Introduction RDF Semantics Querying RDF

RDF Data Model and Query Languages

Sergio Tessaris

April 21, 2006

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

FOAF example

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF Site Summary (RSS) 1.0

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF Site Summary (RSS) 1.0

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Building Blocks RDF Abstract Syntax RDF Vocabulary RDF Semantics RDF model theory Entailment Casting RDF into FOL Querying RDF Introduction Graph Patterns Query languages SPARQL
Sergio Tessaris RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Basic Concepts

RDF: language for representing information about resources (e.g. Metadata)

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Basic Concepts

RDF: language for representing information about resources (e.g. Metadata) information about things identied on the Web
identiable doesnt mean retrievable e.g. goods from an eShop, prices, availability, etc.

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Basic Concepts

RDF: language for representing information about resources (e.g. Metadata) information about things identied on the Web
identiable doesnt mean retrievable e.g. goods from an eShop, prices, availability, etc.

information processed by applications, not human beings

Semantic Web

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Digression: Semantic Web

The Semantic Web is an extension of the current web in which information is given well-dened meaning, better enabling computers and people to work in cooperation. Tim Berners-Lee, James Hendler, Ora Lassila, The Semantic Web, Scientic American, May 2001

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Design Goals

having a simple data model having formal semantics and provable inference using an extensible URI-based vocabulary using an XML-based syntax supporting use of XML schema datatypes allowing anyone to make statements about any resource

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF Statements
RDF is about making statements about resources E.g. Sergio Tessaris is the author of the web page http://www.inf.unibz.it/tessaris/index.html This can be stated as a property of the web page http://www.inf.unibz.it/tessaris/index.html has an author whose value is "Sergio Tessaris" RDF statements
subject: e.g. URL http://www.inf.unibz.it/tessaris/index.html predicate: e.g. property author object: e.g. string "Sergio Tessaris"

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Identifying Resources
RDF identiers: Uniform Resource Identiers (URI) URIs, URLs, and URNs URL identies resources via a representation of their primary access mechanism URN URIs that are required to remain globally unique and persistent Example ftp://ftp.is.co.za/rfc/rfc1808.txt http://www.math.uio.no/faq/compression-faq/part1.html news:comp.infosystems.www.servers.unix telnet://melvyl.ucop.edu/ mailto:someone@example.com
Sergio Tessaris RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Literals
RDF allows the use of values
strings numbers booleans

Literals are basically UNICODE strings plain just strings (w optional language tag) typed have associated datatype URI RDF literals and typing literals are not URIs
e.g. http://www.unicode.org and http://www.unicode.org are dierent

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Triples and Graphs

RDF triples basic element of RDF model

subject predicate object

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Triples and Graphs

RDF triples basic element of RDF model

subject predicate object

triple: two nodes (subject, object) connected by a labelled edge (predicate)

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Triples and Graphs

RDF triples basic element of RDF model

subject predicate object

triple: two nodes (subject, object) connected by a labelled edge (predicate) set of triples: a labelled directed graph

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Blank Nodes

RDF graphs may contain additional nodes arbitrary set of blank nodes (bnodes)
innite disjoint from URIs and literals

given two blank nodes it is possible to determine whether or not they are the same

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Blank Nodes

RDF graphs may contain additional nodes arbitrary set of blank nodes (bnodes)
innite disjoint from URIs and literals

given two blank nodes it is possible to determine whether or not they are the same intuition: a bnode represents the existence of something

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Scope of RDF Terms

URIs and Literals have a global scope two equal URIs (Literals) always represent the same object
equal means that the two unicode strings are the same there are not contextual to the graph

bnodes are contextual to the graph in which they appear

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Scope of RDF Terms

URIs and Literals have a global scope two equal URIs (Literals) always represent the same object
equal means that the two unicode strings are the same there are not contextual to the graph

bnodes are contextual to the graph in which they appear . . . more to came on the role of bnodes

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF Graphs

RDF triple
subject: RDF URI reference or a bnode predicate: RDF URI reference object: literal, RDF URI reference or a bnode

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF Graphs

RDF triple
subject: RDF URI reference or a bnode predicate: RDF URI reference object: literal, RDF URI reference or a bnode

RDF graph: set of RDF triples

nodes of an RDF graph are subjects and objects in the triples

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF Graphs (cont.)

no literals as subject predicates are just URIs URIs are used for both resources (nodes) and predicates (edges) literals can be non well formed datatypes no complete information about any resource

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

On Bnodes
bnodes are dierent from other RDF terms starting from the syntax

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

On Bnodes
bnodes are dierent from other RDF terms starting from the syntax Graph equivalence Denition G , G are equivalent if there is a bijection M between the nodes of the two graphs, s.t.:
1 2 3 4

M maps bnodes to bnodes. M(lit) = lit for literals lit in G . M(uri) = uri for URI in G . s, p, o in G i the triple M(s), p, M(o) in G .

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

On Bnodes
bnodes are dierent from other RDF terms starting from the syntax Graph equivalence Denition G , G are equivalent if there is a bijection M between the nodes of the two graphs, s.t.:
1 2 3 4

M maps bnodes to bnodes. M(lit) = lit for literals lit in G . M(uri) = uri for URI in G . s, p, o in G i the triple M(s), p, M(o) in G .

I.e. a sort of graph isomorphism

Sergio Tessaris RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Syntax vs. Semantics

still talking about (abstract) syntax nothing has been said on the actual semantics of RDF
introduced with an RDF vocabulary given by means of a Model Theory

how do you write/exchange RDF? in particular bnodes and literals several possibilities
N-Triples RDF/XML (normative) Turtle notation (subset of N3)

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

N-Triples

documents contain a set of assertions subject predicate object . URI references written out completely: <http://example.org/resource30> Literals as strings: plain "chat"@fr typed "<a></a>"^^<http://www.w3.org/2000/01/ rdf-schema#XMLLiteral> Bnodes: :anon

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

N-Triples Example
<http://www.inf.unibz.it/~tessaris/myfoaf.xml#me> <http://xmlns.com/foaf/0.1/title> "Dr" . <http://www.inf.unibz.it/~tessaris/myfoaf.xml#me> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <http://www.inf.unibz.it/~tessaris/myfoaf.xml#me> <http://xmlns.com/foaf/0.1/workplaceHomepage> <http://www.unibz.it/inf> . <http://www.inf.unibz.it/~tessaris/myfoaf.xml#me> <http://xmlns.com/foaf/0.1/homepage> <http://www.inf.unibz.it/~tessaris> . <http://www.inf.unibz.it/~tessaris/myfoaf.xml#me> <http://xmlns.com/foaf/0.1/mbox_sha1sum> "758128cdae69fd0fd9e880921d9f4b25259edbf5" . <http://www.inf.unibz.it/~tessaris/myfoaf.xml#me> <http://xmlns.com/foaf/0.1/name> "Sergio Tessaris" . <http://www.inf.unibz.it/~tessaris/myfoaf.xml#me> <http://xmlns.com/foaf/0.1/family_name> "Tessaris" . <http://www.inf.unibz.it/~tessaris/myfoaf.xml#me> <http://xmlns.com/foaf/0.1/givenname> "Sergio" . <http://www.inf.unibz.it/~tessaris/myfoaf.xml#me> <http://xmlns.com/foaf/0.1/phone> <tel:+39-0471-016-125> .

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF/XML

Normative XML serialisation for RDF documents Use namespace abbreviations: e.g.
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:myfoaf="http://www.inf.unibz.it/~tessaris/myfoaf.xml">

Encode paths of the RDF graph There are several ways of encoding the same graph!

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF/XML

document root is rdf:RDF rdf:Description to represent nodes predicates use the corresponding URI
<rdf:Description rdf:about="http://www.w3.org/TR/rdf-syntax-grammar"> <dc:title>RDF/XML Syntax Specification (Revised)</dc:title> </rdf:Description>

bnodes can be omitted

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF/XML Example
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:foaf="http://xmlns.com/foaf/0.1/"> <foaf:Person rdf:ID="me"> <foaf:name>Sergio Tessaris</foaf:name> <foaf:title>Dr</foaf:title> <foaf:givenname>Sergio</foaf:givenname> <foaf:family_name>Tessaris</foaf:family_name> <foaf:mbox_sha1sum> 758128cdae69fd0fd9e880921d9f4b25259edbf5</foaf:mbox_sha1sum> <foaf:homepage rdf:resource="http://www.inf.unibz.it/~tessaris"/> <foaf:phone rdf:resource="tel:+39-0471-016-125"/> <foaf:workplaceHomepage rdf:resource="http://www.unibz.it/inf"/> </foaf:Person> </rdf:RDF>
Sergio Tessaris RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Turtle Notation

Extension of N-Triples Compact representation of graphs

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Turtle Notation

Extension of N-Triples Compact representation of graphs I will use this notation, explaining it on the way

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

Turtle Example
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> . @prefix foaf: <http://xmlns.com/foaf/0.1/> . @prefix : <http://www.inf.unibz.it/~tessaris/myfoaf.xm#> . :me rdf:type foaf:Person ; foaf:family_name "Tessaris" ; foaf:givenname "Sergio" ; foaf:homepage <http://www.inf.unibz.it/~tessaris> ; foaf:mbox_sha1sum "758128cdae69fd0fd9e880921d9f4b25259edbf5" ; foaf:name "Sergio Tessaris" ; foaf:phone <tel:+39-0471-016-125> ; foaf:title "Dr" ; foaf:workplaceHomepage <http://www.unibz.it/inf> .
Sergio Tessaris RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF Data Model

up till now we have

abstract syntax for graphs a way to exchange these graphs

wheres the semantics? how to express rich semantic constructs?

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF Data Model

up till now we have

abstract syntax for graphs a way to exchange these graphs

wheres the semantics? how to express rich semantic constructs? everything is going to be in RDF itself

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF Data Model

up till now we have

abstract syntax for graphs a way to exchange these graphs

wheres the semantics? how to express rich semantic constructs? everything is going to be in RDF itself URIs are global: RDF prescribes the meaning of same URIs

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF, RDF Schema, and more

RDF: basic vocabulary, e.g.

class membership

RDFS: extends the basic vocabulary, e.g.

subclass relation domain and range for predicates

OWL family: extends to a full edged ontology language

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF, RDF Schema, and more

RDF: basic vocabulary, e.g.

class membership

RDFS: extends the basic vocabulary, e.g.

subclass relation domain and range for predicates

OWL family: extends to a full edged ontology language

we wont discuss OWL

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDF Vocabulary
Classes
rdf:Property rdf:XMLLiteral

Properties
rdf:type

Reication
rdf:Statement rdf:subject, rdf:predicate, rdf:object

Collections and Containers

rdf:Bag, rdf:Seq, rdf:Alt rdf:List, rdf:first, rdf:rest, rdf:nil rdf: 1, rdf: 2, rdf: 3,. . . etc.

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Building Blocks RDF Abstract Syntax RDF Vocabulary

RDFS Vocabulary

Classes
rdfs:Resource rdfs:Class rdfs:Literal rdfs:Datatype

Properties
rdfs:range, rdfs:domain rdfs:subClassOf rdfs:subPropertyOf rdfs:label, rdfs:comment

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Meaning and Semantics

the meaning of an RDF document is context dependent
mostly not machine accessible

we are interested in the semantics of RDF(S) as a formal language

implications of the asserted statements entailment as the basic tool (query answering) inference rules to decide entailment between two graphs

semantics provided by means of a model theory (normative)

over the abstract syntax already described

monotonic
no closed-world assumptions no defaults

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDF Interpretations
Consider a set of terms T (URIs and Literals in a graph) Denition (Simple Interpretation) a simple interpretation I over T is composed by non-empty set of resources (domain of I)
set P (properties of I) PL , which contains all the plain literals in T

mapping V from URI references in T into P mapping L from typed literals in T into mapping E from P into the powerset of

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDF Interpretations

double level interpretation the key is in E literals are in the domain no bnodes in T

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Triples Satisability

interpretation I(t) of a term t T

I(t) = t if t is a plain literal I(t) = L(t) if t is a typed literal I(t) = V(t) if t is a URI reference

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Triples Satisability

interpretation I(t) of a term t T

I(t) = t if t is a plain literal I(t) = L(t) if t is a typed literal I(t) = V(t) if t is a URI reference

a triple s p o . is satised by I i
I(s), I(o) E(I(p))

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Triples Satisability

interpretation I(t) of a term t T

I(t) = t if t is a plain literal I(t) = L(t) if t is a typed literal I(t) = V(t) if t is a URI reference

a triple s p o . is satised by I i
I(s), I(o) E(I(p))

Bnodes
B(G ) is the set of bnodes in G A a mapping from B(G ) to IA is the extension of I with A (i.e. IA (b) = A(b))

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Models of RDF Graphs

Ground graphs (without bnodes) Denition (Ground Satisability) I is a model of a ground RDF graph G i satises all the triples in G

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Models of RDF Graphs

Ground graphs (without bnodes) Denition (Ground Satisability) I is a model of a ground RDF graph G i satises all the triples in G Graphs with bnodes Denition (Satisability) I is a model of an RDF graph G i there is a mapping A from B(G ) to s.t. IA satises all the triples in G

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Simple Entailment

Entailment is dened in terms of models G entails G i every model of G is a model of G

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Simple Entailment

Entailment is dened in terms of models G entails G i every model of G is a model of G bnodes are existential variables
I model of G if exists A s.t. IA satises all the triples in G I model of G if exists A s.t. IA satises all the triples in G

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Simple Entailment

Entailment is dened in terms of models G entails G i every model of G is a model of G bnodes are existential variables
I model of G if exists A s.t. IA satises all the triples in G I model of G if exists A s.t. IA satises all the triples in G

What about RDF and RDFS?

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDF(S) Vocabulary

additional semantic conditions over the vocabulary e.g. rdf:type

restrict the set of models derived from the intended meaning (RDF data model) e.g. rdf:type is a rdf:Property

Semantic conditions e.g. x P i x, V(rdf:Property) E(V(rdf:type)) Axiomatic triples e.g. rdf:type rdf:type rdf:Property . RDF-MT doesnt cover reication, containers and collections

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDFS Semantic Conditions

RDFS introduces classes and their properties still based on rdf:type macro C() for unary predicates x C(y ) i x, y E(V(rdf:type))

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDFS Semantic Conditions

RDFS introduces classes and their properties still based on rdf:type macro C() for unary predicates x C(y ) i x, y E(V(rdf:type)) Semantic conditions

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDFS Semantic Conditions

RDFS introduces classes and their properties still based on rdf:type macro C() for unary predicates x C(y ) i x, y E(V(rdf:type)) Semantic conditions
Subclass: if x, y E(V(rdfs:subClassOf)) then C(x) C(y ) E (V (rdfs:subClassOf)) is transitive and reexive

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDFS Semantic Conditions

RDFS introduces classes and their properties still based on rdf:type macro C() for unary predicates x C(y ) i x, y E(V(rdf:type)) Semantic conditions
Subclass: if x, y E(V(rdfs:subClassOf)) then C(x) C(y ) E (V (rdfs:subClassOf)) is transitive and reexive Domain: if x, y E(V(rdfs:range)) then u, v E(x) implies v C(y )

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDFS Semantic Conditions

RDFS introduces classes and their properties still based on rdf:type macro C() for unary predicates x C(y ) i x, y E(V(rdf:type)) Semantic conditions
Subclass: if x, y E(V(rdfs:subClassOf)) then C(x) C(y ) E (V (rdfs:subClassOf)) is transitive and reexive Domain: if x, y E(V(rdfs:range)) then u, v E(x) implies v C(y )

somethings wrong here?

Sergio Tessaris RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Extensional Semantic Conditions

One direction (only if) is missing! Semantic conditions revised

Subclass: x, y E(V(rdfs:subClassOf)) i C(x) C(y ) Domain: x, y E(V(rdfs:range)) i u, v E(x) implies v C(y )

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Extensional Semantic Conditions

One direction (only if) is missing! Semantic conditions revised

Subclass: x, y E(V(rdfs:subClassOf)) i C(x) C(y ) Domain: x, y E(V(rdfs:range)) i u, v E(x) implies v C(y )

:p1 rdfs:range :c1 . :p2 rdfs:range :c2 . :p1 rdfs:subPropertyOf :p2 .

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Extensional Semantic Conditions

One direction (only if) is missing! Semantic conditions revised

Subclass: x, y E(V(rdfs:subClassOf)) i C(x) C(y ) Domain: x, y E(V(rdfs:range)) i u, v E(x) implies v C(y )

:p1 rdfs:range :c1 . :p2 rdfs:range :c2 . :p1 rdfs:subPropertyOf :p2 . implies? :c1 rdfs:subClassOf :c2 .

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Extensional Semantic Conditions

One direction (only if) is missing! Semantic conditions revised

Subclass: x, y E(V(rdfs:subClassOf)) i C(x) C(y ) Domain: x, y E(V(rdfs:range)) i u, v E(x) implies v C(y )

:p1 rdfs:range :c1 . :p2 rdfs:range :c2 . :p1 rdfs:subPropertyOf :p2 . implies? :c1 rdfs:subClassOf :c2 . only with extensional semantic conditions (not normative)

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDFS Semantic Conditions

x C(y ) i x, y E(V(rdf:type)) x, y E(V(rdfs:subClassOf)) x, y E(V(rdfs:subPropertyOf)) x, y E(V(rdfs:range)) x, y E(V(rdfs:domain)) i i i i C(x) C(y ) E(x) E(y ) u, v E(x) v C(y ) u, v E(x) u C(y )

if x C(V(rdfs:Class)) if x C(V(rdfs:Datatype))

then then

C(x) C(V(rdfs:Resource)) C(x) C(V(rdfs:Literal))

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDF(S) Literals
Plain literals (RDFS) PL = C(V(rdfs:Literal))

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDF(S) Literals
Plain literals (RDFS) PL = C(V(rdfs:Literal)) aects logical implication :myself foaf:name "Sergio Tessaris" . entails :myself foaf:name :b1 . :b2 rdf:type rdfs:Literal .

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDF(S) Literals
Plain literals (RDFS) PL = C(V(rdfs:Literal)) aects logical implication :myself foaf:name "Sergio Tessaris" . entails :myself foaf:name :b1 . :b2 rdf:type rdfs:Literal . Note "Sergio Tessaris" rdf:type rdfs:Literal . is not a valid RDF(S) triple!
Sergio Tessaris RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Entailment Rules

a set of inference rules to capture RDF(S)-entailment rules complete an RDF graph add a triple if there is some pattern
rules application terminates in a polynomial number of steps

set of rules for RDF and RDFS (informative)

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Entailment Rules

Lemma (Entailment Lemma) G rdf(s)-entails E i exists G derived from G with axiomatic triples using the entailment rules s.t. G simply entails E . simple entailment is enough eective procedure (needs simple entailment)

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Grounding RDF Graphs

Grounding a graph G Def completed: added axiomatic triples and applied entailment rules Def Herbrand model: each bnode replaced by an URIs or Literal Def Canonical model (G ): bnodes replaced with fresh URIs

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Graph entailment

Theorem RDF graphs entailment: G entails E i some herbrand model of E is a subgraph of the canonical model of G Connects our denition to W3C normative semantics Complexity of entailment
1 2 3

NP-complete in the size of the RDF graphs PTIME in the size of the entailing graph G PTIME if E is acyclic or ground

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

RDFS and FOL

RDF has an high order avour

URIs can play dierent roles ex:o, rdf:type, ex:o

Introduce a dierent model theoretic semantics for RDF

Compatible with FOL Extensibility to more expressive languages (e.g. OWL) Use standard technologies (e.g. databases or theorem provers)

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

FO Compatible Model Theory

key idea: polymorphic interpretation of URIs (contextual PC)

abstract domain u IO : individual + function mapping valid literals to datavalues u IC : class u IR : binary relation

E.g. ex:o, rdf:type, ex:o leads to ex:oIO ex:oIC

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

RDF model theory Entailment Casting RDF into FOL

Classical Logic Interoperability

Def non-high order graph: no blank nodes as objects of rdf:type Def The classical logic translation FO(G ) of a non-high order graph G
URIs and literals are constants blank nodes are existentially quantied variables binary atomic formulas in correspondence with triples in G u1 , rdf:type, u2 triples introduce u2 (u1 ) atomic formulae

Theorem Given an RDF graph G and a non-high order graph E , G entails E i FO(G ) |=C FO(E )

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Querying RDF documents

How do we get informations out of an RDF document? RDF graphs can be stored in a variety of means
RDF/XML documents databases dedicated RDF service providers (e.g. RSS 1.0) generated on the y; e.g. from web pages (Gleaning Resource Descriptions from Dialects of Languages [GRDDL])

Often retrieving the whole graph is not feasible/desirable

too big lot of uninteresting parts dynamic

Solution: a (standard) protocol for querying RDF graphs

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Entailment and Querying

entailment and query answering are strictly related an answer to a query is a set of entailed facts
tuples representing variable bindings complex structures like RDF graphs or XML documents it depends on the query language

RDF aims at big volumes of data

look out for eciency (i.e. low data complexity)

two main factors

representational language (RDF) query language

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Querying RDF

RDF(S) is a simple language

entailment can be checked on a single canonical model see entailment rules and lemma

more freedom on the query language

truly graph based query language (e.g. a la XQuery) WilburQL simple language based on graph entailment

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Querying RDF

RDF(S) is a simple language

entailment can be checked on a single canonical model see entailment rules and lemma

more freedom on the query language

truly graph based query language (e.g. a la XQuery) WilburQL simple language based on graph entailment

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Graph Patterns
Dataset: graph to be queried dene a new kind of graphs: RDF graph patterns
RDF graphs with variables

?x

foaf:nick

"Alice" .

patterns may contain bnodes :b foaf:nick "Alice" .

Query Answering Find all the assignments for the variables that make the pattern a logical consequence of the Dataset
Sergio Tessaris RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Subgraph Matching

can we query in an ecient way?

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Subgraph Matching

can we query in an ecient way? entailment lemma: simple entailment is subgraph matching

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Subgraph Matching

can we query in an ecient way? entailment lemma: simple entailment is subgraph matching subgraph matching is conjunctive query answering

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Subgraph Matching

can we query in an ecient way? entailment lemma: simple entailment is subgraph matching subgraph matching is conjunctive query answering Dataset can be stored in a relational database

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Subgraph Matching

can we query in an ecient way? entailment lemma: simple entailment is subgraph matching subgraph matching is conjunctive query answering Dataset can be stored in a relational database the answer is yes!

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Subgraph Matching

can we query in an ecient way? entailment lemma: simple entailment is subgraph matching subgraph matching is conjunctive query answering Dataset can be stored in a relational database the answer is yes! nothing more than conjunctive queries using a single ternary predicate (e.g. triple(x, foaf:nick, "Alice"))
e.g. Oracle supports RDF and an extension to SQL most SPARQL implementations rely on a database back-end

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

ORACLE SQL Extension

SELECT t.r reviewer, e.emailid emailid FROM TABLE(RDF_MATCH( (?r ReviewerOf ?c) (?r rdf:type Faculty), RDFModels(reviewers), NULL, NULL)) t, employees e WHERE t.r = e.name;

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

SPARQL

query language for RDF becoming a W3C recommendation based on Graph Patterns
patterns extract a set of variable bindings (tuples)

results from dierent graph patterns can be combined using an algebra

union of answersets left outer join ltering based on XQuery operators optionally, an RDF graph can be returned (using a template)

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

SPARQL Example
BASE <http://example.org/> PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> PREFIX foaf: <http://xmlns.com/foaf/0.1/> PREFIX ex: <properties/1.0#> SELECT DISTINCT ?person ?name ?age FROM <http://rdf.example.org/people.rdf> WHERE { ?person a foaf:Person ; foaf:name ?name. OPTIONAL { ?person ex:age ?age } . FILTER ! REGEX(?name, "Bob") } LIMIT 3 ORDER BY ASC[?name]

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

SPARQL Semantics

Semantics for pattern matching: entailment regime

kind of entailment: simple, RDF, RDFS, . . .

Answer set is a set of mappings from variables in Q to terms occurring in G Given an entailment |=E , a query pattern Q, an RDF graph G , then Q E -matches graph G with answer S if:

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

SPARQL Semantics

Semantics for pattern matching: entailment regime

kind of entailment: simple, RDF, RDFS, . . .

Answer set is a set of mappings from variables in Q to terms occurring in G Given an entailment |=E , a query pattern Q, an RDF graph G , then Q E -matches graph G with answer S if:
1

Q graph equivalent to Q (isomorphic to Q)

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

SPARQL Semantics

Semantics for pattern matching: entailment regime

kind of entailment: simple, RDF, RDFS, . . .

Answer set is a set of mappings from variables in Q to terms occurring in G Given an entailment |=E , a query pattern Q, an RDF graph G , then Q E -matches graph G with answer S if:
1 2

Q graph equivalent to Q (isomorphic to Q) G S(Q ) well-formed graph

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

SPARQL Semantics

Semantics for pattern matching: entailment regime

kind of entailment: simple, RDF, RDFS, . . .

Answer set is a set of mappings from variables in Q to terms occurring in G Given an entailment |=E , a query pattern Q, an RDF graph G , then Q E -matches graph G with answer S if:
1 2 3

Q graph equivalent to Q (isomorphic to Q) G S(Q ) well-formed graph G |=E (G S(Q ))

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

SPARQL Semantics

Semantics for pattern matching: entailment regime

kind of entailment: simple, RDF, RDFS, . . .

Answer set is a set of mappings from variables in Q to terms occurring in G Given an entailment |=E , a query pattern Q, an RDF graph G , then Q E -matches graph G with answer S if:
1 2 3

Q graph equivalent to Q (isomorphic to Q) G S(Q ) well-formed graph G |=E (G S(Q ))

Backward compatible with subgraph homomorphism

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

BNodes in Query Answers

Wheres the problem? why not G |=E S(Q )

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

BNodes in Query Answers

Wheres the problem? why not G |=E S(Q ) bnodes in answer sets
graph: :myself foaf:homepage "http://www.inf.unibz.it/" query: :b foaf:homepage ?x

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

BNodes in Query Answers

Wheres the problem? why not G |=E S(Q ) bnodes in answer sets
graph: :myself foaf:homepage "http://www.inf.unibz.it/" query: :b foaf:homepage ?x answers: [ ?x/"http://www.inf.unibz.it/" ], [ ?x/ :myself]

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

BNodes and Literals

which bnodes in answers? graph :myself foaf:name "Sergio Tessaris" . query ?x rdf:type rdfs:Literal answer

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

BNodes and Literals

which bnodes in answers? graph :myself foaf:name "Sergio Tessaris" . query ?x rdf:type rdfs:Literal answer querying precompleted graph graph :myself foaf:name "Sergio Tessaris" . :b rdf:type rdfs:Literal answer {[ ?x/ :b ]}

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

BNodes and Literals

which bnodes in answers? graph :myself foaf:name "Sergio Tessaris" . query ?x rdf:type rdfs:Literal answer querying precompleted graph graph :myself foaf:name "Sergio Tessaris" . :b rdf:type rdfs:Literal answer {[ ?x/ :b ]} in both cases :w rdf:type rdfs:Literal is a logical consequence

Sergio Tessaris

RDF Data Model and Query Languages

Introduction RDF Semantics Querying RDF

Introduction Graph Patterns Query languages SPARQL

Conclusions

RDF has a precise (model theoretic) semantics Several drawbacks, but its a standard we have to deal with it! Strange semantics but relatively easy to deal with (up to RDFS) Extensions (e.g. OWL) require a more careful rethinking of the whole framework
Keeping backward compatibility Interoperability via SPARQL Higher order style semantics (cfg HiLog)

Sergio Tessaris

RDF Data Model and Query Languages