Awareness and Creativity by Evolutive EPM (2017), p. 489
by Fiorini, Rodolfo A.; De Giacomo, Piero

Copyright according to our policy

Caption

Hasse diagrams for the Boolean algebra $\phi(\{1,2,3\})$ on the left side and for a Boolean algebra of formulas from the modal logic S5 with modality ($\Box$, $\Diamond$), on the right side [26]

Logic

Aristotelian family

Jacoby-Sesmat-Blanché Sigma-3

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

Geometry

Shape

Hexagon (irregular)

Colinearity range

0

Coplanarity range

0

Cospatiality range

0

Representation of contradiction

By central symmetry

Vertex description

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

Edge description

Contains definitions of relations

No

Form

solid lines

,

none

Has arrowheads

No

Overlap

No

Curved

No

Hooked

No

As wide as vertices

No

Contains text

No

Label type

none

Style

Diagram is colored

No

Diagram is embellished

No

Tags

Boolean closed

;

non-contingent formulas

;

Hasse diagram