What is the difference in OWL, between a
Both covering axiom and closure axiom are used for Closing Down the Open World assumption in OWL, however i do not really understand the difference between them...
On
A universal restriction (owl:allValuesFrom) such as hasTopping only MozzarellaTopping defines all individuals x that are associated via the hasTopping object property to only individuals y that are of type MozzarellaTopping and of no other type. A source of confusion is that this also includes all individuals x that are not linked via the hasTopping object property to a individual y at all.
A existential restriction (owl:someValuesFrom) such as hasTopping some MozzarellaTopping defines all individuals x that are associated via the hasTopping object property with at least 1 individual y that is of type MozzarellaTopping.
A closure axiom is a particular pattern of axiom use that forms part of the OnlySome design pattern/macro. An example is
hasTopping some MozzarellaTopping and
hasTopping some TomatoTopping and
hasTopping some PeperroniTopping and
hasTopping only (MozzarellaTopping or TomatoTopping or PepperonniTopping)
In this case
hasTopping only (MozzarellaTopping or TomatoTopping or PepperonniTopping)
is the closure axiom for the existential restrictions
hasTopping some MozzarellaTopping and
hasTopping some TomatoTopping and
hasTopping some PeperroniTopping
See this paper for more details on this.
A universal (someValuesFrom) axiom is a specific construct in the OWL specification, see the OWL primer
In contrast, the term “closure axiom” refers to a particular pattern of axiom usage, in which the goal is to “close doors” left open by the open world assumption. Universal restrictions can serve as closure axioms, but not every universal restriction is a closure axiom. Equivalence axioms combined with disjointness axioms can also serve this role. See the explanation in http://ontogenesis.knowledgeblog.org/1001/