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Duality in Logic and Language (2016), -
by Demey, Lorenz; Smessaert, Hans
![]( /diagrams/demey-et-al-_2017_duality-in-logic-and-language_1dvfd7di1__1hl5qsoo6/images/display.jpeg?url=http%3A%2F%2Fpurl.org%2Flg%2Fdiagrams%2Fdemey-et-al-_2017_duality-in-logic-and-language_1dvfd7di1__1hl5qsoo6%2Fimages%2Fdisplay.jpeg )
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Caption
- (a) Aristotelian hexagon (for a modal system that is at least as strong as $\textsf{KD}$), (b) duality ‘hexagon’, and (c–d) its two components.
- 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 central symmetry
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
- modal logic
- Contains definitions of relations
- No
- Form
- dash-double-dotted lines ,
- solid lines ,
- dash-dotted 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