Translate English expression "exactly four" in ALCQO description logic

Question

I have to translate in ALCQO the following sentence:

A square is a polygon with exactly four edges and exactly four vertices which are line segments.

I have tried the following approach using ALCQO:

Square ≡ Polygon ⊓ (≥4hasPart.Edges) ⊓ (≤4hasPart.Edges) ⊓ (≥4hasVertices.LineSegments) ⊓
 (≤4hasVertices.LineSegments)

I am not sure about the following two cases:

Using ≥ and ≤ in the same sentence I am actually achieving to translate the phrase "exactly one".
hasVertices.LineSegments I am actually achieving to translate the phrase "vertices which are line segments".

score 1 · Accepted Answer · answered Dec 28 '22 at 10:44

Yes, using ≥ and ≤ in the same sentence translates to exactly. I have written about this on my blog here.
If you have ≥4hasVertices or ≥4hasVertices.Top it means the filler of hasVertices can be any concept from your domain. When you have ≥4hasVertices.LineSegment the filler of hasVertices can only be LineSegments.

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