First-Order Modal Logic (2023), p. 64
by Fitting, Melvin; Mendelsohn, Richard L.
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Caption
- The modal square of opposition in De. Int. 13
- Aristotelian family
- Classical Sigma-2
- Boolean complexity
- 3
- Number of labels per vertex (at most)
- 2
- Equivalence between (some) labels of the same vertex
- Yes
- Analogy between (some) labels of the same vertex
- No
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- Yes
- 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
- linguistic
- Language
- English
- Lexical field
- modalities
- Contains partial sentences or single words
- No
- Contains abbreviations
- Yes
- Contains definitions of relations
- No
- Form
- solid lines ,
- none
- Has arrowheads
- Yes
- Overlap
- No
- Curved
- No
- Hooked
- No
- As wide as vertices
- No
- Contains text
- No
- Label type
- none
Vertex description
Edge description
- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- duality
Style
Additional notes
- The sentences 'It is not necessary that P' and 'It is not necessary that not P' should be swapped around. (This is a famous interpretation issue from Aristotle's $\textit{Peri Hermeneias}$; cf. also work by Marko Malink et al.)