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A Proposal for an O WLR ules Language
Choi, Cheolhee
[email protected] Intelligent Systems Lab.
Hanyang Univ.
Ian Horrocks & Peter F.Patel-Schneider
WWW2004 New York, USA
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Agenda
IntroductionOverviewDirect Model-Theoretic Semantics
The Power of RulesExample of ORLMapping To RDF Graphs
Summary
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Introduction (1)
The Owl Web Ontology Language addsconsiderable expressive power to theSemantic Web
Limitation of OWLproperties is much weaker than class constructs
It is impossible to capture relationships between acomposite property and another property
Parent(x,z) ,Brother(x,y) and Uncle(y,z)
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Introduction (2)
Solutions To extend OWL with a more powerful language fordescribing propertiesBut, In order to maintain decidability, the constructor issatisfied following
To extend OWL with some form of rule language
P Q P o
Parent(x,z) ,Brother(x,y) and Uncle(y,z)
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Overview
The basic idea of the proposal is to extendOWL DL with a form of rules whilemaintaining maximum backwards
compatibility with OWLs existing syntax andsemanticsRule : antecedent consequentAtom: C(x), P(x,y),Q(x,y), sameAs(x,y), or
differentFrom(x,y)
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Abstract Syntax
This syntax extends the abstract syntax of OWLdescribed in the OWL Semantics and Abstract Syntaxdocument
axiom ::= rulerule ::= Implies({annotation} antecedent consequent)antecedent ::= Antecedent({atom})consequent ::= Consequent({atom})atom ::= description ( i-object )
| individualValuePropertyID ( i-object i-object )| datavaluedPropertyID ( i-object d-object )| sameAs ( i-object i-object )
| differentFrom ( i-object i-object )
i-object ::= i-variable | individualIDd-object ::= d-variable | dataLiterali-variable ::= I-variable( URIreference )d-variable ::= D-variable( URIreference )
atom: C(x),P(x,y),Q(x,y),atom: C(x),P(x,y),Q(x,y),sameAs(x,y), orsameAs(x,y), ordifferentFrom(x,y)differentFrom(x,y)
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Abstract Syntax (2)
Human Readable Syntax
antecedent consequent
Both antecedent and consequent are conjunctions of atoms Variables are indicated using prefixing them with a question mark
Parent(?a,?b) Brother(?b,?c) Uncle(?a,?c)
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Direct Model-Theoretic Semantics
The basic idea is that we define binding -extensions of OWL interpretationsA rule is satisfied by and interpretation iff
every binding that satisfies the antecedentalso satisfies the consequent
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Interpreting Rules
, , , , , I R EC ER L S LV =< >Atom Condition on Interpretation
C(x)P(x,y)Q(x,z)sameAs(x,y)differentFrom(x,y)
S(x) EC(C) ER(P) ER(Q)S(x) = S(y)S(x) S(y)
S i s a mapping from individual names to elements of EC(owl:Thing)L is a mapping from typed literals to elements of LV
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Interpreting Rules (2)
A binding B(I) satisfiesAn antecedent A iff A is empty or B(I) satisfies everyatom in AA consequent C iff C is not empty and B(I) satisfies
A rule is satisfied !
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Interpreting Rules (3)
Example
, , ( : ).
(( , ) ( ) ( , ) ( ))
( , ) ( )
a b c EC owl Thing
a b ER parent b c ER brother a c ER uncle
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XML Concrete Syntax(1)
Person(x1)
Persons having at least one parent who is a Physician(x2)Atom:Atom:C(x)C(x) P(x,y)P(x,y)Q(x,y)Q(x,y)sameAs(x,y)sameAs(x,y)differentFrom(x,y)differentFrom(x,y)
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XML Concrete Syntax(2)
4
hasParent(x1, John)
grade(x1, 4)
Atom:Atom:C(x)C(x)P(x,y)P(x,y)Q(x,y)Q(x,y)sameAs(x,y)sameAs(x,y)differentFrom(x,y)differentFrom(x,y)
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XML Concrete Syntax(3)
sameIndividualAtom(Clinton, Bill_Clinton)
Atom:Atom:C(x)C(x)P(x,y)P(x,y)Q(x,y)Q(x,y)
sameAs(x,y)sameAs(x,y)differentFrom(x,y)differentFrom(x,y)
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XML Concrete Syntax(4)
parent(?a, ?b)
brother(?b, ?c)
-> uncle(?a,?c)
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The Power of Rules
In OWL, the only relationship that can beasserted between properties is subsumption between atomic property names
By using rules, we have increased expressivepowerFor extensions of language such as OWL DL,the undecidability of the consistency problem
is often proved
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The Power of Rules(3)
The proposed form of OWL rules seem to gobeyond basic Horn clauses in allowing:
Conjunctive consequents
Class description as well as class names aspredicated in class atomsEqualities and inequalities
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The Power of Rules(4)
These are syntactic sugar Conjunctive consequents
Class descriptions
Equalities and inequalities(? ) (? ,? )Thing x Eq x x
1 2 A C C 1
2
A C
A C
( , )( ) ( )
differentFrom x yC x D y
( , ) EquivalentClasses D d
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Example of ORL
Artist(?x) Style(?y) artistSyle(?x,?y) Creator(?x,?z)
-> sytle/period(?z,?y)
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Mapping to RDF Graph
The semantic Web will be based on ahierarchy of language with RDF/XML providingthe syntactic and semantic foundation
Unlike OWL, rules have variables so treatingthem as a semantic extension of RDF is verydifficult
Provide an RDF syntax for rules
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Mapping to RDF Graph (2)
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Summary
A proposed extension to OWL to include asimple form of Horn-style rules
Simplicity and tight integration with the existingOWL language
ORL extends OWL with the most basic kind of Horn rulePredicates are limited to being OWL classes andpropertiesno disjunctions or negations of atomsno built-in predicate
no non-monotonic featuresrules are given a standard first order semanticsORL is defined as a syntactic and semantic extension of OWL DL
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