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Leonardi.DB

a logical geometry project

Opposition, Obversion, and Duality (1993), p. 107
by Simons, Peter

Copyright according to our policy

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: Square (regular)
Colinearity range: 0
Coplanarity range: 0
Cospatiality range: 0
Representation of contradiction: By central symmetry

Graph structure: I

Contradiction with E

Subcontrariety with O

Subalternation from A

E

Contradiction with I

Contrariety with A

Subalternation to O

O

Contradiction with A

Subcontrariety with I

Subalternation from E

A

Contradiction with O

Contrariety with E

Subalternation to I

Conceptual info: No
Mnemonic support (AEIO, purpurea ...): Yes
Form: none
Label type: symbolic
Symbolic field: logic
Contains partial formulas or symbols: Yes
Logical system: syllogistics
Contains definitions of relations: No
Form: solid lines
Has arrowheads: No
Overlap: No
Curved: No
Hooked: No
As wide as vertices: No
Contains text: No
Label type: symbolic
Symbolic field: logic
Contains partial formulas or symbols: Yes
Logical system: propositional logic

Diagram is colored: No
Diagram is embellished: No

Additional notes: The edges are labeled with propositional connectives in Polish notation.

The edges are labeled with propositional connectives corresponding to the Aristotelian relations (cf. Theorem 1 of Smessaert & Demey, 2014, Logical Geometries and Information in the Square of Oppositions, Journal of Logic, Language and Information 23 : 527 - 565).

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