FullSemanticsAxiomAnnotations

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The OWL 2 Full semantics of Axiom Annotations.

Note: According to the resolution of Issue 67, a shadow vocabulary has been introduced, instead of using genuine RDF reification.

Axiom Annotations

Syntax

 x rdf:type owl:Axiom
 x owl:subject s
 x owl:predicate p
 x owl:object o
 x ap_i av_i 1 ≤ i ≤ n

where each triple

 x ap_i av_i

is a single annotation of the axiom "s p o", performed by an annotation property ap_i and its annotation value av_i.

Semantics

Axiomatic triples:

 owl:Axiom rdf:type rdfs:Class

 owl:subject rdf:type rdf:Property
 owl:subject rdfs:domain owl:Axiom
 owl:subject rdfs:range rdf:Resource

 owl:predicate rdf:type rdf:Property
 owl:predicate rdfs:domain owl:Axiom
 owl:predicate rdfs:range rdf:Predicate

 owl:object rdf:type rdf:Property
 owl:object rdfs:domain owl:Axiom
 owl:object rdfs:range rdf:Predicate

Main semantic condition:

 IF
   x ∈ CEXT_I(S_I(owl:Axiom)) 
   (x,s) ∈ EXT_I(S_I(owl:subject))
   (x,p) ∈ EXT_I(S_I(owl:predicate))
   (x,o) ∈ EXT_I(S_I(owl:object))
 THEN
   (s,o) ∈ EXT_I(p)

Considerations

• Comparison with 2-DL: The only meaning of this construct is that the denoted axiom exists in the ontology. In 2-DL the annotations themselves are regarded to be "semantic-free".
• The main purpose of the semantic condition is to "materialize" the axiom "s p o", so that it actually exists in the ontology at all.
  • In the current RDF mapping, there is either the axiom triple or the reified version. But RDF Reification doesn't provide the triple (it has very week semantics). So the existence of the triple has to be provided by the OWL 2 Full semantics.
  • If the reification quad would exist in an ontology in addition to the original axiom triple, then there wouldn't be any need for semantics for axiom annotations at all.
• The semantic condition ignores all annotation triples. In this way, no additional meaning is given to these annotation triples, aside from the meaning which they already have. Since OWL-Full will have a monotonic semantics, there is no way to "cancel out" existing meaning. So not saying anything else is probably the best one can do to approximate the notion of "semantic free" annotations.
• "IF" instead of "IF AND ONLY IF": I believe that the back direction would not make much sense: If the axiom itself is given in its triple form, then the result would be just the reified version without annotation triples. This would not result in any new information, neither semantically, nor informally.

Annotations of Multi-triple axioms

• ISSUE-12 has been resolved.
• Only relevant case: If there is already a bNode representing this axiom, then the annotation is added to this bNode.
  • Example: owl:AllDifferent
  • Ramifications:
    • In principle, this approach adds to the semantics of the bNode, which represents the axiom.
    • This additional meaning is determined by the meaning of the annotation property and its value.
    • This does not seem to be a heavy problem, since annotation properties have typically very weak semantics in OWL Full.
    • This additional semantics cannot be prevented.
    • Further additional semantic conditions seem to be neither necessary nor desired in order to cope with this case.

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