(11) semantic web technologies - rules

Semantic Web Technologies

LectureDr. Harald Sack

Hasso-Plattner-Institut für IT Systems EngineeringUniversity of Potsdam

Winter Semester 2012/13

Lecture Blog: http://semweb2013.blogspot.com/This file is licensed under the Creative Commons Attribution-NonCommercial 3.0 (CC BY-NC 3.0)

Dienstag, 8. Januar 13

http://semweb2013.blogspot.com


http://creativecommons.org/licenses/by-nc/3.0/

http://creativecommons.org/licenses/by-nc/3.0/

Semantic Web Technologies , Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam

2 1. Introduction 2. Semantic Web - Basic Architecture

Languages of the Semantic Web - Part 1

3. Knowledge Representation and LogicsLanguages of the Semantic Web - Part 2

4. Applications in the ,Web of Data‘

Semantic Web Technologies Content


Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität Potsdam

3 OWL

Extension

SHROIQ(D)

SHOIN(D)

OWL2last lecture



4 OWLOWL 2

Erweiterung

SHROIQ(D)

SHOIN(D)

SHROIQ(D) Overview

Class Expressions• Class names A,B• Conjunction C ⊓ D• Disjunction C ⊔ D• Negation ¬C• Exist. property restriction ∃R.C• Univ property restriction ∀R.C• Self ∃S.Self• Greater-than ≥n S.C• Less-than ≤ S• Enumerated classes {a}

Properties• Property names R,S,T• Simple properties S,T• Inverse properties R-

• Universal property U

Tbox (Class axioms)• Inclusion C ⊑ D• Equivalence C ≣ D

Rbox (Property Axioms)• Inclusion R1 ⊑ R2

• General Inclusion R(-)1 º R (-) 2 º ..... º R (-) n ⊑ R• Transitivity• Symmetry• Reflexivity• Irreflexivity• Disjunctiveness

Abox (Facts)• Class membership C(a)• Property relation R(a,b)• Negated property relation ¬S(a,b)• Equality a=b• Inequality a≠b



5

OWLOWL 2

Erweiterung

SHROIQ(D)

SHOIN(D)

• OWL2 is a semantic fragment of FOL• OWL2 exists in different flavors

• OWL2 EL, OWL2 RL, OWL QL2 ⊆ OWL2 DL ⊆ OWL2 Full

Turmbau zu Babel, Pieter Brueghel, 1563

OWL2 – Web Ontology Language

OWL1 DL SHOIN(D)

OWL2 Full

OWL2

OWL2 DL SHROIQ(D)

OWL2 EL EL++OWL2 RL

OWL2 QL DL-Lite

undecidable

2NExpTimeComplete

NExpTimeComplete

PTimeComplete

AC0



6 Can we do SPARQL with OWL?


Vorlesung Semantic Web, Dr. Harald Sack, Hasso-Plattner-Institut, Universität PotsdamTurmbau zu Babel, Pieter Brueghel, 1563

7

Using SPARQL with OWL Knowledge Bases

foaf:Person rdfs:subClassOf foaf:Agent . foaf:Person rdfs:subclassOf [ a owl:Restriction ; owl:onProperty :hasFather ; owl:someValuesFrom foaf:Person. ] foaf:knows rdfs:range foaf:Person. :Magnus a Person . :Magnus foaf:knows :Nadine .

•Consider the following OWL KB

•SPARQL 1.0 returns only :Magnus but it should also return :Nadine

SELECT ?X { ?X a foaf:Person }



8


•SPARQL 1.0 is a Query Language for RDF Graphs•does not support RDFS/OWL entailment

•Complex (OWL) ontologies cannot be represented with an explicit graph, there exist numerous possible interpretations

•In difference to RDF, there is no most specific interpretation as foundation for a graph

•OWL DL Interpretations might contain an (possibly) infinite number of elements



9


foaf:Person rdfs:subClassOf foaf:Agent . foaf:Person rdfs:subclassOf [ a owl:Restriction ; owl:onProperty :hasFather ; owl:someValuesFrom foaf:Person. ] foaf:knows rdfs:range foaf:Person. :Magnus a Person . :Magnus foaf:knows :Nadine .

•Consider the following OWL KB

•SPARQL 1.1 enables OWL entailment and returns :Magnus :Nadine

SELECT ?X { ?X a foaf:Person }



10

SPARQL 1.1 with RDFS/OWL Entailment

•Challenges and Pittfalls•possibly infinite answers

•non-distinguished variables

•other SPARQL 1.1 features, e.g. aggregates

•SPARQL 1.1 follows a simple pragmatic approach:•Restrict results to terms occurring in the graph

•Answers must result from BGP matching

•Aggregates are evaluated as post-processing after BGP matching



11

Alternative Variant for Querying OWL DL

•Conjunctive Queries

•no official specification

•Goal: more expressive queries about individuals

•Formatting or post-processing of results is not considered

•practical relevance for applications•various implementations available



12 •conjunctive queries are simple•Example:

•„Which books are published by Springer and who is the author?“

•Syntax similar to FOL

•Main elements: Properties/Classes/Individuals, Variables, Conjunction ∧

Syntax and Intuition of Conjunctive Queries

Book(x) ∧ publishedBy(x, Springer) ∧ hasAuthor(x, y)



13•Main elements (Atoms):

•C(e) or ¬C(e) , C is class name, e is variable or name of an individual

•R(e,f), R is property name, e and f are variables or names of individuals

•Example:

Syntax and Intuition of Conjunctive Queries

Book(x) ∧ publishedBy(x, Springer) ∧ hasAuthor(x, y)



14

Semantics of Conjunctive Queries

•Conjunctive Queries are similar to logical formulas•Queries without variables might be entailed directly from the ontology

•Variables are used as placeholders for individuals

•Function μ is result of a conjunctiven query q for an OWL DL Ontology O, iff:(1) Domain of μ is the set of free variables in q(2) Range of μ is the set of all individuals in O(3) O ⊨ μ(q), i.e. conjunctive query q with given variable

assignment is entailed by O

•no partial function – all Variables must be assigned

•Literals (Datatypes) are not considered for simplicity



15

Elements Without Names

•Variables are placeholders for (named) individuals•OWL Ontologies can entail the existence of not named individuals

•Example:

Book(a) (a is a book)Book ⊑ ∃hasAuthor.⊤ (every book has an author)

Anfrage:Book(x) ∧ hasAuthor(x,y)

→ no possible solution



16

Non-distinguished Variables

•How to consider not named elements for the query?•Output of not named elements as part of the result is problematic

•But a statement of existence is possible vianon-distinguished variables(=variables bound via existential quantification)

Anfrage:∃y.(Book(x) ∧ hasAuthor(x,y))

Solution {x ↦ a}, but y is NOT PART of the result

Book(a) (a is a book)Book ⊑ ∃hasAuthor.⊤ (every book has an author)



17

SPARQL vs. Conjunctive Queries

SPARQL Conjunctive Queries

graph patterns logical conjunctions

canonical model many possible models

options, alternatives, filters -

query for arbitrary elements only query for individuals (strict typing)

variables for arbitrary elements distinguished and non-distinguished variables



18•KAON2: conjunctive queries without non-distinguished variables, restricted negation possible

•Pellet: conjunctive queries with non-distinguished variables and negation, not complete for OWL DL

•further implementations with special query languages (RacerPro) or restrictions to simpler DLs (QuOnto for OWL2 QL)

• see also http://www.cs.man.ac.uk/~sattler/reasoners.html

Restrict the problem and the implementation gets simpler

Implementations of Conjunctive Queries


http://www.cs.man.ac.uk/~sattler/reasoners.html

http://www.cs.man.ac.uk/~sattler/reasoners.html


19 3. Knowledge Representation and LogicsThe Languages of the Semantic Web - Part 2

• Excursion: Ontologies in Philosophy and Computer Science

• Recapitulation: Propositional Logic and First Order Logic

• Description Logics

• RDF(S) Semantics• OWL and OWL-Semantics• OWL 2

• Rules & The Semantic Web




20 Can we model everything with

OWL?



21

Rules

&

the Se

mantic

Web



22

3.7 Rules & The Semantic Web3.7.1 Rules from a Semantic Web Perspective3.7.2 Rules for OWL with SWRL3.7.3 Rules expressible in OWL3.7.4 Exchanging Rules with RIF



23

• The Semantic Web concentrates on declarative forms of knowledge representation• OWL, RDFS

• Rules are a common form of procedural knowledge representation in Knowledge Engineering• Expert Systems• Prolog, CLIPS, JESS, OPS, …

• Knowledge representation formalisms of the Semantic Web have expressive limitations which can be overcome by rule-based knowledge• e.g. composition of complex classes from classes and

properties

The Role of Rules



24

What are Rules?

•Interpretation of a rule depends on context• General Inference:

Premise → Conclusion• Hypothesis:

Cause → Effect• Production:

Condition → Action

IF A .... THEN B ....

A ! B



25

What are Rules?

•Logical Rules (FOL implication):•F ! G is equivalent with ¬F ∨ G•Logical extension of the KB (static)•Open World, declarative

•Procedural Rules (e.g. Production Rules):•If X then Y else Z •executable machine instructions (dynamic)•operational (semantics = effect at application)

•Logic Programming Rules (e.g. Prolog, F-Logic):•„woman(X) <- person(X) AND NOT man(X)“•Approximation of logical semantics with operational aspects•Closed World (mostly), semi-declarative



26

FOL as Rule Language•Rules as FOL implications (Horn Clause)

•semantically equivalent with

•where Ai, H are atomic formulas•Quantification most times ommitted, free variables are considered to be universally quantified•i.e. the rule holds for all possible assignments

A1 ∧ A2 ∧ . . . ∧ An ! H

⎧ ｜｜

｜

｜ ⎨ ｜

｜

｜

｜ ⎩Body

¬A1 ∨ ¬A2 ∨ . . . ∨ ¬An ∨ H

→

⎧ ⎨ ⎩

Head



27

FOL as Rule Language•Rules as FOL implications (Horn Clause)

•semantically equivalent with

•where Ai, H are atomic formulas•Quantification most times ommitted, free variables are considered to be universally quantified•i.e. the rule holds for all possible assignments

H ← A1 ∧ A2 ∧ . . . ∧ An

⎧ ｜｜

｜

｜ ⎨ ｜

｜

｜

｜ ⎩Body

¬A1 ∨ ¬A2 ∨ . . . ∨ ¬An ∨ H

←⎧ ⎨ ⎩

Head

often written from right to left ( ← or :- )


•Lloyd-Topor Transformation•Several atoms in the head are usually considered as conjunction

•is equal to

•this transformation is called Lloyd-Topor Transformation


28

Variants of FOL Rules

A1 A2...An ! H1 H2...Hm

A1 A2...An ! H1A1 A2...An ! H2

...

A1 A2...An ! Hm


•Disjunctive Rules•Disjunction of several non-negated Atoms

•reverse implication, as e.g.„if I see someting, then the light is on or the sun is shining“


29


⎧ ｜｜

｜

｜ ⎨ ｜

｜

｜

｜ ⎩⎧ ｜

｜

｜

｜ ⎨ ｜

｜

｜

｜ ⎩

A1 ∧ A2 ∧ . . . ∧ An → H1 ∨ H2 ∨ . . . ∨ Hm

Body Head



30•FOL Rules

•Clause: Disjunction of atomic formulas or negated atomaric formulas

•Horn Clause: Claus with at most one not negated atom

•Definite Clause: Clause with exactly one not negated atom

•Fact: Clause of a single not negated atom

¬p ∨ ¬q ∨ . . . ∨ ¬t ∨ u can be written as p ∧ q ∧ . . . ∧ t ! u



•Examples

•Semantic of rules complies to FOL semantics


31

Person(x) ! Woman(x) ∨ Man(x) (clause)

Man(x) ∧ hasChild(x,y) ! Father(x)(definite clause)

hasBrother(mother(x),y) ! isUncle(x,y)(with function symbol)


Man(x) ∧ Woman(x) ! (horn clause)

Woman(Nadine) (fact)



32

Description Logics vs. Rules

•Rules are usually considered to apply only to known constants.

•No possibility to „create“ new things „on the flight“by using existential quantification ∃

•If rules are considered FOL formulas, then combining rules with ALC leads to undecidability.

Human ⊑ ∃hasParent.Human



33

DATALOG

• is a logical rule language that consists of •horn clauses without function symbols

•conjunction, constants, universally quantified variables, predicate symbols

•no disjunction, no negation, no existential quantification, no function symbols

•originally developed as foundation of deductive databases•Knowledge Bases (Datalog Programs) are sets of horn

clauses (without function symbols)•DATALOG is decidable

•DATALOG is computationally efficient, complexity corresponds to OWL Lite, i.e. ExpTime



34

DATALOG

•Datalog Term: constant c or variable v

•Datalog Atom: p(t1,...,tn) with predicate p, terms t1,...,tn

•Datalog Rule: ∀x1,...,∀xn (B1 ⋀ ... ⋀ Bn → H) with B1,...,Bn,H atoms and x1,...,xn variables of the atoms

•Datalog Program: set of Datalog rules



35

DATALOG

Examples

(1) Vegetarian(x) ⋀ FishProduct(y) → dislikes(x,y) (2) orderedDish(x,y) ⋀ dislikes(x,y) → Unhappy(x)(3) orderedDish(x,y) → Dish(y)(4) dislikes(x,z) ⋀ Dish(y) ⋀ contains(y,z) → dislikes(x,y)(5) → Vegetarian(Matthias)(6) Happy(x) ⋀ Unhappy(x) →



36

DATALOG Semantics

• Interpretation I with Domain ΔI

• Interpretation of variables: variable assignment Z (mapping of variables to ΔI)

• Interpretation of rules and terms wrt. I (and Z):

• Interpretation of a constant: aI,Z = aI∈ΔI

• Interpretation of a variable: xI,Z = Z(x)∈ΔI

• Interpretation of an n-ary predicate: pI ∈ ΔI n

• I,Z ⊨ p(t1,...,tn) iff (tI,Z1,...,tI,Zn)∈pI,

• I ⊨ B!H iff for all variable assignments Z it holds: either I,Z ⊨ H or I,Z ⊭ B.

• I is a Model for a rule set (program), iff:I ⊨ B!H for all rules B!H of the rule set



37

How to combine OWL and Datalog?



38



39




40

•W3C Submission (bereits im Mai 2004)(developed by the Joint US/EU ad hoc Agent Markup Language Committee (JC),in collaboration with RuleML Initiative)

•based on combination of parts of OWL and RuleML/Datalog•here OWL DL and Unary/Binary Datalog RuleML

•Idea: Datalog Rules that apply on OWL ontologies

•Symbols in rules can be OWL identifiers (or new Datalog identifiers)

•Syntax: XML Concrete Syntax (extends OWL XML Presentation Language), RDF Concrete Syntax and abstract Syntax

•Rules are represented as Implication of an Antecedent (Body) and a Consequent (Head)

•SWRL is undecidable

SWRL SemanticWeb Rule Language



41

SWRL SemanticWeb Rule Language

•Antecedent and Consequent are Conjunctions of

assertions (atoms) of the form•C(x) or P(x,y) •sameAs(x,y), differentFrom(x,y)

•where x,y are variables, OWL individuals or elements of an OWL concrete domain,

•C(x) is an OWL class description P(x,y) is an OWL property description

Antecedent → Consequent



42

SWRL - Abstract Language Definition

•SWRL Rule

•SWRL Knowledge Base

•Atoms are defined as

•C ... Class, D ... Datatype

•R ... Object Property

•U ... Datatype Property

• i,j ... Variable / Individual identifier

a ← b1,...,bn where a: head, b1,...,bn: body

Atom ← C(i) | D(v) | R(i, j) | U(i,v) | builtIn(p, v1, ..., vn) | i = j | i ≠ j

•v,v1,...vn ... Datatype Variable / Value Identifier

•p ... name of a BuiltIn function

k=(Σ,P) where Σ is an OWL knowledge base P is a finite rule set



43

SWRL - Semantics

•OWL DL (Description Logics) and Datalog are applying the same interpretations•OWL individuals are Datalog constants•OWL classes are unary Datalog predicates•OWL properties are binary Datalog predicates

•Interpretation can be model for OWL ontology as well as for a set of Datalog rules

Entailment for OWL/Datalog combination is possible



44

SWRL - Semantics

•Let I=(ΔI, ΔD,.I ,.D) an interpretation with

•ΔI = Object Interpretation domain

•ΔD = Datatype Interpretation domain•.I = Object Interpretation function•.D = Datatype Interpretation function•with ΔI ∩ ΔD =⊥

•VIX are object variables with VIX ! 2ΔI

•VDX are datatype variables with VDX ! 2ΔD



45

SWRL - Semantics

•Interpretation of SWRL atoms:

SWRL atom Interpretation

C(i) iI∈CI

R(i,j) (iI,jI)∈RI

U(i,v) (iI,vD)∈UI

D(v) vD∈DD

builtIn(p,v1,...,vn) v1D,...,vnD∈pD

i=j iI=jI

i≠j iI≠jI



46

SWRL - Semantics

•SWRL Antecedent is satisfied, iff•antecedent is empty (trivial)•all atoms of the antecedent are satisfied

•SWRL Consequent is satisfied, iff•it is not empty and•the atom of the consequent is satisfied

•A rule is satisfied for an Interpretation I, iff•the Interpretation I, which satisfies the antecedent also satisfies the consequent.



47

SWRL - ExamplehatOnkel(?x,?z) ← hatVater(?x,?y) Λ hatBruder(?y,?z)

<ruleml:imp> <ruleml:_rlab ruleml:href="#onkel"/> <owlx:Annotation> <owlx:Documentation>Bruder des Vaters</owlx:Documentation> </owlx:Annotation> <ruleml:_body> <swrlx:individualPropertyAtom swrlx:property=“&family;hatVater"> <ruleml:var>x</ruleml:var> <ruleml:var>y</ruleml:var> </swrlx:individualPropertyAtom> <swrlx:individualPropertyAtom swrlx:property=“&family;hatBruder"> <ruleml:var>y</ruleml:var> <ruleml:var>z</ruleml:var> </swrlx:individualPropertyAtom> </ruleml:_body> <ruleml:_head> <swrlx:individualPropertyAtom swrlx:property=“&family;hatOnkel"> <ruleml:var>x</ruleml:var> <ruleml:var>z</ruleml:var> </swrlx:individualPropertyAtom> </ruleml:_head></ruleml:imp>



48

SWRL is undecidable

•Logical Inference for OWL+SWRL is undecidable

•There is no known algorithm that is able to entail all possible inferences for all SWRL knowledge bases, even with unlimited resources and time

•But, from a practical perspective, there are•Algorithms that are able to entail all possible inferences for

some SWRL knowledge bases•Algorithms that are able to entail some inferences for all

SWRL knowledge bases



49

Tool Support for SWRL•Bossam, R2ML, Hoolet, Pellet, KAON2, RacerPro,•Jess, SWRLTab, SWRLQueryTab



50




51

Decidable Fragments of SWRL

•Which SWRL knowledge bases enable complete inference algorithms?

•All SWRL knowledge bases that exist only of OWL / OWL2 axioms

•All SWRL knowledge bases that exist only of sets of Datalog programs

•Every static finite class of SWRL knowledge bases

•Are there more SWRL fragments that are decidable?(1)Description Logics Rules

SWRL Rules that can already be expressed with OWL2

(2)DL-safe Rules Restriction of SWRL Rules via variable assignment constraints



52

Description Logics Rules

•General Idea:Find out, which rules can be expressed via OWL2

•Simple Rules in OWL2

•become

Class1 ⊑ Class2Property1 ⊑ Property2

Class1(x) ! Class2(x)Property1(x,y) ! Property2(x,y)



53•Some classes can be fragmented into rules

A ⊓ B ⊑ ⊥ becomes A(x) ∧ B(x) !

A ⊓ ∃R.∃S.B ⊑ CbecomesA(x) ∧ R(x,y) ∧ S(y,z) ∧ B(z) ! C(x)

A ⊑ ∀R.B becomes A(x) ∧ R(x,y) ! B(y)

A ⊑ ¬B ⊔ C becomes A(x) ∧ B(x) ! C(x)

⊤ ⊑ ≤1R.⊤ becomes R(x,y) ∧ R(x,z) ! y=z

Description Logics Rules



54

(1) Description Logics Rules

•Some classes can be fragmented into rules

{a} ≣ {b} becomes ! a=b

A ⊓ ∃R.{b} ⊑ C becomes A(x) ∧ R(x,b) ! C(x)

A ⊑ B ⊓ C becomes A(x) ! B(x) and A(x) ! C(x)

A ⊔ B ⊑ C becomes A(x) ! C(x) and B(x)! C(x)



55


•In general:•A DL axiom α can be translated into rules, if after translating α into a FOL expression α‘, and after normalizing this expression into a set of clauses M, each formula in M is a Horn clause (i.e. a rule)

•What about complex properties (property chains)?



56


•Property chains can be expressed as rules:

•becomes

•in general

hasParent(x,y) ∧ hasBrother(y,z) ! hasUncle(x,z)

hasParent ∘ hasBrother ⊑ hasUncle

R ∘ S ⊑ T becomes R(x,y) ∧ S(y,z) ! T(x,z)



57


•Problems:•What if on both sides of the rule are not only properties or not only classes ?

•How to express this in OWL2?

Example.: Man(x) ∧ hasChild(x,y) ! fatherOf(x,y)



58



•Idea: •substitute Man(x) with a property to make a property chain

•Apply „Self“ to transform classes into properties•Auxiliary property PMan•Auxiliary axiom Man ≣ ∃PMan.Self

•Thus:

PMan ∘ hasChild ⊑ fatherOf

Example.: Man(x) ∧ hasChild(x,y) ! fatherOf(x,y)



59


•Rolification of concept/class

A(x) ∧ R(x,y) ! S(x,y) becomes PA ∘ R ⊑ S

A(y) ∧ R(x,y) ! S(x,y) becomes R ∘ PA ⊑ S

A(x) ∧ B(y) ∧ R(x,y) ! S(x,y) becomes PB ∘ R ∘ PB ⊑ S



60


•More problems:


•Idea:•Apply universal property U to connect classes•Auxiliary properties: PVegetarian und PFishproduct

Example.: Vegetarian(x) ∧ Fishproduct(y) ! dislikes(x,y)

Vegetarian ≣ ∃PVegetarian.SelfFishproduct ≣ ∃PFishproduct.SelfPVegetarian ∘ U ∘ PFishproduct ⊑ dislikes


•More Problems:

•How to express this in OWL 2?

•Is it possible to eliminate variable y to form a class inclusion in OWL2?

?


61


?

Example.: orderedDish(x,y) ∧ dislikes(x,y) ! Unhappy(x)

∃orderedDish.⊤ ⊓ ∃dislikes.⊤ ⊑ Unhappy

∃orderedDish.∃dislikes–.⊤ ⊑ Unhappy



62

Decidable Fragments of SWRL

•Which SWRL knowledge bases enable complete inference algorithms?

•All SWRL knowledge bases that exist only of OWL / OWL2 axioms

•All SWRL knowledge bases that exist only of sets of Datalog programs

•Every static finite class of SWRL knowledge bases

•Are there more SWRL fragments that are decidable?(1) Description Logics Rules

SWRL Rules that can already be expressed with OWL2

(2) DL-safe Rules Restriction of SWRL Rules via variable assignment constraints



63

(2) DL-Safe Rules

•Idea:•Restrict SWRL to guarantee decidability via restricting the number of possible variable assignments

•Arbitrary Datalog rules are allowed with names of OWL classes and OWL properties

•Rules must be DL-safe: each variable must also be represented within an expression of the rule body that doesn‘t use an OWL class or OWL property (= Datalog Atom)

•Semantics can be adopted from OWL+SWRL (FOL).

DL-safety restricts the application of rules to known individuals



64

Forcing DL-Safety

•Example:

•NOT DL-safe, if „bruder“ and „father“ are OWL properties

•Force DL-Safeness by Restricting the rules to known individuals

•whereby the fact O(a) has to be asserted for all OWL individuals

•Rule is only applicable to known OWL individuals (Named Individuals)

brother(x, z) ⋀ father(z, y) ! uncle(x, y)

O(x) ⋀ O(y) ⋀ O(z) ⋀ bruder(x, z) ⋀ vater(z, y) ! onkel(x, y)



65

Forcing DL-Safety

•Example: „He, who hates his brother, is evil.“

•this implies: evil(Kain), evil(Romulus)•this implies (safe): evilsafe(Kain), BUT NOT: evilsafe(Romulus)

Knowledge Base:father(Kain, Adam) "

father(Abel, Adam) "hates(Kain, Abel)

∃father.father—{Remus}(Romulus) " hates(Romulus, Remus)

father(x,z) ⋀ father(y,z) ⋀ hates(x,y) ! evil(x)O(x)⋀O(y)⋀O(z)⋀father(x,z)⋀father(y,z)⋀hates(x,y) ! evilsafe(x)

O(Kain), O(Abel), O(Adam), O(Romulus), O(Remus)



66

Summary

•SWRL („OWL + Datalog“) is not decidable•Description Logic Rules

•SWRL fragment that can be expressed with OWL2•indirectly supported by OWL 2 reasoners

•DL-safe Rules•SWRL fragment where variables only can be assigned to concrete values (constants)

•supported by OWL reasoner•DL-safety can be forced

•Standard and Best-Practice for rules still does not exist



67




68

RIF - Rule Interchange Format

•W3C Standard (June 2010)•Goal: Definition of a standard to exchange rules (esp. for web-based rule engines)

Rule Engine A

Rule Engine B

RIF dialect X

semantic preservicemapping

semantic preservingmapping



69

RIF - Rule Interchange Format

•Components:•RIF BLD (Basic Logic Dialect) - language standard•RIF-RDF / RIF-OWL - interoperable Semantic with existing knowledge representation languages of the semantic web

•RIF-PRD (Production Rules Dialect) - standard for production rules

•RIF-DTB (Data Types and Builtins)•RIF-FLD (Framework of Logic Dialects)

•W3C RIF Working Grouphttp://www.w3.org/2001/sw/wiki/RIF

RIF Core


http://www.w3.org/2005/rules/wiki/PRD

http://www.w3.org/2005/rules/wiki/PRD

http://www.w3.org/2005/rules/wiki/RIF_Working_Group

http://www.w3.org/2005/rules/wiki/RIF_Working_Group


70

RIF - CORE

•RIF-Core is •restricted variant of RIF BLD (definite Horn rules without function symbols, i.e. similar to Datalog)

•part of RIF PRD (Production Rule Dialect)

•W3C recommendation since 2010

•Syntax variants:•(readable) BLD presentation syntax•XML-based serialization



71

RIF-CORE Dialect

•Example.: uncle(x,y) ← brother(x,z) ⋀ father(z,y)

brother(Martin, Johannes)

father(Johannes, Max)

Document (

Prefix(ex <http://example.com/>)

Group(

Forall ?x ?y ?z(

ex:uncle(?x,?y) :- And(ex:brother(?x,?z) ex:father(?z,?y))

)

ex:brother(ex:Martin ex:Johannes)

ex:father(ex:Johannes ex:Max)

)

)


http://example.com

http://example.com


72

•Property values can be assigned comfortably via ‘Frames‘

•Example.:

ex:book[ex:authoredBy -> ex:Harald

ex:title -> “Internetworking“^^xsd:string

ex:publishedBy -> ex:Springer]

Forall ?person ?book (

?person[ex:authorOf -> ?book :- ?book [ex:hasAuthor -> ?person]]

)

subject [ property -> object ]

RIF-CORE Dialect



73

•Another RIF Example:

Document(

Prefix(dbp <http://dbpedia.org/property/>)

Prefix(my <http://mydata.org/resource#>)

Prefix(rdfs <http://www.w3.org/2000/01/rdf-schema#>)

Group ( Forall ?mname ?aname ?movie ?actor

my:actorIn(?aname ?mname) :-

And( ?movie[dbp:starring -> ?actor rdfs:label -> ?mname]

?actor[rdfs:label ?aname]

)

)

)

RIF-CORE Dialect


http://dbpedia.org/property/

http://dbpedia.org/property/

http://mydata.org/resource#

http://mydata.org/resource#

http://www.w3.org/2000/01/rdf-schema#

http://www.w3.org/2000/01/rdf-schema#


74

RIF-CORE XML Syntax

𝜒 = mapping function to map presentation syntax to XML syntax

<Document>

<payload>

<Group>

<sentence>𝜒(regel1)</sentence>

...

<sentence>𝜒(regeln)</sentence>

</Group>

</payload>

</Document>



75

RIF-CORE XML Syntax

RIF presentation Syntax RIF XML Syntax

Forall ?x1...?xn (content)

<Forall>

<declare>𝜒(?x1)</declare)

...

<declare>𝜒(?xn)</declare)

<formula>

𝜒(content)

</formula>

</Forall>

𝜒 = mapping function to map presentation syntax to XML syntax



76

RIF-CORE XML Syntax


head :- body

<Implies>

<if>𝜒(body)</if)

<then>𝜒(head)</then>

</Implies>

And(content1...contentn)

<And> <formula> 𝜒(content1)

</formula> ...<formula> 𝜒(contentn)

</formula> </And>



77

RIF-CORE XML Syntax


predicate(t1...tn)

<Atom>

<op>𝜒(predicate)</op)

<args ordered=“yes“>

𝜒(t1)

...

𝜒(tn)

</args>

</Atom>



78

RIF-CORE XML Syntax


subject(p1-> o1 ... pn-> on)

<Frame>

<object>𝜒(subject)</object)

<slot ordered=“yes“> 𝜒(o1)

𝜒(p1)

</slot> ... <slot ordered=“yes“> 𝜒(on)

𝜒(pn)

</slot></Frame>



79

RIF-CORE XML Syntax


“literal“^^datatype<Const type=“datatype“> literal</Const>

?variablenname

<Var> variablenname</Var>



80




81 3. Knowledge Representation and LogicsThe Languages of the Semantic Web - Part 2

• Excursion: Ontologies in Philosophy and Computer Science

• Recapitulation: Propositional Logic and First Order Logic

• Description Logics

• RDF(S) Semantics• OWL and OWL-Semantics• OWL 2

• Rules & The Semantic Web




Next Lecture:

82

Ontolo

gical

Engine

ering



83

• P. Hitzler, S. Roschke, Y. Sure: Semantic Web Grundlagen, Springer, 2007.

• P. Hitzler, M. Krötzsch, S. Rudolph:Foundations of Semantic Web Technologies,CRC Press, 2009.

Bibliography

3. Knowledge Representation & Logic3.7 Rules & the Semantic Web


http://www.amazon.de/gp/product/3540339930/ref=as_li_ss_tl?ie=UTF8&tag=moresemantic-21&linkCode=as2&camp=1638&creative=19454&creativeASIN=3540339930

http://www.amazon.de/gp/product/3540339930/ref=as_li_ss_tl?ie=UTF8&tag=moresemantic-21&linkCode=as2&camp=1638&creative=19454&creativeASIN=3540339930

http://www.amazon.de/gp/product/142009050X/ref=as_li_ss_tl?ie=UTF8&tag=moresemantic-21&linkCode=as2&camp=1638&creative=19454&creativeASIN=142009050X

http://www.amazon.de/gp/product/142009050X/ref=as_li_ss_tl?ie=UTF8&tag=moresemantic-21&linkCode=as2&camp=1638&creative=19454&creativeASIN=142009050X


84

□Bloghttp://semweb2013.blogspot.com/

□Webseitehttp://www.hpi.uni-potsdam.de/studium/lehrangebot/itse/veranstaltung/semantic_web_technologien-3.html

□bibsonomy - Bookmarkshttp://www.bibsonomy.org/user/lysander07/swt1213_11

3. Knowledge Representation & Logic3.7 Rules & The Semantic Web




http://www.hpi.uni-potsdam.de/studium/lehrangebot/itse/veranstaltung/semantic_web_technologien-3.html






http://www.bibsonomy.org/user/lysander07/swt1213_11




(11) semantic web technologies - rules

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