In OWL 1; What is the difference between:
Parent subclassOf hasChildren min 1 Thing
and
Parent subclassOf hasChildren some Thing
Are they equivalent as both of them assert that each Parent instance must has at least one value from any class through hasChildren? as we don't specify a particular range for the someValuesFrom restriction?
In OWL 1; What is the difference between:
Parent subclassOf hasChildren min 1 Thing
and
Parent subclassOf hasChildren some Thing
OWL1 doesn't have qualified cardinality restrictions. You can't say
property min n Class
in OWL1. You can use unqualified cardinality restrictions (1), and qualified existential restrictions, like:
property min n
property some Class
In OWL 2, where you do have qualified cardinality restrictions, you have the ability to write
property min n Class
and you're absolutely right that the following are equivalent:
property min 1 Class
property some Class
and as a special case, the following are equivalent:
property min 1 owl:Thing
property some owl:Thing
The someValuesFromin OWL is equivalent to the existential quantifier in predicate logic:
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists," "there is at least one," or "for some." It expresses that a propositional function can be satisfied by at least one member of a domain of discourse. In other terms, it is the predication of a property or relation to at least one member of the domain. It asserts that a predicate within the scope of an existential quantifier is true of at least one value of a predicate variable.
Keeping this in mind, please refer to the definition of Restirction:
OWL Lite allows restrictions to be placed on how properties can be used by instances of a class.
And the definition of Cardinality:
OWL (and OWL Lite) cardinality restrictions are referred to as local restrictions, since they are stated on properties with respect to a particular class. That is, the restrictions constrain the cardinality of that property on instances of that class.
In OWL, someValuesFrom has been defined as:
The restriction someValuesFrom is stated on a property with respect to a class. A particular class may have a restriction on a property that at least one value for that property is of a certain type.
And minCardinality has been defined as:
If a minCardinality of 1 is stated on a property with respect to a class, then any instance of that class will be related to at least one individual by that property.
So, although logically they are the same, they represent different ideas.
Related
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...
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/
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.
The functional object property axiom - here in functional syntax - has the form
FunctionalObjectProperty(P)
P is an Object Property Expression, which is one of:
a named object property (PN). Example: FunctionalObjectProperty(:hasBase)
the owl:topObjectProperty
the owl:bottomObjectProperty
an inverse property. Example: FunctionalObjectProperty(ObjectInverseOf(:isBaseOf))
The first is expected. What's the use of the three other variants? These seem to only increase the complexity of parsers, reasoners and APIs. (Yes, marginally.)
The last looks redundant since OWL has an "InverseFunctionalObjectProperty". And who declares top- or bottomObjectProperty as functional ?
I searched through ontologies like geneontology.org. So far, they use nothing else than a named property (PN) as parameter.
Anyway, OWL allows P here, and I may miss the forest for the trees. What is it good for ?
Remark:The same can be asked for other unary property axioms like SymmetricObjectProperty.
See: https://www.w3.org/2007/OWL/refcard
This definition is used in OWL to define what the language syntax considers correct. However there can be some language constructs that are broadly used and other that are syntactically correct but have limited usage.
The definition of the FunctionalObjectProperty axiom allows one to state that an object property expression is functional — that is, that each individual can have at most one outgoing connection of the specified object property expression. 1
The syntax definition of FunctionalObjectProperty is:
Functional Object Properties:
FunctionalObjectProperty := 'FunctionalObjectProperty' '('
axiomAnnotations ObjectPropertyExpression ')'
This definition refers to the ObjectPropertyExpression which is defined as follows.
Object Property Expression definition
ObjectProperty := IRI
ObjectPropertyExpression := ObjectProperty | InverseObjectProperty
InverseObjectProperty := 'ObjectInverseOf' '(' ObjectProperty ')'
This basically mean that there are 2 ways to define an object property.
The first way is to directly define an IRI as an object property.
The second way is to indirectly define an object property as the inverse of an already defined object property.
The difference can be demonstrated in these examples:
Example A: FunctionalObjectProperty(:isGoodFor)
Example B: FunctionalObjectProperty(ObjectInverseOf(:isBaseOf))
The Example A uses an existing Object Property :isGoodFor while the Example B uses the inverse of the defined Object Property :isBaseOf without defining an IRI for it.
The syntax definition for ObjectPropertyExpression includes any Object Property IRI, since it does not exclude it. Therefore the TopObjectProperty and BottomObjectProperty are syntactically valid choices.
So the following are syntactically valid:
FunctionalObjectProperty(owl:topObjectProperty)
FunctionalObjectProperty(owl:bottomObjectProperty)
However owl:topObjectProperty and owl:bottomObjectProperty have predefined semantics in OWL2. So while the above statements are syntactically correct, it would not be a good practice to use them.
Definitions of TopObjectProperty and BottomObjectProperty
Owl defines 2 built-in object properties with the IRIs owl:topObjectProperty and owl:bottomObjectProperty. And have predefined semantics.
The object property with IRI owl:topObjectProperty connects all possible pairs of individuals.
The object property with IRI owl:bottomObjectProperty does not connect any pair of individuals.
In OWL, is there a way to state that an individual of a particular class must be related to another individual via a specific object property?
For example, I would like to state that:
forall(x) Object(x) -> exists(y) Shape(y) ^ hasShape(x, y)
i.e., "For all objects, there exists a shape that is the shape of the object."
so that if there is an individual of the type Object that has no shape associated with it, a reasoner would find it to be inconsistent.
I tried an axiom:
Object SubClassOf hasShape min 1 Shape
but it's not working.
It seems like the issue is because Object Property in OWL has no identity, but is there a workaround for this issue?
(I'm using Protege 5.2.0)
You are correct that the meaning of Object SubClassOf hasShape min 1 Shape is that every individual of Object is associated with an individual of Shape via the hasShape property.
So if you create an individual x of type Object without x being associated with an individual of Shape, why does the reasoner not determine that your ontology is inconsistent? The reason for this is due to the open world assumption. Informally it means that the only inferences that the reasoner can make from an ontology is based on explicit information stated in the ontology or what can derived from explicit stated information.
When you state x is an Object, there is no explicit information in the ontology that states that x is not associated with an individual of Shape via the hasShape property. To make explicit that x is not is such a relation, you have to define x as follows:
Individual: x
Types:
Object,
hasShape max 0 owl:Thing
Btw, this problem has nothing to do with identity as you stated.
One solution I found was to make the ontology "closed world", by making owl:Thing equivalent to the set of all individuals defined so far.
Is it possible to express the meaning of xs:unique in OWL?
Say, I define a property hasID whose range is integer. 2 different individuals A and B could not have the same ID. So you don't have A hasID 1 and B hasID 1 at the same time.
That's an inverse functional property. In OWL, there are inverse functional object properties, such that if p is an inverse functional object property then p(A,C) and p(B,C) imply A = B.
From the specification:
9.2.8 Inverse-Functional Object Properties
An object property inverse functionality axiom
InverseFunctionalObjectProperty( OPE ) states that the object property
expression OPE is inverse-functional — that is, for each individual x,
there can be at most one individual y such that y is connected by OPE
with x. Each such axiom can be seen as a syntactic shortcut for the
following axiom:
SubClassOf( owl:Thing ObjectMaxCardinality( 1 ObjectInverseOf( OPE ) ) )
However, OWL doesn't have inverse functional datatype properties. This is the subject of What's the problem with inverse-functional datatype properties? on answers.semanticweb.com. (I'm providing a link to the WaybackMachine's archived version of that page, since the actual site seems to be down.)
I have OWL ontology without individuals. Given two classes
Cs
and
Cd
How will the query look like an what type of reasoners can be used to find all the property chains such that:
(Cs subClassOf PropertyP exactly 1 Cd)
Where Cs is the domain of PropertyP and Cd is its range.
Chain means that this inference must be transitive, i.e. if
(Cs subClassOf PropertyP1 exactly one Ctemp) and (Ctemp subClassOf PropertyP2 exactly one Cd)
then, {PropertyP1, PropertyP2} must be considered a property chain between Cs and Cd.
Please note that I'm not talking about property chain such that one in OWL2, because in the case of OWL2, I have to define this chain previously, while in my case I cannot do so.