1. Using Rules with Ontologies in the Semantic Web
Chimezie Ogbuji Thoracic and Cardiovascular Surgery Cleveland Clinic Foundation
July 25th, 2006
Presented to W3C HCLSIG ACPP Group

2. Rule Languages
RuleML
SWRL
Notation 3 (N3)

3. Semantic Web Reasoners
Closed World Machine (CWM)
Euler
Pychinko
RDFEngine
Jena

4. Using Rules to Describe Rules
A Rule consists of a body (antecedent) and a head (consequent)
In N3:
{?X :has ?body. ?X :has ?head. :body log:implies :head } => {?X a :Rule }
In SWRL’s abstract syntax:
Implies(Antecedent(has(I-variable(X), I-variable(body) has(I-variable(X), I-variable(head)) log:Implies(I-variable(body), I-variable(head))) Consequent(Rule(I-variable(X)))

5. Origin / Background of Rules
Logic Programming
Production systems (RETE, etc.)
Prolog
SQL
Horn-clause Logic
Efficient theorem proving, and reasoning

6. Complexity and Abstraction
Kurt Cagle
“You can never eliminate complexity from a system, you can only move it from place to place”
Important point regarding how / why rules are used with ontology languages

7. DL Semantics as Analogy for Rules
Description Logics (DL)
Strict subset of FOL with decidability in mind
DL are more palatable and (therefore) more ubiquitous
Ontology language constructs correspond to DL constructs
Some DL (ontology) reasoning can be done via explicit rules

8. Some DL Semantics as N3 Rules
Transitive Roles
{?P a owl:TransitiveProperty. ?X ?P ?Y. ?Y ?P ?Z } => {?X ?P ?Z}
Class inclusion
{?B rdfs:subClassOf ?C. ?A rdfs:subClassOf ?B} => {?A rdfs:subClassOf ?C}.
Inverse Roles
{?P owl:inverseOf ?Q. ?S ?P ?O} => {?O ?Q ?S}.
Functional Restrictions
{?P a owl:FunctionalProperty. ?S ?P ?X. ?S ?P ?Y} => {?X owl:sameAs ?Y}.

9. Restriction on Expressivenes
Certain implications cannot be expressed in DL:
“Individuals who live and work at the same location are ‘Home Workers’”
In N3:
{?X :work ?Y. ?X :live ?Z. ?Z :located ?W. ?Y :located ?Y} => {?X a :HomeWorker}

10. Restriction on Expressiveness (Cont.)
Specific logical restrictions (Horn logic) make it difficult to express certain statements:
“Every person has a father (known or unknown)”
However, this is straight forward in OWL (and Description Logics):
:Person a owl:Class;
rdfs:subClassOf [
a owl:Restriction;
owl:onProperty :father;
owl:cardinality “1”. ]

11. Rule Inference Methods
Given:
Set of rules
Set of facts
Backward chaining is goal-oriented:
Question: can a fact be inferred from the rules and existing facts?
Forward chaining exhaustively infers new facts from the rules
The resulting facts combined with the original facts are often referred to as the ‘closure’

12. Concerns with Reasoning
Logic Programming reasoners and algorithms are more mature
RETE algorithm for production (forward chaining) systems
Euler cycle detection for backward chaining inference
Logic Programming systems are at the mercy of the explicit rules

13. Complexity and Abstraction (Revisited)
Kurt Cagle
“You can never eliminate complexity from a system, you can only move it from place to place”
DL abstracts Knowledge Representation at the expense of the reasoning mechanism.
DL reasoners are implemented to support only a limited kind of inference: class subsumption and consistency detection.

14. Compromise
Use DL semantics where the domain falls nicely into Categories / Roles and decidability is an issue
Use rules everywhere else
The combination covers the full spectrum of expressiveness and decidability
Including both in the thought process improves Knowledge Engineering
Some DL semantics can be expressed as rules to take advantage of efficient pattern matching algorithms

15. References
Description Logic Programs: Combining Logic Programs with Description Logic
Description Logic Complexity Navigator
Web Ontology Reasoning with Logic Databases
Euler’s RDF Plus OWL N3 Rules
Description Logics as Ontology Languages for the Semantic Web