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I am trying to understand the cases where OWL classes "overlap" based on existential property restrictions.

No Intersection

Here there's no overlap in the number of name properties each class has, so there can be no individuals that belong to both classes. The reasoner therefore infers their intersection to be unsatisfiable (equivalent to owl:Nothing).

# Declared
DataProperty: name

Class: A
    SubClassOf: 
        name max 1 xsd:string

Class: B
    SubClassOf: 
        name min 2 xsd:string

# Inferred (pseudocode)
(A and B)
    EquivalentTo:
        owl:Nothing

Proper Subclass

Here the restriction of one class completely includes the other's, so I would've thought the individuals of Person1 would be implied to belong to Person2, and the reasoner would infer A is a subclass of B or infer that the class (A and not B) is unsatisfiable, but this does not happen. I'm looking for an explanation of why this is the case. Thanks!

# Declared
DataProperty: name

Class: A
    SubClassOf: 
        name exactly 2 xsd:string

Class: B
    SubClassOf: 
        name min 2 xsd:string

# Nothing Inferred
Spencer Crosswy
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  • `SubClassOf` axioms provide necessary conditions for belonging to a class, but not sufficient ones. All you know is that i) `B` is in (at least or evens equals, but we don't know) a larger set `S1` defined by the class expression `name min 2 xsd:string` and ii) `A` is in a subset `S2` defined by `name exactly 2 xsd:string` of that larger set `S1` – UninformedUser Aug 12 '22 at 06:40
  • but how would you know if the set of individuals of `B` would be in `A`? That can't be decided here. Take a sheet of paper and visualize the 4 sets with circles, you'll see that you can never make the decision to put the circle for `A` inside `B` with any evidence, right? I mean, it could be the case that `A` is in `B` or they overlap or they just exist besides each other, but we never know – UninformedUser Aug 12 '22 at 06:41
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    If you make both axioms `EquivalentTo` instead of `SubClassOf` that would indeed work. – UninformedUser Aug 12 '22 at 06:44

0 Answers0