description-logic

Translate English expression "exactly four" in ALCQO description logic

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:

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

    1. Yes, using ≥ and ≤ in the same sentence translates to exactly. I have written about this on my blog here.

    2. 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.