Abstract

The W3C Web Ontology Working Group is continuing work on the Web Ontology Language, OWL. The syntax of OWL is mostly determined, but the semantics of OWL has been the subject of continuing debate, with an agreement-in-principle on the general outlines of the semantics of OWL being decided only in early October 2002. The semantics of OWL will be determined by means of two model-theoretic semantics, a more-complex semantics for general OWL knowledge bases and a simpler one for OWL knowledge bases that meet certain syntactic restrictions. These two semantics coincide on the restricted OWL knowledge bases.

What is OWL?

1. A very-expressive frame formalism?
2. A very-expressive description logic?
3. A hybrid modal logic?
4. A useful fragment of some first-order logic?
5. An extension of RDF and RDFS?
6. All of the above?

What is the Syntax of OWL?

Frames (like OIL)?

Class(Student partial Person 
  restriction(institution 
              allValuesFrom(EducationalInstitution))
  restriction(ID someValueFrom(xsd:Decimal)))

Description Logics?

Student ≤ Person ∩ 
          &forall institution : EducationalInstitution ∩
          &exist ID : xsd:Decimal

What is the Syntax of OWL? (continued)

RDF Triples (like DAML+OIL)?

<Student rdf:subClassOf _:x> 
<_:x owl:intersectionOf _:l1>
<_:l1 rdf:first Person> <_:l1 rdf:rest _:l2>
<_:l2 rdf:first _:r1> <_:l2 rdf:rest _:l3>
<_:l3 rdf:first _:r2> <_:l3 rdf:rest rdf:nil>
<_:r1 owl:onProperty institution>
<_:r1 owl:allValuesFrom EducationalInstitution> 
<_:r1 owl:onProperty ID>
<_:r1 owl:someValuesFrom xsd:Decimal> 

What are the inferences of OWL?

• Is intersectionOf(Person Student)
  a subclass of Person?
• Does an empty knowledge base entail

       < _:x owl:intersectionOf _:l1 >
       < _:l1 rdf:first Person > 
       < _:l1 rdf:rest _:l2 > 
       < _:l2 rdf:first Student > 
       < _:l2 rdf:rest rdf:nil > 
       < _:x rdfs:subClassOf Person >
       

What are the inferences of OWL? (continued)

• Does Individual(john type(Person) type(Student))
  entail Individual(john type(Student) type(Person))?
• Does

       <john rdf:type _:x>
       <_:x owl:intersectionOf _:l1>
       <_:l1 rdf:first Person>  <_:l1 rdf:rest _:l2> 
       <_:l2 rdf:first Student> <_:l2 rdf:rest rdf:nil> 

  entail

       <john rdf:type _:y>
       <_:y owl:intersectionOf _:l3>
       <_:l3 rdf:first Student> <_:l3 rdf:rest _:l4> 
       <_:l4 rdf:first Person>  <_:l4 rdf:rest rdf:nil> 

What are the inferences of OWL? (continued)

• Does

       <john rdf:type _:r1>
       <_:r1 owl:onProperty bar>
       <_:r1 owl:maxCardinality xsd:integer;0> 

  entail

       <john rdf:type _:r2>
       <_:r2 owl:onProperty bar>
       <_:r2 owl:allValuesFrom _:r2>
       

What kind of Semantics to use for OWL?

• Standard Model Theory?
• Embedding into FOPC with Equality?
• Translation into FOPC with Equality plus an Axiomatization?
• Embedding into Lbase?
• Extension of RDF semantics?

Possible Kinds of Semantics for OWL

• Standard Model Theory (from Description Logics)
  • Easy to do; Well understood
  • Can't be an extension of RDF semantics
  • Only works for KBs that look like description logic KBs
• Embedding into First-Order Predicate Calculus with Equality
  (classes and properties become predicates)
  • Easy to do; Well understood
  • Can't be an extension of RDF semantics
  • Only works for KBs that look like description logic KBs

Possible Kinds of Semantics for OWL (continued)

• Translation into First-Order Predicate Calculus with Equality
  (classes and properties become domain elements)
  • Not so easy to do; needs an axiomatization
  • Prone to Errors
  • Can be an extension of RDF semantics
• Embedding into Lbase (a different first-order logic)
  • Easy to do
  • Not as well understood
  • Works for KBs that use classes as objects

Possible Kinds of Semantics for OWL (continued)

• Extension of RDF semantics
  (triples are given their RDF meaning)
  • A version of embedding into LBase
  • Hard to do
  • Not well understood
  • Works for KBs that use classes as objects
  • Handles most triple KBs correctly, but not all

The Semantics of OWL (Desiderata)

• To handle KBs in triple form want an extension of RDF semantics.
  • This is very complex.
  • It might not work correctly.
  • It might not work at all.
• A standard model theory is much better where it is applicable.
  • It is much less complex.
  • It will work correctly.
  • Intuitions can be depended on.
  • Existing reasoners can be used.

The Semantics of OWL

Two-part Semantics:

1. An extension of RDF semantics to handle OWL KBs that
   • use classes as instances
   • mix individuals and data values
   • play with RDF or RDFS or OWL vocabulary
2. A standard model theory for OWL KBs that
   • don't use classes as instances
   • don't mix individuals and data values
   • don't play with the RDF vocabulary
   • i.e., that look like Description Logic KBs

The Semantics of OWL (continued)

What if the two semantics disagree?

• A proof that the two semantics agree on KBs that look like Description Logic KBs
  • But, of course, proofs can have bugs.
• The standard model theory is normative where it applies
• A fall-back position just in case the other semantics doesn't work, or doesn't work right.

Benefits of the Two-Part Semantics

• Almost all the desirable inferences are supported.
• OWL KBs that don't do unusual things will work as expected.
  • Entailment is decidable.
  • Description Logic provers such as RACER and FACT can be used.
• For OWL KBs that do slightly unusual things, such as mixing individuals and data values,
  • entailment is almost certainly undecidable;
  • first-order provers will be usable.
• For OWL KBs that do quite unusual things, such as using classes as instances or playing with the RDF vocabulary,
  • entailment is almost certainly undecidable;
  • first-order provers might be usable, but their efficiency would be compromised.