Web Ontologies

Victor Charpenay

Outline

  1. Ontologies
  2. Open and Closed Worlds
  3. The Web Ontology Language (OWL)
  4. Ontology Alignment
  5. Beyond OWL

Onto…?

Philosopher: an ontology is a theory of what is.

Aristotle stated that all things belong to one of ten categories.

Some of his contemporaries agreed with his theory, others disagreed.

Computer scientist: an ontology is
 a specification
of
 a conceptualization.

Computer scientist: an ontology is
 e.g. a formal description
of
 concepts and relationships.

SUMO, BFO or DOLCE are examples of ontologies aiming to capture all known concepts.

BFO ontology (source: Wikipedia)
Basic Formal Ontology 2.0

Ontology engineer: an ontology defines the vocabulary with which queries and assertions are exchanged among agents.

That is, ontologies are specifications of shared conceptualizations.

Agreement across all humans over a common ontology is not reachable, though.

Partial agreement over small sets of concepts is much more realistic.

Web researcher: a Web ontology is a consistent set of concepts exposed on the Web, such that others can (partially) reuse and align with these concepts.

Graph of alignments between IoT ontologies

Web ontologies are commonly layered as:

  • Upper-level ontologies
    SUMO, BFO, DOLCE, …
  • Domain ontologies
    for manufacturing, social networks, art, …
  • Application-specific ontologies

Open and Closed Worlds

If anyone can publish their ontology on the Web, they must decide what to do with the unknown.

One cannot assert all what is true with a finite vocabulary.

The designer of an ontology must define its frame:

  • what is within the frame is known for certain
  • what is outside the frame is unknown

The two possible treatments for unknown statements are:

  • the Closed World assumption
    what is not stated is false
  • the Open World assumption
    what is not stated is undefined

Constraint satisfaction
is typically done under the
Closed World assumption.

Whatever is valid in a closed world remains valid in an open world.

Inference
is typically done under the
Open World assumption.

Whatever is inferred in an open world remains inferred in a closed world.

Ontologies should be:

  • easy to extend
  • hard to validate

Ontology engineers should therefore design ontologies under the
open-world assumption.

The Web Ontology Language (OWL)

The Web Ontology Language (OWL) is the reference language to define ontologies. 

Declaration( Class( :Person ) )
Declaration( ObjectProperty( :knows ) )
Declaration( DataProperty( :familyName ) )
Declaration( DataProperty( :birthDate ) )

SubClassOf( :Person
  ObjectAllValuesFrom( :knows :Person ))
SubClassOf( :Person
  DataSomeValuesFrom( :familyName xsd:string ))

DataPropertyRange( :birthDate xsd:date )
Example in the functional syntax of OWL 
:Person a owl:Class .
:knows a owl:ObjectProperty .
:familyName a owl:DatatypeProperty .
:birthDate a owl:DatatypeProperty .

:Person rdfs:subClassOf [
  a owl:Restriction ;
  owl:onProperty :knows ;
  owl:allValuesFrom :Person
], [
  a owl:Restriction ;
  owl:onProperty :familyName ;
  owl:someValuesFrom xsd:string
] .

:birthDate rdfs:range xsd:date .
Example of mapping to RDF 
Class: Person
  SubClassOf: knows only Person
  SubClassOf: familyName some string

ObjectProperty: knows

DataProperty: familyName

DataProperty: birthDate
  Range: date
Example in the OWL Manchester syntax

OWL includes:

  • all of RDF Schema
  • class combinations
    union, intersection, complement
  • property characteristics
    transitivity, symmetry, inverse, …
  • property chains

OWL also includes so-called restrictions, including:

  • existential restrictions
  • universal restrictions
  • cardinality constraints

For an introduction to OWL, see the OWL quick reference document.

Reference documentation also includes the OWL 2 Primer and the Manchester syntax quick reference.

Ontology Alignment

Inference can be used to automatically align RDF graphs of various origins. 
Class: foaf:Person
  EquivalentTo: schema:Person

Class: foaf:Image
  EquivalentTo: schema:ImageObject

Class: foaf:Document
  SubClassOf: schema:CreativeWork
Alignment between FOAF and schema.org.

Ontology-based data access (OBDA) is a common approach to data integration. It generally requires inference from alignment axioms.

Virtual Knowledge Graph (VKG) architecture (source: Diego Calvanese)

Beyond OWL

For practical use, several OWL profiles exist:

  • OWL QL
    for OBDA, among others
  • OWL EL
    with applications in the medical domain
  • OWL RL
    for implementation with a rule engine

Yet, OWL is not a universal ontological language.

For instance, it is not possible to express such things as:

  • Job interviews for the same position are always followed by at least one hiring event.

Rule languages, such as SWRL, can express ontological constraints that OWL cannot. And vice-versa.

Mixing arbirary OWL axioms and rules is powerful but inference is not guaranteed to terminate.

Predicate logic is (assumed to be) the most universal language.

Common logic is an international standard to define ontologies in predicate logic.

See Introduction to Common Logic by John F. Sowa.