The Semantic Web

Presented by Zhimin Chen

HTML Is Human Readable, Not Machine understandable A Course Schedule Web Page

Consequence: agents can’t effectively process information on the web automatically

XML May Help, But Can Only Help XML fragment for the course

schedule…<course-offered>

<catalog> 92809 </catalog><course>

<number> 500 </number><session> 201 </session><name> Algorithm Design </name>

</course><room> cisr 104 </room><instructor> Evans </instructor>

…

XML May Help, But Can Only Help (Cont’d) Tags in XML carry no semantics

<course><ID> 500 </ID><Session> 201 </Session><Name> Algorithm Design </Name>

</course>

<H1><H2> 500 </H2><H3> 201 </H3><H4> Algorithm Design </H4>

</H1>

is no more meaningful than

Expressing Meanings Of Tags Semantic network, a graph composed of

Two Kinds of Nodes Taxonomic categories or property (labeled by

relation constants) Objects in the domain (labeled by object constants)

Three Kinds of Arcs IS-A arc Set membership arc Function arc

Meanings of tags as taxonomic concepts or property

Example Of Semantic Network

[Tim Berners-Lee, James Hendler and Ora Lassila]

Use Case – Precise Search Current search engine

Key word based Single page only

Semantic search Assemble knowledge spanning many pages

Example Scenario: locating a person her last name is "Cook“ she works for a company on your client list she has a son attending your alma mater,

Avondale University

Architecture Of The Semantic Web

[Tim Berners-Lee]

Where the standard

progress stands

Outline of the talk RDF and RDF Schema DAML+OIL and OWL Description Logic

RDF An RDF statement is a triple

<subject, property, value> Reification is statement about

statement, i.e., subject is a statement

Each subject identified by a URI Semantics represented as a set of

triples and serialized as XML

RDF Example

http://www.bob-stacy.com/cook

http://www.bob-stacy.com

<rdf:Description rdf:about=“http://www.bo

b-stacy.com/cook”><works-for

rdf:resource=“www.bob-stacy.com” />

</rdf:Description>

<rdf:Description rdf:about=“http://w

ww.bob-stacy.com/cook”>

<lives-in>Johannesburg</

lives-in> </rdf:Description>

RDF Schema RDF schema provides a way to define the

meanings of tags A tag is a class

Employee rdf:type rdf:class <rdf:Description rdf:ID="Employee">

<rdf:type rdf:resource = "http://www.w3.org/2000/01/rdf-schema#Class"/> </rdf:Description>

A tag is a property Works-for rdf:type rdf:property Works-for rdf:domain Employee Works-for rdf:range Company

RDF Schema (Cont’d) XML as a shorthand for RDF

descriptions of a semantic network

Class ClassProperty

Employee Company

type

type

Works-forrangedomain

type

Mrs. Cook Bob-StacyWorks-for

type

type

RDF Schema (Cont’d)

<Company rdf:ID=“Bob-Stacy” /><Employee rdf:ID=“Cook”>

<Works-for rdf:resource=“#Bob-Stacy” />

</Employee>

RDF Schema (Cont’d) Other modeling mechanisms

Rdf:subClassOf Rdf:subPropertyOf Rdf:container and Rdf:collection Reification (rdf:type is rdf:statement)

daml+oil provides more

Outline of the talk RDF and RDF Schema DAML+OIL and OWL Description Logic

DAML+OIL DAML+OIL adds richer expressive

mechanism to RDF schema Constraints on properties Boolean combination of classes Equivalence and disjointness Property of property

Constraints On Property A class is defined as all objects

satisfying constraints on property Universal constraint

E.g.: All objects working for companies<daml:restriction>

<daml:onProperty rdf:resource=“#works-for” />

<daml:toClass rdf:resource=“#Company” /></daml:restriction>

Existential constraint (hasClass and hasValue)

Constraints On Property (Cont’d)

Cardinality constraint (minCardinality, maxCardinality, exactCardinality)

E.g.: All objects having more than 1 child<daml:restriction>

<daml:onProperty rdf:resource=“#parentOf” />

<daml:minCardinality> 2 <daml:minCardinality/></daml:restriction>

Boolean Combination of Classes Intersection, union, complement

E.g.: all objects working for Bob-Stacy and having more than 1 child<daml:Class ID=“BobStacyParentWorker”>

<daml:intersectionOf daml:parseType=“daml:collection”><daml:restriction><daml:onProperty rdf:resource=“#works-for” /><daml:hasValue rdf:resource=“#Bob-Stacy” /></daml:restriction> <daml:restriction><daml:onProperty rdf:resource=“#parentOf” /><daml:minCardinality> 2 <daml:minCardinality/></daml:restriction></daml:intersectionOf>

</daml:Class>

Equivalence and Disjointness Equivalence

sameClassAs samePropertyAs sameIndividualAs

Disjointness disjointWith differentIndividualFrom

Property of property inverseOf transitiveProperty uniqueProperty and

unambiguousProperty

OWL OWL DL DAML + OIL

Add/remove/rename some language constructs

Version management Knowledge modularization (import)

OWL Full allows class to be an individual (undecidable)

Outline of the talk RDF and RDF Schema DAML+OIL and OWL Description Logic

ALC Concept descriptions are formed

using constructs: A (atomic concept) C D (daml:intersectionOf) C D (daml:unionOf) C (daml:complementOf) R.C (daml:toClass) R.C (daml:hasClass)

SHIQ ALC plus

Transitive role R* (daml:transitiveRole)

Concept hierarchy and role hierarchy (subClass and subProperty)

Inverse role R- (daml:inverseOf)

Qualified number restriction nR, etc (daml:minCardinality, etc)

Basic Inference Problem Concept subsumption C T D Reduction to unsatisfiability

C T D there exists no model I for T s.t. (C D)I is not empty.

Tableau algorithm to find such a model

Tableau D is a concept sub(D) is the closure of concept

subexpressions in D’s definition S is a set of individuals L : S 2sub(D) maps each individual to a

subset of sub(D) E : R 2SS maps each role to a set of

pairs of individuals There is some s in S s.t. D is in L(s)

Tableau For ALC Concepts T=<S, L, E> is a tableau for ALC concept

D if it holds L(s) does not contain both C and C If C E L(s), then C L(s) and E L(s) If C E L(s), then C L(s) or E L(s) If R.C L(s) and <s,t> E(R), then C L(t) If R.C L(s), then there is some s s.t. <s,t>

E(R) and C L(t) Further constraints for other concept

constructs can be added for more expressive DL.

Tableau Algorithm For ALC Completion tree

Node x labeled with a set L(x) sub(D) Edge <x,y> labeled with a set L(<x,y>) of

roles occurring in D Tree expansion rules

- rule: Condition: C1 C2 L(x) and {C1, C2} L(x) Action: L(x) {C1, C2} L(x)

- rule: Condition: C1 C2 L(x) and {C1, C2} L(x) = Action: for some C {C1, C2} , L(x) {C} L(x)

Tableau Algorithm For ALC (Cont’d)

- rule: Condition: R.C L(x) and there is a R-

successor y of x s.t. C R Action: L(y) {C} L(y)

- rule: Condition: R.C L(x) and x has no R-

successor y s.t. C L(y) and no other rule is applicable to any of its ancestors

Action: create a R-successor y for x with L(<x,y>)=R and L(y)={C}

Tableau Algorithm For ALC (Cont’d) A node has clash if {C, C} L(x) Algorithm starts with a node x

labeled with L(x)={D} Applying expansion rules until

A clash happens No rules can be further applied to the

tree

Tableau Example Check (R.A) (R.B) R.(A B) D = (R.A) (R.B) (R.(A

B))x{(R.A) (R.B) (R.(A B))}{(R.A), (R.B), (R.(A B))}

y

R

{A}{A, (A B)}{A, A}

clash {A, B} z

R

{B}{B, A B}

{B, A }

Transitive Role and Blocking + - rule:

Condition: R.C L(x) where R is a transitive role and there is a R-successor y of x s.t. R.C L(y)

Action: L(y) {R.C} L(y) May lead to infinite loop Subset blocking: if L(y) is a subset

of an ancestor’s label L(x), then block the expansion

Blocking Example

xL(x)={C, R.C, R.(R.C)}

y

R

L(y)={C}L(y)={C, R.C}

L(x)={C, R.C, R.(R.C)}

Blocked

More Expressive DL For additional concept construct

(inverse role, quantifier, etc.), add more expansion rules and blocking rules

Optimizations Backjumping

L(x)={C1 D1, …, Cn Dn, R.(A B), R.(A)}

[Horrocks-Satter-Tobies]

backjumping

pruning

Optimizations (Cont’d) Absorption

Reasoning w.r.t. axiom C D needs to add (C D) to every node

CN D (CN D) only need to add D (D) to the nodes that contain CN (CN)

Transforming axiom into this form CN C D CN C D CN C, CN D CN C D Similar rules for the cases

Optimizations (Cont’d) Cache

Cache the satisfiability of L(x) for node x

Caching partial tableaus of concepts to check obvious satisfiability (E.g., merge the tableau of C and D to check satisfiability of C D (and thus C D))

Optimizations (Cont’d) Lazy expansion of concept Semantic branching search C1, …, Cn, C1 … Cn D D Heuristic guided search

Oldest-first: select the disjunctions dependent on the least recent branching point

Summary The semantic web tries to make www

machine accessible OWL is the current standard to define

vocabulary, and a large part of OWL is DL Challenges (DB-related)

Scalibility (techniques of reasoning with individual in DL unlikely can scale up)

Query Ontology design and integration

References W3C standards:

Resource Description Framework (RDF) Model and Syntax Specification W3C Recommendation 22 February 1999 Ora Lassila, Ralph R. Swick, eds. http://www.w3.org/TR/1999/REC-rdf-syntax-19990222/

RDF Vocabulary Description Language 1.0: RDF Schema W3C Working Draft Dan Brickley, R.V. Guha, eds. http://www.w3.org/TR/rdf-schema/

RDF Primer W3C Working Draft Frank Manola, Eric Miller, eds. http://www.w3.org/TR/rdf-primer/

DAML+OIL (March 2001) Reference Description. Dan Connolly, Frank van Harmelen, Ian Horrocks, Deborah L. McGuinness, Peter F. Patel-Schneider, and Lynn Andrea Stein. W3C Note 18 December 2001. http://www.w3.org/TR/daml+oil-reference

OWL Web Ontology Language Reference W3C Working Draft Mike Dean, Guus Schreiber eds., Frank van Harmelen Jim Hendler Ian Horrocks Deborah L. McGuinness Peter F. Patel-Schneider Lynn Andrea Stein http://www.w3.org/TR/owl-ref/

References (contd.) Description logic:

Basic Description Logics Description Logic Handbook, edited by F. Baader, D. Calvanese, D.L. McGuinness, D. Nardi, P.F. Patel-Schneider, Cambridge University Press, 2002, pages 47-100. http://www.cs.man.ac.uk/~franconi/dl/course/dlhb/dlhb-02.pdf

Practical Reasoning for Very Expressive Description Logics I. Horrocks and U. Sattler and S. Tobies Logic Journal of the IGPL, Volume 8, Issue 3: May 2000. http://www3.oup.co.uk/igpl/Volume_08/Issue_03/pdf/horrocks1.pdf