闭包公理、覆盖公理与普遍限制关系的区别

Question

What is the difference in OWL, between a

• universal restriction: which restrict the relationships for a given property to individuals that are members of a specific class.
• closure axiom: consists of a universal restriction that acts along the property to say that it can only be filled by the specified fillers.
• covering axiom

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...

Answer 1

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/

Answer 2

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.