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Leonardi.DB
a logical geometry project

Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics (2021), p. 2
by Demey, Lorenz

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Caption

Aristotelian diagrams for $\{\Box p, \Diamond p, \Box \neg p, \Diamond\neg p\}$ with respect to two systems of modal logic. Full, dashed, and dotted lines visualize contradiction, contrariety, and subcontrariety, respectively; arrows visualize subalternations. (b) Degenerate square of opposition in the modal logic K.

Logic

Aristotelian family
Degenerate Sigma-2 with Unconnectedness 4
Boolean complexity
4
Number of labels per vertex (at most)
1
Uniqueness of the vertices up to logical equivalence
Yes
Errors in the diagram
No

Geometry

Shape
Rectangle (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
Leuven
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