Combinatorial Bitstring Semantics for Arbitrary Logical Fragments (2018), p. 348
by Demey, Lorenz; Smessaert, Hans

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Caption

Aristotelian squares for the categorical statements and their bitstring representations a in syllogistics ($\mathsf{SYL}$) and b in first-order logic ($\mathsf{FOL}$)

Logic

Aristotelian family

Degenerate Sigma-2 with Unconnectedness 4

Boolean complexity

4

Number of labels per vertex (at most)

2

Equivalence between (some) labels of the same vertex

No

Analogy between (some) labels of the same vertex

No

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

bitstrings

,

logic

Contains partial formulas or symbols

No

Contains protobitstrings

No

Bitstring length

4

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

;

existential import