- Leuven ;
- duality
Style
Additional notes
- 'L' and 'R' stand for left (= external) and right (= internal) negation, respectively.