OWL and OWL Semantics Flashcards
(95 cards)
1
Q
OWL Week 5 Summary
A
OWL (Web Ontology Language) is a language that allows us to represent rich and complex knowledge about things (or groups of things) and relations between them. OWL is a logic-based language and is computationally efficient, therefore knowledge expressed in OWL can be exploited by computer programs, e.g., to verify the consistency of that knowledge or to make implicit knowledge explicit. OWL documents (ontologies) can be published in the World Wide Web and may refer to or be referred from other OWL ontologies.
In discussing OWL, we start by identifying the requirements for an ontology language, we look at the two OWL specifications, OWL1 and OWL2, then we present OWL syntax and semantics
2
Q
Key week 5 points to remember:
A
RDFS simple representation model with efficient deduction and querying, but limited expressivity:
- Disjointness of Classes
- Property characteristics (inverse, transitive, ….)
- Local scope of properties
- Complex concept definitions (Boolean combination of classes)
Wishlist for ontology languages;
OWL as an extension of RDFS that satisfies the wishlist.
3
Q
OWL Week 6 Summary
A
This week we continue exploring OWL as a knowledge representation for knowledge about a domain. This means not only defining the entities (classes, properties and individuals), but also the constraints that apply to them. In these videos we focus on modelling knowledge in OWL, and on the semantics of OWL which supports reasoning with the constraints modelled in an ontology. This is crucial for ensuring that the individuals in a KG (the A-box) and the KG schema (the T-box) are consistent and coherent.
4
Q
Key week 6 points to remember:
A
Being familiar with the semantics of OWL helps to understand the effect of restrictions
- Useful in debugging an ontology.
Set based semantics of:
- Classes and properties;
- Restrictions;
5
Q
What features can RDFS not provide?
A
- Disjointness of classes
- property characteristics (inverse, transitive)
- local scope of properties (the range of values for the property ‘rents’ is restricted to all the values of the class apartment)
- complex concept definitions (such as boolean combinations of classes, like the intersection of two classes)
- cardinality restrictions (an individual ResidentialUnit has at most 1 address)
- a way to distinguish between classes and instances (Building is a class, AmsterdamBuilding is an instance of the class Building)
- a way to distinguish between language constructors and ontology vocabulary (e.g. rdfs:Class is a language constructor and ex:teacher is a ontology vocabulary)
- detection of inconsistent-seeming assertions (Romeo is not the wifeOf Juliet)
6
Q
What can we say about RDFS entailment?
A
You can entail a lot of things however not all types of inferences are possible. The RDFS rules are not encompassing, e.g. we can’t model symmetry, x marriedTo y implies y marriedTo x
7
Q
What is OWL?
A
OWL (Web Ontology Language) extends RDFS with more expressive axioms (statements).
8
Q
What is the Semantic Web?
A
- It represents web content in an easier machine-processable form
- It describes meta-data about resources on the web (descriptions about data, model and constraints used to represent them)
9
Q
What are the conflicting aims for a semantic language?
A
- Ontologies provide structured vocabulary for describing meta-data (we model the domain)
- languages representing ontologies must be expressive as possible whilst permitting automated deduction
- to describe meta-data we want a logic based language
- to simulate human deduction efficiently we want a logic that permits efficient automated deduction
- the logic of choice is a compromise between expressiveness and complexity of deduction
10
Q
Ontology language wishlist: Compromise between expressivity and scalability:
A
- Balance of expressivity and scalability
- A well defined syntax for automatic machine processing of information
11
Q
Ontology language wishlist: Formal Semantics:
A
- These describe the meaning of knowledge precisely, allowing computers to reason. Inconsistencies should be recognised through classification
12
Q
What are the 3 types of formal semantics for an Ontology language?
A
- Class Membership: if x ∈ A and A ⊆ B then we can infer that x ∈ B
- Consistency: x ∈ A, A ⊆ B ∩ C, A ⊆ D and B ∩ D = ∅ then we have an inconsistency!
- Classification: if some property-value pairs are a sufficient condition for membership in A and x satisfies them, infer x ∈ A
13
Q
Ontology language wishlist: Efficient reasoning:
A
- derivation can be computed mechanically
- consistency, classification, detection of unintended relationships between classes
14
Q
Ontology language wishlist: Sufficient expressive power:
A
- Compatibility with RDF and RDFS
15
Q
Ontology language wishlist: Open World Assumption:
A
- the absence of a particular statement means (in principle) that the statement has not been made explicit yet
- whether the statement is true or not is irrelevant
- thus from the absence alone, a deductive reasoner cannot infer the statement is false
16
Q
What are the 5 main requirements of Ontology Languages?
A
- A well defined syntax (RDFS/OWL)
- A formal Semantics (RDFS/OWL)
- Convenience of expression (RDFS/OWL)
- Efficient (complex) reasoning support (OWL)
- sufficient expressive power (OWL)
17
Q
Why isn’t simply extending the RDF Schema enough to give us a semantic web language?
A
- Extending RDFS wouldn’t give us expressive power and efficient reasoning simultaneously
- Combining RDFS with logics leads to uncontrollable computational properties and layering issues
18
Q
What are the OWL logical expressions syntax’s?
A
And, Or, Not
* :Woman = :Human and :Female
* :Person = :Man or :Woman
* :Man = not (:Woman)
19
Q
What is the OWL local properties syntax?
A
only
* :Tenant only :rents :ResidentialUnits
20
Q
What are the OWL Equality/Inequality syntax’s?
A
differentFrom / sameAs
* :john differentFrom :mary
* :JKRowling sameAs :RobertGalbraith
Important as operating under open world assumption, so if we don’t state john and mary are different, we could infer from the facts in the schema they’re the same.
21
Q
What is the OWL required/optional properties syntax’s?
A
- :rents :ResidentialUnit is a required property for :Tenant
22
Q
What is the OWL Required values syntax’s?
A
- :AmsterdamBuilding :hasLocation = :Amsterdam
The value for the :hasLocation property for the class :AmsterdamBuilding can only be :Amsterdam
23
Q
What is the OWL enumerated classes syntax’s?
A
- DaysOfTheWeek = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
24
Q
What do formal semantics allow?
What should the reasoner raise?
A
They allow for the automatic deduction of new facts and possible conflicts between class definitions (consistency).
The reasoner should raise facts that we have stated incorrectly. E.g. :Mammals and :Fish are disjoint classes i.e. they cannot have any common individuals :dolphin?
25
What does automatic reasoning allow?
It allows us to automatically perform checks that detect the correctness of the model + instances.
26
What 3 checks does automatic reasoning perform?
- check the consistency of the ontology
- check for unintended relations between classes
- check for unintended classification of instances
27
How can an ontology language be provided with formal semantics and reasoning support?
By mapping it to a known logical formalism and using reasoning tools developed for the chosen formalism
28
What are the shared features of OWL1 and OWL2?
- Rationale for OWL: Open World Assumption
- Reasonable trade-off between expressivity and scalability
- fully declarative semantics
29
What are the features of OWL DL?
- fragment of first order predicate logic, decidable
- known complexity classes
- reasonably efficient for real ontologies + instances
30
What are the 3 species of OWL1, describe them?
- OWL Full
- OWL DL (sublanguage of OWL Full)
- OWL Lite (sublanguage of OWL DL without nominals and XML datatypes)
31
Describe OWL Full
- Very high expressiveness, uses OWL primitives
- fully compatible with RDF and RDFS
- Though we lose decidability, not complete or efficient reasoning support
- all syntactic freedom of RDF, primitives can be combined in arbitrary ways with RDF/RDFS
32
Describe OWL DL
- It imposes restrictions on the use of OWL/RDFS constructors
- Applies OWL's constructors to each other not permitted (so limits RDFS expressivity)
- Provides reasonably efficient reasoning support
33
Describe OWL Lite
- Simple classification hierarchy and constraints.
- Excludes enumerated classes, disjointness statements and arbitrary cardinality.
- Reasoning is not tractable
34
What are the 3 profiles of OWL2, describe them?
- OWL2 EL
- OWL2 RL
- OWL2 QL
(sublanguages of OWL2 trade expressive power for efficient reasoning. Each supports different application scenarios)
35
Describe OWL2 EL
- Represents very large ontologies, efficient reasoning performance, guaranteed at the expenses of expressive power
36
Describe OWL2 RL
- subclass axioms interpreted as rule like implication, with head - superclass and body - subclass
- different restrictions on subclasses and superclasses
- allows integration of OWL with rules
37
Describe OWL2 QL
- useful for querying data rich applications
- different restrictions on subclasses and superclasses
- suitable for simple, lightweight ontologies with numerous individuals and it's necessary to access data directly via SQL queries
- fast implementation on top of legacy DB systems, relational or RDF
38
What two layers does the OWL syntax consist of?
- A syntax layer and a semantics layer. OWL is only an ontology languages, all the data is still represented by an RDF graph.
39
What are DLs?
DLs: Description Logics are a family of KR languages that vary in expressivity levels between Propositional Logic (v simple) and First Order (more complex) Logic
- They provide a logical formalism for ontologies and the sematic web
- OWL and it's profiles are based on DLs
40
What are features of the core reasoning problems for most DLs?
- They are usually decidable
- The decision procedures implementing them are typically efficient and decidable.
- For some problems it’s not possible to produce a result to a query in a certain amount of time
41
How are DL logical axioms and assertions are stated?
DL logical axioms and assertions are stated in T-boxes and A-boxes
42
Explain what the T-Box is and give an example?
The T-Box contains terminological knowledge expressing the vocabulary
- It's independent from the instances and generally consists of subsumption (⊑) and equivalence (≡) axioms
- Can be represented in OWL
E.g.
* LuxuryKitchenApartment ⊑ ∀ hasKitchen.LuxuryKitchen (declares that a LuxuryKitchenApartment must have the following properties to be a subclass of LuxuryKitchen - a LuxuryKitchenApartment is something that for all the values of the property hasKitchen the values are of class LuxuryKitchen)
* LuxuryApartment ≡ Apartment ⊓ ∀ hasKitchen.LuxuryKitchen (declares that a LuxuryApartment is an Apartment and is something that hasKitchen that only has values of type LuxuryKitchen).
43
Explain what the A-Box is and give an example?
The A-Box contains assertional knowledge i.e. facts about the instances structured according to the T-Box. This includes:
- facts about individuals, e.g. a, b, c
- a set of concept membership assertions C(a)
- role assertions (assertions of properties that hold for specific individuals)
- Can be represented in RDF
E.g.
* LuxuryApartment(BaronWayApartment) - BaronWayAparment is an instance of LuxuryApartment
* locatedIn(BaronWayApartment, Amsterdam) - BaronWayAparment is locatedIn Amsterdam, we assume Amsterdam is an instance of class city and BaronWayAparment is an instance of class apartment according to some namespace.
44
Describe the OWL Ontology Header
- Starts with the OWL namespace
- Embedded within the OWL ontology tag is a number of housekeeping assertions (e.g. comments, priorVersion, imports, label)
45
What can we describe with OWL? give examples
OWL ontologies describe a world in terms of:
- individuals (corresponding to constants): Homer, Lisa
- classes (corresponding to unary predicates): man(x), woman(x), clever(x), silly(x)
- properties/roles (corresponding to binary predicates): sisterOf(x, y), worksFor(y, z)
46
What can we say about OWL assertional knowledge?
We can make assertions about instances (these typically assert information about named individuals).
- what we can assert can be restricted to what can be stated in RDF
47
When do we use rdf:ID and rdf:about?
We can use them interchangeably, however
- If referring for the first time to an individual that you don't intend to use again in the document, use rdf:ID
- If referencing an individual that's been referred to before and will be used many times, use rdf:about
48
Does OWL abide by the UNA?
UNA = Unique Name Assumption
- Despite this being a feature of DL, OWL does not hold this assumption
- this is because the web is a scattered dataset where anyone can make statements referring to the same item (named differently) or refer to different items (named identically)
49
What does OWL provide, since it doesn't hold the UNA?
As it doesn't hold the unique name assumption, it provides two constructs:
* owl:sameAs - URIs refer to the same entity or individual
* owl:differentFrom - URIs refer to different entities or individual
50
What are the two Predefined OWL classes, and how are they linked?
* owl:Thing, ⊤ (in DL formalism), class containing all individuals (a class that contains every class)
* owl:Nothing, ⊥ (in DL formalism), “empty” class containing no individuals
* For every class C, owl:Nothing is a subclass of C, C is a subclass of owl:Thing
51
How are classes expressed in OWL?
classes are defined as owl:class (this is a subclass of rdfs:class).
We can state classes are:
- x rdfs:subClassOf y
- x owl:disjointWith y
- x owl:equivalentClass y
Note: Classes/subclasses appear in the T-Box part of a DL ontology
52
What do we know if we state x owl:equivalentClass y?
That every instance in class x is also an instance of class y and vice versa
53
Why are OWL class constructors useful?
We can use existing classes to define (new) classes, using the union, intersection and complement of one or more declared classes.
- owl:complementOf
- owl:unionOf
- owl:intersectionOf
E.g. single is the complementOf the class married
54
What does owl:oneOf allow?
This allows for defining a class through enumeration: Owl syntax example:
55
As in rdfs, what are the two types of properties in OWL?
Datatype properties relate objects to data type values e.g. name, phoneNo, age
- owl:DatatypeProperty
Object properties relate objects to other objects e.g. marriedTo, father, spouse
- owl:ObjectProperty
56
Explain the owl:inverseOf and owl:equivalentTo constructs in relation to a property
owl:inverseOf allows us to specify that by swapping the domain and range of one property the relationship is equal to another property. E.g. childOf owl:inverseOf parentOf
owl:equivalentProperty allows us to say all pairs with this property also have this equivalentProperty. E.g. offspringOf owl:equivalentProperty childOf
57
What do OWL property restrictions allow?
They allow us to define new classes from existing class, property and individual names
58
Describe the property restriction Existential quantification
Existential quantification allows us to define a class that consists of all objects for which there exist at least one individual among the values
* the restriction defines an anonymous class with no ID and only local scope - it can only be used in the place the restriction appears
* Owl syntax: owl:Restriction, owl:someValuesFrom
* E.g. motherOfToddler will have some toddler. Amongst all the values that motherOf can have as it’s range, at least one of them must be of type toddler.
59
Describe the property restriction Universal qualification
Universal quantification allows us to define a class that consists of all objects for which all values of motherOf are babies.
* So all values of the property motherOfBaby's range must be baby, despite the range of MotherOf being wider than just the class baby.
* Owl syntax: owl:Restriction, owl:allValuesFrom
60
How can we use cardinality restrictions in OWL and what is the owl syntax for them?
Can use cardinality restrictions to build new classes, by specifying how many values a given property should have in terms of:
* min, max and exactly cardinality restrictions
61
Give the owl syntax to say motherOfChildren must have more than 1 child
62
Give the owl syntax to say motherOf has a maximum of 4 children
63
Give the owl syntax to specify the exact cardinality of number of children a mother has
64
What owl syntax do we use to specify what the type of values a property should have:
owl:Restriction, owl:hasValue
E.g. We impose the restriction that children are offspringOf Marge. We define a specific value that must occur for a property, in the place of the range or domain.
65
What are owl property characteristics, list them:
They state the characteristics of object properties, and use these characteristics to refine reasoning:
- owl:TransitiveProperty
- owl:SymmetricProperty
- owl:FunctionalProperty
- owl:inverseOf
- owl:InverseFunctionalProperty
66
Give the formal logic and some examples of the owl:TransitiveProperty
For all x, y, z if R(x, y) and R(y, z) then R(x, z), e.g. isTallerThan, hasSameGradeAs, isSiblingOf
67
Give the formal logic and some examples of the owl:SymmetricProperty
For all x, y if R(x, y) then R(y, x) e.g. isSiblingOf, hasSameGradeAs, isFriendOf ...
68
Give the formal logic and some examples of the owl:inverseOf
For all x, y if R(x, y) then R(y, x) ≡ R-(x, y) e.g. hasParent has inverse isParentOf
69
Describe functions in OWL semantics:
A function from a set A to a set B is a binary relation R ⊆ A × B in which every element of A is R-related to a unique element of B, so for each a ∈ A, there is precisely one pair (a, b) in R.
70
Give the formal logic and some examples of the owl:FunctionalProperty
For every x there's at most 1 y with R(x, y)
* at most one value is associated to each object e.g. directSupervisor
71
Give the formal logic and some examples of the owl:InverseFunctionalProperty
For every y there's at most 1 x with R(x, y)
* two different objects cannot have the same value associated to them e.g. hasStudentNumber
* for each StudentNumber, there can only be one student associated to that number.
72
Describe OWL property chains:
In OWL an object property is a binary predicate used to state facts in the form of a triple. The subject/object entities are identified by an IRI (or interchangeably URI)
- OWL2 allows for the composition of two or more object property statements in a chain
- The object position of one statement is the subject of the following fact (taking two statements and put them together in a chain). Similar to equijoin in databases
73
What are the 3 types of OWL2 properties and give an example?
- owl:DatatypeProperty is a property where the range is a set of data values, e.g. foaf:birthday rdf:type owl:DatatypeProperty
- owl:ObjectProperty is a property where the range is a set of individuals, e.g.:rents rdf:type owl:ObjectProperty
- owl:AnnotationProperty doesn’t yield any logical implication, e.g. rdfs:label rdf:type owl:AnnotationProperty
74
What is important to remember about the set of classes, named individuals and properties (datatype, object and annotation)?
They are all mutually disjoint.
- Classes, Named Individuals, and Properties are three distinct categories.
- An entity in an ontology can belong to only one of these categories at a time.
- There's no overlap between them.
75
How do we use the rdfs:subClassOf property to state the cheesy toppings have some ingredient "cheese" as their “main ingredient”?
We have to define that Cheesy topping is a subclass of all things that have as main ingredient some cheese.
E.g.
:CheeseTopping
a owl:Class ;
rdfs:subClassOf [ a owl:Restriction ;
owl:onProperty :mainIngredient
owl:someValueFrom Cheese ].
76
How do we say a MeatyPizza is the EquivalentClass of any pizza that has, amongst other things, at least one meat topping?
We define that this class name corresponds to the class definition given on the right hand side of the axiom and is equivalent to the intersection between the class pizza and the class of all things for which the hasTopping property applies. In this case we want the restriction that at least one value is of type meatTopping.
:MeatyPizza rdf:type owl:Class ;
owl:equivalentClass [ rdf:type owl:Class;
owl:intersectionOf (:Pizza
[ rdf:type owl:Restriction ;
owl:onProperty :hasTopping;
owl:someValuesFrom :MeatTopping])
]:
77
How can we use the owl:EquivalentTo property to state that CheeseTopping is exactly the same as the class of things that have as a main ingredient at least one thing that is cheese.
:CheeseTopping
a owl:Class ;
owl:EquivalentTo
[ a owl:Restriction ;
owl:onProperty :mainIngredient
owl:someValueFrom Cheese ].
78
What does the someValuesFrom property indicate, when used to declare primitive or defined classes?
When used it indicates the property has to have some or at least one of the value
79
How is domain expressed in owl description logic?
R rdfs:domain C means anything to which R applies is in C, e.g. :hasTopping rdfs:domain :Pizza
* Description logic as ∃R. ⊤ ⊑ C
* ∃hasTopping Pizza. ⊤ ⊑ → domain hasTopping Pizza
The local scope for relationship R:
* Pizza ⊑ ∃hasTopping.Topping
80
What does the allValuesFrom property indicate when used to declare primitive or defined classes?
It indicates only or no values except, e.g. A VegetarianPizza is any pizza that has only topping from the class VeggieTopping
- It defines the exclusivity of values.
81
How is range expressed in owl description logic?
Range R rdfs:range C when applied to a relationship means anything one can reach by R is in C
* :hasTopping rdfs:range :VeggieTopping
* Description logic as ⊤ ⊑ ∀R.C
* ⊤ ⊑ ∀hasTopping.VeggieTopping
Local scope for R:
* VeggiePizza ⊑ ∀hasTopping.VeggieTopping
82
What is R-Box?
The set of property axioms
- R-Box (Role Box) is the component of an ontology that deals with roles (relationships or properties) between concepts.
such as:
- Symmetric: If R(x, y), then R(y, x). (e.g., isMarriedTo)
- Transitive: If R(x, y) and R(y, z), then R(x, z). (e.g., ancestorOf)
- Reflexive/Irreflexive: R(x, x) must/must not hold.
- Functional: An individual can have at most one value for R. (e.g., hasSSN)
- Inverse: If R(x, y), then S(y, x), where S is the inverse of R. (e.g., hasChild and isParentOf
83
What is punning?
- Punning allows treating a class as both a class and an individual (instance of another class).
- This is useful when you want to describe metadata about classes themselves.
84
How do we define the semantics of description logics?
By providing an interpretation of
* classes as sets of individuals
* properties (roles) as sets of ordered pairs of individuals (these individuals are typically assumed from a given domain)
85
How can we define interpretations?
Interpretations (ℐ) are thought of as possible “realities”
* we can see them as a function from abstract representations to the actual elements in set theory (things that exist in the domain)
* the function assigns values to elements and may be the model of a graph or an ontology
86
owl:Class specialises rdfs:Class and is used to represent classes. A set of individuals can be:
* atomic (i.e. identified by an IRI) :Building rdf:type owl:Class
* complex, i.e. built as boolean combination from other entities (classes and properties)
87
owl:NamedIndividual is the set of concrete individuals, used instead of rdfs:Resource
- give an example
* :BaronWayApartment rdf:type owl:NamedIndividual
* :BaronWayApartment rdf:type :Building → BaronWayApartment is an instance of Building
88
The T-Box (classes only) is composed by Subsumption and Equivalence Axioms. Explain the difference in interpretations when each is used:
* Subsumption Axioms: C ⊑ D → the interpretation of class C is contained in the interpretation of class D. Declares Primitive classes.
* Equivalence Axioms: C ≡ D → the interpretation of class C is equal to the interpretation of class D. Declares Defined classes.
89
What are the semantics for union and intersection?
* A ⊑ C ⊓ D e.g. MargheritaTopping ⊑ CheeseTopping ⊓ TomatoTopping
A is contained in the individuals that belong to the intersection of C and D.
* A ⊑ C ⊔ D e.g. VegetarianPizza ⊑ CheeseTopping ⊔ VegetableTopping
A is contained in the individuals that belong to the union of C and D.
90
What are the semantics for negation and disjointness?
* C ⊑ ¬ D → A C is not a D
* VegetarianTopping ⊑ ¬ MeatTopping
* Everything that is contained in a vegetarianTopping is not a MeatTopping
* Considers every element of the domain of I that belongs to D but doesn’t belong to C
* C ⊓ D ⊑ ⊥ → Nothing is both a C and a D
* Equivalent to C ⊑ ¬ D (and D ⊑ ¬ C)
* C is not D and D is not a C simultaneously
* The classes are disjoint, the intersection must be empty
91
What is important to note about disjointness?
Disjointness states that all disjoint classes belong to different branches in the ontology tree
* When writing ontologies the default is for classes to overlap, so disjointness needs to be stated explicitly to define that instances of classes are mutually exclusive.
92
What is an advantage of OWL over RDF?
An important advantage of the use of OWL over RDF Schema is the possibility to detect inconsistencies
93
When is an ontology an incoherent ontology?
An ontology is an incoherent ontology if there’s at least one unsatisfiable class, a class that cannot have any instance
94
What are some examples of common inconsistencies:
* incompatible domain and range definitions for transitive, symmetric, or inverse properties
* cardinality constraints/properties
* differences in requirements on property values can conflict with domain and range restrictions
95
How are the cardinality restrictions defined?
minQalifiedCardinality, maxQualifiedCardinality, exactCardinality
* Can be used to declare primitive or defined classes
* Restricts the number of relations an object can have (min, max, exactly)
owl:minQalifiedCardinality "4"^^xsd:nonNegativeInteger;
