I have learned till now that, by definition, a Tbox is called unfoldable if the left hand side of the axioms (defined concepts) are atomic, and if the right hand side (the definitions) contain no direct or indirect reference to the defined concept.

But, I don't think I understand this completely. I would appreciate it if anyone can explain this to me, an example would be great too. Thanks.

asked 12 Nov '12, 20:30

Pavanred's gravatar image

Pavanred
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To give credit where credit is due, know that I simply googled for "Unfoldable TBox" to find an example on the Web. I found a slide set by Boontawee Suntisrivaraporn, entitled "Introduction to the Semantic Web - Description Logics" where you find on slides 15 and 16 the following definition and examples (I improve the examples a bit):

Unfoldable TBox: Only concept de nitions can be used, and the following conditions must be respected: (de nitional) there can be at most one de nition for each concept name, for instance, it is impossible to have A ≡ C and A ⊑ D in the TBox; (acyclic) there is no cyclic dependency in the TBox, for instance, it is impossible to have A ≡ B ⊓ C and B ≡ ∃r.A in the TBox.

This is an example of an unfoldable TBox:

Man ≡ Person ⊓ Male
Male ≡ ∀hasGender.{♂}
Woman ≡ Person ⊓ Female
Female ≡ ∀hasGender.{♀}
Parent ≡ Person ⊓ ∃child.Person

Remark that there are things on the left hand side that appear on the right hand side. If a concept appears on the right hand side and is also defined on the left hand side, it can be replaced by its definition, e.g.:

Man ≡ Person ⊓ ∀hasGender.{♂}

and it can be done recursively, which is what is called "unfolding". However, the following is not unfoldable:

Man ≡ Person ⊓ Male
Woman ≡ Person ⊓ Female
Parent ≡ Person ⊓ ∃child.Person
Person ≡ Man ⊔ Woman

because from the fourth axiom defining Person, one would replace Man and Woman by concepts that contain Person, which would then unfold to Man ⊔ Woman again. It's cyclic, thus not unfoldable.

link

answered 13 Nov '12, 03:55

Antoine%20Zimmermann's gravatar image

Antoine Zimm... ♦
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accept rate: 32%

edited 13 Nov '12, 14:49

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Asked: 12 Nov '12, 20:30

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Last updated: 13 Nov '12, 14:49