Applications of Squares of Oppositions and Their Generalizations in Philosophical Analysis (2008), p. 25
by Woleński, Jan
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- Aristotelian family
- A Single PCD
- Boolean complexity
- 2
- Number of labels per vertex (at most)
- 1
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Digon (regular)
- 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
Vertex description
Edge description
- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- Boolean closed
Style
Additional notes
- "We interpret $\alpha$ as $\Box A$, $\beta$ as $\Box\neg A$" (p. 14).
"In this section, the symbol $\Box$means 'is true'." (p. 24).
"we assume the following equivalence [...] $\Box\neg A \Leftrightarrow \neg\Box A$." (p. 25)
Semantic note: on Kripke frames, the equivalence $\Box\neg A \Leftrightarrow \neg\Box A$ corresponds to the accessibility relation being a (total) function: $\Rightarrow$ corresponds to seriality (every world sees at least one world), while $\Leftarrow$ corresponds to functionality (every world sees at most one world).