On Integrating Rules into the Semantic Web

June 13, 2003

WFLP'03, Valencia

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On Integrating Rules into

the Semantic Web

Jan Maluszynski

Linköping University

Sweden

June 13, 2003

WFLP'03, Valencia

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Overview

“Semantic Web” – do we need it? XML and web languages Rules on the web: the RuleML approach The W3C vision of the Semantic Web Towards typed rules Summary

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Do we need ”Semantic Web”? Google query: FLP ?

gives ~170 000 answers: Forever Living Products Family Living Program Forest Legacy Program Finish Line Performance … I admit, the query is not smart…

Functional Logic Programming Conference ?

Michael Hanus

Conferences related to FLP …WFLP …

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Adding semantics to the contents Annotate web content with a description of its meaning

=> metadata FLP – is a branch of CS

Workshop is a Conference Symposium is a Conference

Use metadata for reasoning/querying FLP conference / CS ? => WFLP, FLOPS

Logical foundations? Various web languages needed:

how to define them? what is their semantics?

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Rules

Can a software agent plan my travel to WFLP ? Constraints/preferences expressed as rules?

Database views Bussiness rules …

Using them on the web?

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Web needs standards Standard notation for data:

XML Standard for creating unique names:

Namespaces Standard for defining web languages

(sets of XML elements):

XML Schema, (DTD) …

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XML <person age=“25” > <name>John Smith </name> <address> <street> Dalav. 21 </street> <city> Lund </city> </address></person>

person

address

street city

name

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John Smith Dalav. 21 Lund

Tags, Attributes, Standard format facilitates:

•Definition of self-describing structured data

•Integration from various sources

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Is XML element a term ?<CD price="10.90$" year="1985">

Empire Burlesque

<artist>Bob Dylan</artist>

<country>USA</country>

<company>Columbia</company>

</CD>

CD[&{price[10.90$],year[1985]},

Empire Burlesque,

artist[Bob Dylan],

country[USA],

company[Columbia]]

Arity of function symbols is not predefined; unordered subterms

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Creating unique names Universal Resource Identifier: URI

identifies unique resource

special case: URL Used for creating unique names Namespaces

The URL may point to a description of the names

(unique meaning?).

<contact xmlns:work="http://www.liu.ida.se/"> <name>John Smith</name> <phone>013/175347</phone> <work:phone>013/281400</work:phone> </contact>

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Defining a web language: syntax

Language: a set of XML elements Elements ~ trees

Define language as a tree-grammar (DTD), place on web

could we define language in XML? XML Schema language: elements are XML documents for any XML Schema document S:

The meaning of S is a set of XML documents L(S)

the function L is the semantics of XML Schema standard on-line validator can check whether any given XML

document is in L(S); The validator implements the semantics of the XML Schema

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A flavour of XML Schema

<xsd:schema xmlns:xsd="http://www.w3.org/2001/XMLSchema"> < xsd: element name=“purchaseOrder” type=“POT” /> < xsd: complexType name=“POT”/> < xsd: sequence> < xsd: element name=“addr” type=“USAddress”/> < xsd: element name=“items” type=“Items”/> < /xsd: sequence> < xsd: attribute name=“orderDate” type=“xsd:date”/> < /xsd: complexType> …. < / xsd: schema> Roughly reflected by a rule: POT purchaseOrder(USAddress Items)

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Regular tree grammars for XML languages

ERTG: Nonterminals X in N {POT, USAddr,…} Terminals t {pOrder, addr,…} /XML tags Start S in N POT Rules X t ( R) R - a regular expression over N

pOrder

addr…

items

it …

it

art …

qua …

<pOrder>

<addr>

...

</addr>

<items>

<it>

...

</it>

<it>

...

</it>

</items>

</pOrder>

POT pOrder( USAddr Items) USAddr addr( Mail Street ZIP City State) Items items( Item*)

Item it(Artno Quantity) ….

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Regular tree languages RTG: each function symbol has fixed arity

ERTG: arguments of a function symbol defined by a regular expression

Regular tree language: a language defined by an RTG Regular tree languages are closed under:

intersection union …

Inclusion is decidable The same holds for languages defined by ERTG

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Defining web languages: summary

XML schema S defines syntax of L L=L(S) S accessible by a URL A document x can be validated wrt S x

L ? XML Schema validators Operational semantics: an

interpreter for L accessible on the web Declarative semantics ?

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RuleML: rules on the web Rule Markup Language Initiative: => Standardize mark-up for selected rule languages! A small family sufficient to embed various applications (?) Develop XML schema for XML encoding of a rule

language L e.g. for Datalog Put it on the web: URL

Operational semantics: rule engine(s) Declarative semantics,

XML schema for L

XML code XML code

L Rules in syntax 1

L Rules in syntax 2

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Logic on the web

Define XML syntax for logic languages (different logics) Model-theoretic semantics, Automatic reasoners

Proposed logics include: Description logics (work in progress DAML+OIL, OWL) Datalog….

In a chosen logic: Provide a set of formulae (encoded in XML)

specific axioms Automatic reasoning system answers queries

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W3C view of the Semantic Web Layers of tightly connected langugages.

XML provides the syntactic basis for all layers What are the connections between the layers?

XML + NS + XML Schema

Unicode

Rules

RDF Schema

RDF

URI

Ontology

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RDF + RDF Schema

A (still evolving) notation encoded in XML [Beckett D. (ed.) 2002]

For modeling application domains Classes, Subclasses, Properties(Slots), Literals

Basic construct: sentence: Subject Predicate Object Encoded in XML, Can be seen as ground atomic formula, Represented as graph

Model theoretic semantics [P. Hayes (ed.) 2003] Editors, query tools exist

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A flavour of RDF Schema

rdfs:Resource

xyz:MotorVehicle rdfs:Class

s s

t

t

xyz:Truck

s

t

xyz:PassengerVehicle

s = rdfs:subClassOf t = rdf:type

xyz:Van

s

s

xyz:MiniVan s

s

t

t

t

t

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Description Logics

A family of KR formalisms, based on FOPL decidable, supported by automatic reasoning systems

Used for modelling of application domains Classification of concepts and individuals

concepts (unary predicates), subconcept (subsumption), roles (binary predicates), individuals (constants), constructors for building concepts, equality …

[Baader et al. 2002]

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Example DL: ALR atomic role, A atomic concept

C,D A | (atomic concept)

T | (universal concept)

| (bottom concept)

A | (atomic negation)

C D | (intersection)

R.C |(value restriction)

R.T | limited ex. Quantification

Add more constructors: another DL

RI I I AI I

TI = I

I = Ø

(A)I = I \ AI

(CD)I = CIDI

( R.C)I =

{a I|b.(a,b) RIb CI }

( R.T)I = {a I| b.(a,b) RI}

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Modelling with DLs A set of equational axioms T (terminology, T-box)

Woman Person Female Man Person Female

Automated check for (C, D concepts): Satisfiability of C:

is there a model I of T such that CI nonempty?

Man Woman ? Subsumption: CI DI for every model I of T ?

Reduces to unsatisfiability C D Add assertions about individuals: Man(Peter) …

Query the obtained knowledge base K. Ground membership query: Person(Peter)?

Find all the individuals in K that are instances of a given concept

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W3C Ontology Language OWL

An expressive description logic Under development [Dean et al. (eds) 2002]

Encoded in XML Extending (?) RDFS

Some problems with that [Patel-Schneider, Fensel 2002] Ontology: a conceptual model of the application domain; OWL ontology: a set of OWL statements – XML encoding of a set of DL axioms

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RDF Schema primitives in DL perspective

Class : Atomic concept

Property: Atomic role

A is a subclass of B: A B

P is a subproperty of R: P R

A is a range of R :

T R.A

A is a domain of R

T R-.A

A,B atomic concepts

P,R atomic roles,

T universal concept

( R.C)I =

{a I|b.(a,b) RIb CI }

R- inverse

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Ontologies and XML Schema

Ontology: a conceptual model of the application domain Data will be represented in XML;

document structure must be imposed A systematic approach for translating an ontology into

a specific XML Schema [Klein, Fensel et al. 2000]: represent: a class C by an element definition; the properties of C correspond to subelements subclasses modelled by XML Schema extension multiple inheritance cannot be directly expressed

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Modeling Ontology with RT Grammar ?

Man Person Woman Person Taxpayer PersonSTsexpartnertax

Person p(S (M|W)? T?)

TaxP p(S (M|W)? T)

M p( sex(m) W? T?)

W p( sex(f) M? T?)

T tax(#Pcdata)

S sex(m|f)

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Adding rule level Should build-up on the ontology level

How ontologies relate to XML data on the web? What kind of rules?

Datalog, (extensions: negation, prioritized rules, fuzzy,…)

Query rules for XML-data

….. What kind of integration?

How to add rules on top of ontologies (RDFS, DLs) ? Integrate Description Logic(s) with Datalog

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Integration of Datalog with DL (1)CARIN [Levy, Rousset 1998], a family of languagesTwo sets of axioms are provided:

(1) T-box in a description logic (2) Rules and ground facts:

p1(X1),…,pn(Xn) q(Y) Xi Y vectors of variables

concept predicates, role predicates, can be used in the body but not in the head; the other: ordinary predicates

all variables of the head appear in the body; no/limited recursion

Ground atomic queries only; special inference procedure needed/provided

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Integration of Datalog with DL (2)

Description Logic Programs [Grosof et al. 2003]

A restricted DL language, where DL axioms can be transformed into logically equivalent Horn clauses., e.g. PQ Q(X) P(X)

The syntactic restrictions are somewhat complex DLP is less expressive than DAML+OIL but

can model a subset of RDFS

The advantage: use of LP engines for query answering; non-monotonic extensions possible

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Typing Datalog with DLs Rationale:

An ontology describes classes of application data; Rules describe data manipulation;

Man Person Woman Person Taxpayer Personlives(X,M), couple(X,Y), interestpaid(Y,Z) taxdeduction(X,Z,M)

TYPES: lives: Person, Municipality couple: Man,Woman interestpaid: Person, Amount taxdeduction: Taxpayer, Amount, Municipality

X:Person X:ManCheck in DL : (Man Person) Taxpayer NO! Clear separation of reasoning in DL from answering Datalog queries;

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Typechecking of rules

q1(X … Y) … qn(X … Y) r(X … Y)

T1(X)…T1(Y) Tn(X)…Tn(Y) T(X)…T(Y)

T(q1) T(qn) T(r)

T(X) = T1(X)…Tn(X)

T(Y) = T1(Y)…Tn(Y)

T(r(X …Y))

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Conceptual vs. Concrete

Ontology

Datalog rules

XML Schema

XML rules ?

typed

XML encoding

typed

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Towards a typed XML rule language Query and transformation rule:

q1,…, qn c

inproc[[ author[X],title[Y] ]], article[[ author[X],title[Y] ]] multi[X]

[[…]] – allows matching term to include additional subterms Xcerpt: Query and Transformation Language [Bry, Schaffert 2002]

Types: approximate the XML database by a regular tree language T : Matching qi ,c against T gives T(qi ), T(c) Matching : intersection of regular tree languages T(qi ) binds variables: T(Xi ) Compute T(X) =T(X1 ) …T(Xn), construct T’(c) Check T’(c) T(c)

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Summary

A perspective of the ongoing development Research issues:

Integration of rules and ontologies Deriving XML schemata from ontologies Type checking of rules

Datalog rules typed by DLs XML transformation rules typed by RTLs

derived from XML schemata

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ReferencesF.Baader, D. Calvanese, D. McGuiness, D.Nardi and P. Patel-Schneider (eds) The

Description Logic Handbook. Cambridge University Press, 2002.D. Beckett (ed.) RDF/XML Syntax Specification (Revised) W3C November 2002.F.Bry and S. Schaffert. Towards a Declarative Query and Transformation Language for

XML and Semistructured Data. Proc. ICLP2002H.Comon, M.Dauchet, R.Gilleron, F.Jacquemard, D.Lugiez, S.Tison and M. Tommasi. Tree

Automata Techniques and Applications. http://www.grappa.univ-lille3.fr/tataM.Dean, D.Connolly, F.van Harmelen, J.Hendler, I.Horrocks, D.L.McGuiness, P.F.Patel-

Scheider and L.A.Stein (Eds.). OWL Web Ontology Language, Reference Version 1.0, W3C,Working Draft November 2002

B. N. Grosof, I. Horrocks, R.Volz and S.Decker. Description Logic Programs: Combining Logic Programs with Description Logic. Proc. of WWW2003, Budapest.

P.Hayes (ed.) RDF Semantics, W3C Working Draft January 2003

M. Klein, D. Fensel, F. van Harmelen and I. Horrocks, The relation between ontologies and schema-languages: translating OIL specifications in XML Schema.Proc of the Workshop on Ontologies and Problem Solving Methods, ECAI 2000

A.Levy and M-C.Rousset. CARIN: A Representation Language Combining Horn rules and Description Logics. Artificial Intelligence 104(1-2), 1998, 165-209.

P.F. Patel-Schneider and D.Fensel. Layering the Semantic Web: Problems and Directions. Proc. ISWC2002, LNCS2342 pp. 16-29

Rule Markup Language Initiative. http://www.ruleml.org