A Proposal for an OWL Rules Language

8/8/2019 A Proposal for an OWL Rules Language

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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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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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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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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

Documents

A Proposal for an OWL Rules Language