First of all, my English is poor, so sorry if my writing is confusing.
I'm trying to create the following relationship between instances: if A propertyX B, and C propertyY A, then C propertyX B. In my case, I want to specify that if a ManagerA "manages" an employee, and ManagerB has the same job as ManagerA, then he also manages the same employee.
I tried to use chain properties to do that, but the reasoner (FaCT ++ 1.6.5) doesn't work when I activate it (the log says a non-simple property is being used as one). I think the problem is in the fact that the property "manages" is asymmetric and irreflexive and the property "sameJob" is transitive and symmetric, but I'm not sure if that's the case. I applied the chain property in the "manages" property, stating: sameJob o manages SubPropertyOf: manages.
I'm just starting with Protégé and will appreciate any help a lot.
The reason for the error is due to manages not being a simple role, i.e. if you have r1 o ... o rn subPropertyOf r where n>1 then r is a non-simple role. Non-simple roles cannot be used in IrreflexiveObjectProperty and AsymmetricObjectProperty. See section 11 of OWL 2 syntax. The reason for the constraint on roles is to maintain decidability.
However, you can achieve the desired result by adding a SWRL rule:
manages(?x, ?y) ^ sameJob(?x, ?z) -> manages(?z, ?y).
Related
I want to find out if an Individual belonging to Class A, has a least one relation with ALL the Individuals of Class B.
I have a problem finding a suitable expression that gives me the DL query results I desire. For the below example:
Classs: Course {CourseA, CourseB, CourseC, CourseD}
Class: Program {UG_CE, G_CE}
Class: Student {John}
ObjectProperty: is-PartOf (Course,Program)
ObjectProperty: hasEnrolledIn (Student, Course)
for Individuals: CourseA and CourseB, I asserted the property:
is-PartOf UG_CE
For Individual John, the following 3 properties were asserted:
hasEnrolledIn CourseA
hasEnrolledIn CourseB
hasEnrolledIn CourseC
I also added to individual type
hasEnrolledIn only ({CourseA , CourseB , CourseC})
to address OWA problems.
I want to know if John has enrolled in all the courses that are required for UG_CE, note that John has enrolled in all courses and an additional course.
After invoking the reasoner, the following query will not give me the desired result:
Student that hasEnrolledIn only (is-PartOf value UG_CE)
since "only" is limited to defining the exact number of relationships, it does not serve the intended purpose. Also, I can't use Max or Min since the number of courses are inferred and not known in advance.
Can another approach address my problem?
While it's good to "close" the world with regard to what classes John is taking, it's just as important to close it with regard to what classes are required for UG_CE. I think you need an approach like this:
M requires A.
M requires B.
M : requires only {A, B}.
J enrolledIn A.
J enrolledIn B.
J enrolledIn C.
J : enrolledIn only {A, B, C}.
For an individual student J, you can find out whether they are enrolled in all the classes required for M by asking whether the set of classes required by M is a subset of the set of classes enrolled in by the student:
(inverse(requires) value M) SubClassOf (inverse(enrolledIn) value J)
or, in DL notation, with enumerated classes (lots of possible ways to express this):
∃ requires-1.{M} ⊑ ∃ enrolledIn-1.{J}
Now, if OWL had property negation, you could get the set of students who are only not enrolled in classes not required by an expression like this:
not(enrolledIn) only not(inverse(requires) value M)
That asks for things such that the only courses they're not enrolled in are courses not required by M. However, OWL doesn't have property negation expressions, so I'm not sure where that leaves us. The simplest thing to do would be add a "not enrolled in" property, though that doesn't seem as elegant.
I am using Protege5.0, and i want to implement SWRL rule ie
User(?u), isInActivity(?u, ?cm), ContextMeeting(?cm) -> FamilyContact(?f), hasStatus(?f, "Reject")
which means "if user is in meeting then familycontact has status "reject".
This syntax should work and protege doesn't show any error. However, its not working.
And when i write
User(?u), isInActivity(?u, ?cm), ContextMeeting(?cm), FamilyContact(?f) -> hasStatus(?f, "Reject")
This syntax works perfectly but its useless when i write complex rules in such format.
Can anyone explain me the difference between the two formats and also give me a perfect solution?
More explanation:
i have a main class People & subclasses of People are Contact & User. The subclasses of Contact are FamilyContact, EmployeeContact etc. **The User and Contact are related by an object property isContactOf(People,Contact).In my ontology there should be only one individual of class User. Now, i want to implement SWRL rules, ie If **user is in meeting then FamilyContact hasStatus "Reject".** This reject simply means that Family members can not call the user. Other rule is If user is in meeting then EmployeeContact hasStatus "Pass". hasStatus(Contact,String) is a functional property.
the second rule syntax works perfectly, however when I want to implement a rule for those instances which are both EmployeeContact and FamilyContact then i get problem. eg if i write a rule i.e
User(?u), isInActivity(?u, ?cm), ContextMeeting(?cm), FamilyContact(?f), EmployeeContact(?e), DifferentFrom(?f,?e)-> hasStatus(?f, "Reject").
It works somehow but i get a problem. It makes the other instances of EmployeeContact also the Instances of FamilyContact and vice versa.
The rule
User(?u) ∧ isInActivity(?u, ?cm) ∧ ContextMeeting(?cm) → FamilyContact(?f) ∧ hasStatus(?f, "Reject")
uses ?f in the right hand side (the consequent) of the rule, but not on the left (the antecedent). That's not allowed in the language (emphasis added):
2.1. Rules
Atoms may refer to individuals, data literals, individual variables or
data variables. Variables are treated as universally quantified, with
their scope limited to a given rule. As usual, only variables that
occur in the antecedent of a rule may occur in the consequent (a
condition usually referred to as "safety"). This safety condition does
not, in fact, restrict the expressive power of the language (because
existentials can already be captured using OWL someValuesFrom
restrictions).
If it were legal, then your rule would mean:
For every u, cm, and f,
if u is a User and cm is a ContextMeeting and u is in cm,
then f is a family contact and has status "reject".
But since there are no constraints on ?f, this says that any user is in any context meeting, then everything is a family contact with status "reject", and that's probably not what you want. Shouldn't ?f be related to ?u somehow? The proposed alternative:
User(?u) ∧ isInActivity(?u, ?cm) ∧ ContextMeeting(?cm) ∧ FamilyContact(?f) → hasStatus(?f, "Reject")
has a similar problem. It would mean:
For every u, cm, and f,
if u is a User and cm is a ContextMeeting and u is in cm and f is a family contact,
then f has status "reject".
There's still no connection between u and f, so this says that if any user is in any context meeting, then every family contact has status "reject". That doesn't seem like what you'd want either.
In an OWL-DL ontology, consider a property p with domain D and range R where D has a restriction over p to have cardinality of exactly one:
D SubClassOf p exactly 1 Thing
(D ⊑ =1 p.Thing)
Can we then infer that p is a functional property, since each d of type D will have exactly one value for p? If this is correct, can a reasoner infer this knowledge?
In OWL, a property is function when each individual has at most one value for the property. That "at most" is important; it is permitted for something to have no value for the property. (That means that a functional property in OWL is actually more like a possibly partial function in mathematics.) That said, if every individual has a exactly one value for a property, then it clearly has at most one value for the property, so the property would, as you suspect, be functional. We can walk though a specific case, though, to be sure that this is general, and because we need to make sure that the property p here actually has at most one value for every individual.
Proof: Suppose the property p has domain D, and D is a subclass of =1 p.Thing, so that every D has exactly one p
value. Is it the case that every individual x has at most one value
for p? There are two cases to consider:
x is a D. Then by the subclass axiom with the restriction, x must have exactly one value for p, and one is less than or equal to
one.
x is not a D. Then x has no values for p. If it did, then it would be in the domain of p, which is D, and that is a
contradiction. Then x has zero values for p, and zero is less
than or equal to one.
Then any individual x at most one value for the property p, which
is the definition of p being functional. Thus, p is functional.
QED
An OWL DL reasoner should be able to confirm this, and it shouldn't be hard to check.
Suppose I have the following instance data and property axiom:
Mary hasChild John
Ben hasChild Tom
Mary hasHusband Ben
hasHusbandChild: hasHusband • hasChild
How can I create the property hasChilds such that:
hasChilds: hasChild ⊔ hasHusbandChild
is true?
OWL doesn't support union properties where you can say things like
p ≡ q ⊔ r
but you can get the effects of:
q ⊔ r ⊑ p
by doing two axioms:
q ⊑ p
r ⊑ p
Now, 2 is not the same as 1, because with 1, you know that if p(x,y), then either q(x,y) or r(x,y), whereas with 2, p(x,y) can be true without either q(x,y) or r(x,y) being true.
Similarly, you can't define property chains in OWL like:
q • r ≡ p
but you use property chains on the left-hand side of subproperty axioms:
q • r ⊑ p
The difference between the two, of course, is that with 6 you can have p(x,y) without x and y being connected by a q • r chain.
It's not quite clear what you're asking, but I think what you're trying to ask is whether there's a way to say that the child of x's spouse is also a child of x. You can do that in OWL2 using property chains, specifically that
hasSpouse • hasChild ⊑ hasChild
This is equivalent to the first-order axiom:
∀ x,y,z : (hasSpouse(x,y) ∧ hasChild(y,z)) → hasChild(x,z)
A number of other questions on Stack Overflow are relevant here and will provide more guidance about how to add this kind of axiom to your OWL ontology:
OWL2 modelling a subclass with one different axiom
Adding statements of knowledge to an OWL Ontology in Protege)
owl:ObjectProperty and reasoning
Using Property Chains to get inferred Knowledge in an OWL Ontology(Protege)
As an alternative, you could also encode the first-order axiom as a SWRL rule.
Lots of commonly useful properties of functions have concise names. For example, associativity, commutativity, transitivity, etc.
I am making a library for use with QuickCheck that provides shorthand definitions of these properties and others.
The one I have a question about is idempotence of unary functions. A function f is idempotent iif ∀x . f x == f (f x).
There is an interesting generalization of this property for which I am struggling to find a similarly concise name. To avoid biasing peoples name choices by suggesting one, I'll name it P and provide the following definition:
A function f has the P property with respect to g iif ∀x . f x == f (g x). We can see this as a generalization of idempotence by redefining idempotence in terms of P. A function f is idempotent iif it has the P property with respect to itself.
To see that this is a useful property observe that it justifies a rewrite rule that can be used to implement a number of common optimizations. This often but not always arises when g is some sort of canonicalization function. Some examples:
length is P with respect to map f (for all choices of f)
Converting to CNF is P with respect to converting to DNF (and vice versa)
Unicode normalization to form NFC is P with respect to normalization to form NFD (and vice versa)
minimum is P with respect to nub
What would you name this property?
One can say that map f is length-preserving, or that length is invariant under map fing. So how about:
g is f-preserving.
f is invariant under (applying) g.