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Is the following interpreted as the intersection (AND) in the sense that members of class A are members of B and C; or as the disjunction (OR) that members of A are a member of B, or a member of C, or member of both?

A rdf:type owl:Class ;
   rdfs:subClassOf some B; 
   rdfs:subClassOf only C.

Thanks for clarification how this is interpreted!

I found it as AND: Protege OWL Subclass of two classes

But Hermit breaks it and uses single axioms (e.g. A rdfs:subclassOf B) as explanation for A to B. I thought that would not be possible ...? Since I would say that A is a subclassOf (B and C) and not only A.

user3352632
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1 Answers1

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I can quote RDFS, and considering OWL should follow from that, I don't expect any difference there:

If a class C is a subclass of a class C', then all instances of C will also be instances of C'. The rdfs:subClassOf property may be used to state that one class is a subclass of another.

Class inheritance axioms in RDFS are built so that a contradiction can never occur, thus a statement like this can only be "additive" in a sense. Additionally, from the nature of triples in RDF, we know that A rdfs:subClassOf B, C. means A rdfs:subClassOf B. A rdfs:subClassOf C..

Expressed in the language of sets, such a construction means A ⊆ B ∧ A ⊆ C. Any member of A is also a member of B, and any member of A is also a member of C, thus any member of A must be a member of both B and C. We can see that A ⊆ (B ∩ C), from the duality of set and logical operators.

Expressed equivalently, any member of B not found in C must also not be in A (and the same for B and C swapped).

IS4
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  • Thanks for your clarification. Is there any reason why you use first ∧ and later ∩ for a logical and? A ⊆ B ∧ A ⊆ C vs. A ⊆ (B ∩ C). First is the logical and and second the intersection symbol. – user3352632 Feb 01 '22 at 21:19
  • So as a summary: If there is not any OR (i.e. union-operator) written / shown in a turtle serialization, it is interpreted as an intersection. – user3352632 Feb 01 '22 at 21:40
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    @user3352632 For the symbols, this is what is used in logic when working with sets. In the first case it is a logical conjunction of statements, i.e. both must be true. This can be satisfied if and only if A is a subset of their intersection. – IS4 Feb 02 '22 at 12:24
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    @user3352632 RDF statements are normally treated in conjunction, i.e. all triples in a graph hold at the same time, not just a single one of them. So the universe of truth is gradually narrowed by every triple, until what results is the intersection of all of that. – IS4 Feb 02 '22 at 12:33
  • thanks, that makes sense! Now I think I got it! Thanks for your help! – user3352632 Feb 02 '22 at 21:09