# How to Square Knowledge and Belief (2012), p. 311

by Lenzen, Wolfgang

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### Caption

- Square of complex epistemic modalities

- 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
- epistemic logic

### Vertex description

### Edge description

- Diagram is colored
- No
- Diagram is embellished
- No

### Style

### Additional notes

- Given the equivalence of $C(a,p)$ with $\neg K(a, \neg K(a,p))$ (cf. p. 311), this diagram can equivalently be rewritten as follows:

$C(a,p)\ \ \ \ \ \ \ \ \ $ $C(a,\neg p)$

$\neg C(a,\neg p)\ \ \ $ $\neg C(a,p)$