I know that reasoning doesn't work in general when combining SWRL and OWL2 because the combination is not decidable. However, it is decidable when only certain things/rules are used. So assuming I only want to use the SWRL math built-ins, is decibability given or not?
Related
I have a background in frame-based ontologies, in which classes represent concepts and there's no restriction against assertion of class:class relationships.
I am now working with an OWL2 ontology and trying to determine the best/recommended way to represent "canonical part-of" relationships - conceptually, these are relationships that are true, by definition, of the things represented by each class (i.e., all instances). The part-of relationship is transitive, and I want to take advantage of that so that I'd be able to query the ontology for "all parts of (a canonical) X".
For example, I might want to represent:
"engine" is a part of "car", and
"piston" is a part of "engine"
and then query transitively, using SPARQL, for parts of cars, getting back both engine and piston. Note that I want to be able to represent individual cars later (and be able to deduce their parts by reference to their rdf:type), and of course I want to be able to represent sub-classes of cars as well, so I can't model the above-described classes as individuals - they must be classes.
It seems that I have 3 options using OWL, none ideal. Is one of these recommended (or are any discouraged), and am I missing any?
OWL restriction axioms:
rdfs:subClassOf(engine, someValuesFrom(partOf, car))
rdfs:subClassOf(piston, someValuesFrom(partOf, engine))
The major drawback of the above is that there's no way in SPARQL to query transitively over the partOf relationship, since it's embedded in an OWL restriction. I would need some kind of generalized recursion feature in SPARQL - or I would need the following rule, which is not part of any standard OWL profile as far as I can tell:
antecedent (body):
subClassOf(B, (P some A) ^
subClassOf(C, (P some B) ^
transitiveProperty(P)
consequent (head):
subClassOf(C, (P some A))
OWL2 punning: I could effectively represent the partOf relationships on canonical instances of the classes, by asserting the object-property directly on the classes. I'm not sure that that'd work transparently with SPARQL though, since the partOf relationships would be asserted on instances (via punning) and any subClassOf relationships would be asserted on classes. So if I had, for example, a subclass six_cylinder_engine, the following SPARQL snippet would not bind six_cylinder_engine:
?part (rdfs:subClassOf*/partOf*)+ car
Annotation property: I could assert partOf as an annotation property on the classes, with values that are also classes. I think that would work (minus transitivity, but I could recover that easily enough with SPARQL paths as in the query above), but it seems like an abuse of the intended use of annotation properties.
I think you have performed a good analysis of the problem and the advantages/disadvantages of different approaches. I don't know if any one is discouraged or encouraged. IMHO this problem has not received sufficient attention, and is a bigger problem in some domains than others (I work in bio-ontologies which frequently use partonomies, and hence this is very important).
For 1, your rule is valid and justified by OWL semantics. There are other ways to implement this using OWL reasoners, as well as RDF-level reasoners. For example, using the ROBOT command line wrapper to the OWLAPI, you can run the reason command using an Expression Materializing Reasoner. E.g
robot reason --exclude-tautologies true --include-indirect true -r emr -i engine.owl -o engine-reasoned.owl
This will give you an axiom piston subClassOf partOf some car that can be queried using a non-transitive SPARQL query.
The --exclude-tautologies removes inferences to owl:Thing, and --include-indirect will include transitive inferences.
For your option 2, you have to be careful in that you may introduce incorrect inferences. For example, assume there are some engines without pistons, i.e. engine SubClassOf inverse(part_of) some piston does not hold. However, in your punned shadow world, this would be entailed. This may or may not be a problem depending on your use case.
A variant of your 2 is to introduce different mapping rules for layering OWL T-Tboxes onto RDF, such as described in my OWLStar proposal. With this proposal, existentials would be mapped to direct triples, but there is another mechanism (e.g. reification) to indicate the intended quantification. This allows writing rules that are both safe (no undesired inferences) and complete (for anything expressible in OWL-RL). Here there is no punning (under the alternative RDF to OWL interpretation). You can also use the exact same transitive SPARQL query you wrote to get the desired results.
I am working on building a simple software ontology in Protege v5.2 and I am trying to classify pieces of software (using a reasoner plugin) as CPU intensive if their CPU time is larger than 80% of their physical execution time.
For this reason, each individual has the following data properties filled with float values:
a) hasCPUTime
b) hasPhysicalExecutionTime
I have created a class CPUIntensive and I want to add a restriction that individuals which have hasCPUTime > 0.8 * hasPhysicalExecutionTime belong in this class.
Can this be done in Protege?
OWL 2 doesn't allow arithmetic computations, e.g. multiplication (though some kind of comparison is possible using data ranges).
You need SWRL with builtins:
hasCPUTime (?ind, ?cpu) ^
hasPhysicalTime (?ind, ?phy) ^
swrlb:greaterThan (?cpu, ?mul) ^
swrlb:multiply (?mul, 0.8, ?phy)
-> CPUIntensive(?ind)
The swrlb:multiply builtin is satisfied iff the first argument is equal to the arithmetic product of the second argument through the last argument, and if the first argument is unbound, binds it to the arithmetic product of them, much like Mul is 0.8*Phy. works in Prolog.
Pellet does support those builtins:
What are the OWL ontology language boundaries? Like:
Can I use a class with different parents? (Multiple inheritance) Protege doesn't allow this.
What characters I can or cannot use? e.g. Cannot use '#' or '^' in Protege. Why?
Case-sensitive classes? e.g. class A and a are two different classes?
What else?
The boundaries of OWL are determined by the boundaries of logic of the respective OWL dialect. This is the taxonomy of the OWL2 dialects:
-First Order Logic
--SWRL/RIF
---OWL DL
----OWL EL, RL, QL
-----Concept Hierarchies
--OWL Full
---OWL DL
----OWL EL, RL, QL
-----Concept Hierarchies
---RDFS
-----Concept Hierarchies
You can find more about these dialects here.
The most used dialect is OWL-DL, as it offers a good balance between expressiveness and decidability. There is a classification system for Description Logic to determine expressiveness:
"AL" allows: Atomic negation; Concept intersection; Universal restrictions; Limited existential quantification
"FL" allows:Concept intersection; Universal restrictions; Limited existential quantification; Role restriction
"EL" allows: Concept intersection; Existential restrictions
Then there are the following extensions:
"F" - Functional properties, a special case of uniqueness quantification.
"E" - Full existential qualification
"U" - Concept union.
"C" - Complex concept negation.
"H" - Role hierarchy (subproperties - rdfs:subPropertyOf).
"R" - Limited complex role inclusion axioms; reflexivity and irreflexivity; role disjointness.
"O" - Nominals. (Enumerated classes of object value restrictions - owl:oneOf, owl:hasValue).
"I" - Inverse properties.
"N" - Cardinality restrictions (owl:cardinality, owl:maxCardinality), a special case of counting quantification
"Q" - Qualified cardinality restrictions
"D" - Use of datatype properties, data values or data types.
According to this classification the expressiveness of OWL2-DL is (SHROIQ(D)), where "S" stands for An abbreviation for "ALC" with transitive roles. (Note: there is a terminological difference between DL and OWL, for example OWL specification uses "properties", while DL uses "roles").
So, the short answer to you question is: the boundaries of OWL2-DL are (SHROIQ(D)).
Can I use a class with different parents? (Multiple inheritance)
Protege doesn't allow this
You should be careful when trying to apply metaphors from other modelling paradigms. Strictly speaking "Parents" and "inheritance" are not applicable in OWL. We can say that there is something like sharing of properties but its direction - unlike in the Object Oriented paradigm - is upwards, not downwords. OWL uses "classes" but you should think of them as sets, not as "classes" from OO. Being sets, a class can be as sub-class of different classes and Protégé allows this. In fact it is used quite often. "Boar" is a subclass of both "Bear" and "Male", just as "Bull" would be a subclass of both "Cattle" and "Male". We can always find a set of properties to create a new class. All examples so far would be of course subclasses of "Mammal"and then of "Animal", but they can be also subclasses of e.g. "Two-eyed agents", a class, which can have subclasses that are not animals, for example "two-eyed robots".
What characters I can or cannot use
OWL has different serialisations such OWL/XML, Turtle etc. Each has it's own syntax.
As you asked for useful resources, one such would be of course the OWL primer. I would also recommend this free course.
This might be a stupid question but it has been troubling me for quite some while.
I know that OWL has three variants (Full, Lite and DL) and that the newer OWL2 has three profiles (EL, QL and RL).
Now my questions:
- if a semantic reasoner supports OWL2, does that mean that is supports OWL Full too?
- if a reasoner supports OWL2 EL, does it support OWL DL then or is it simply a reasoner that is only focussed on the OWL2 EL profile?
- continuation of the above question, if it supports OWL2 EL, can such a reasoner be used to reason on normal ontologies?
Thx for your time
There is no reasoner that supports OWL 2 Full or OWL Full because they are undecidable - i.e., no reasoner can be complete on these languages.
The OWL and OWL 2 profiles overlap to a point, but do not match exactly - OWL 2 DL includes a few more constructs than OWL DL, and there are features like keys which were not defined at all in OWL.
A reasoner that supports OWL 2 EL can be used on an ontology of any expressivity, but it will not return inferences that are only valid within OWL 2 DL - which means you'll still get correct answers, but they will be incomplete wrt the answers you would get from an OWL 2 DL capable reasoner.
Reasoners that support a less expressive profile can be faster than reasoners that support a more expressive profile, since the underlying worst case complexity of reasoning is lower - i.e., for OWL 2 EL there are polynomial algorithms to compute inferences. That is not true for OWL 2 DL. This does not mean that any OWL 2 DL ontology will take more time to reason than any OWL 2 EL ontology, only that the simpler ontology is more predictable in terms of its requirements.
If I extract certain association rules from a sample itemset consisting of let's say:
a, b -> c
c, d -> e
a, c -> d
b, c -> c
Is there a way to combine the found rules into one formula depending on a fixed item count number were all rules are aggregated to get the most likely combination of all association rules combined?
Let's say the fixed item number is four and the above association rules have to be mixed to get the most likely combination. How would I do that? Are there algorithms or programmes for this?
Each association rule has a confidence and support.
For example A --> BC support : 50 % confidence : 50%.
If you combine several association rules, then how you would calculate the support and confidence of the resulting rule ? That would be a problem.
Actually, you could look at CBA: Classification by Associations. This project use association rules to perform classification. Instead of trying to combine association rules, it uses some heuristics to select the rule that is the most appropriate for classifying a new instance. To choose the best rule, it considers the support, the confidence and the size of the left par of the rule. There is other similar works.
But I have not seen any work trying to combine association rules... maybe if you search "association rule clustering" in Google you could find something related to your idea.
By the way, besides confidence and support, some people use other interestingness measures like the lift, J-Measure, etc.