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semantic-webdescription-logic

Can this be expressed using ALCQ syntax?

Is it valid, using ALCQ, to write:

likes ≡ ¬dislikes   
¬∃(Dog ⊓ dislikes.(Colourful ⊓ Toy))

in order to express that every dog likes the colourful toys?

Also, is it valid to write:

Cute(∀Pomeranian)

in order to express that every pomeranian is cute?

Solution

  • No, formula likes ≡ ¬dislikes doesn't belong to ALCQ because it's missing role hierarchies (H in its name).

    if you don't have to use dislike explicitly:

    Dog ⊑ ∃likes.(Colourful ⊓ Toy)

    then Cute(∀Pomeranian) is not a valid ALCQ formula, instead simply use:

    Pomeranian ⊑ Cute