Ontology Reasoning for the Semantic Web and Its Application to Knowledge Graph
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Transcript of Ontology Reasoning for the Semantic Web and Its Application to Knowledge Graph
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Guilin Qi
Knowledge Science and Engineering (KSE) Lab
Southeast University
Ontology Reasoning for the Semantic Web and Its Application to
Knowledge Graph
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Plan of the Talk Part I: Introduction of Ontology Languages for the
Semantic WebPart II: Application of Ontology Reasoning Part III: Reasoning with Large Imprecise Knowledge on
the Semantic Web
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Ontology
Different definitions: philosophy, AI,…
Definition in Semantic Web:
An ontology is an explicit specification of a conceptualization
Gruber, 1993
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What is an Ontology?
A model of (some aspect of) the worldIntroduces vocabulary
relevant to domain, e.g.:Anatomy
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A model of (some aspect of) the worldIntroduces vocabulary
relevant to domainSpecifies meaning (semantics)
of terms Heart is a muscular organ that is part of the circulatory system
What is an Ontology?
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Ontologies The core of an ontology is usually a taxonomy:
classes of things, arranged in a hierarchy
Human
MaleHuman [every MaleHuman is a Human]
Son [every Son is a MaleHuman]
Father [every Father is a Son]
FemaleHuman
Daughter
Aunt
Niece
Mother
GrandMother
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RDF (Resource Description Framework)Specifies relationship between data
RDFS(Resource Description Framework Schema)Specifies relationship between schema
OWL (Web Ontology Language)Specifies more complex relationship
between schema based on description logics
Ontology languages
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RDF idea
Use (directed) graphs as data model
Subject Predicate Object
“Resource Description Framework”
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RDF Schema (RDFS)
part of the W3C Recommendation RDFfor schema/terminological knowledgeuses RDF vocabulary with pre-defined
semantics
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Classes and Instances
Classes stand for sets of things.In RDF: Sets of URIs.
book:uri is a member of the class ex:Textbook
a URI can belong to several classes
classes can be arranged in hierarchies:each textbook is a book
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Implicit knowledge if an RDFS document contains
and
then
is implicitly also the case: it’s a logical consequence. (We can also say it is deduced (deduction) or inferred (inference)
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Implicit knowledge – another example
From
the following is a logical consequence:
I.e. rdfs:subClassOf is transitive.
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Using implicit knowledge
• Ontology (Knowledge Base)• e.g. RDF or OWL
• Reasoner (produces implicit knowledge)
• Completed (materialized) knowledge base
• Application
Used like a
databaseoffline
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The same as graph
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OWL – Web Ontology Language
<owl:Class rdf:about="project"> <rdfs:subClassOf> <owl:Class> <owl:unionOf rdf:paseType="Collection"> <owl:Class rdf:about="internal"/> <owl:Class rdf:about="external"/> </owl:unionOf> </owl:Class> </rdfs:subClassOf></owl:Class>
Why do we need OWL?
ProjectInternal
External
Is either
or
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OWL 2 Profiles
The OWL 2 spec describes three profiles (fragments, sublanguages) which have polynomial complexity.OWL EL (the description logic EL++)
• Represent medical knolwedge
OWL QL (the description logic DL LiteR)• Targeted to data integration
OWL RL (the description logic DLP)• inspired by intersecting OWL with Datalog• implemented e.g. in Oracle 11g
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Description LogicsDescription logics
Are (mostly) decidable fragments of first-order predicate logic
Provide logical underpinning of W3C standard OWL
Building blocksConcepts (unary predicates/formulae with
one free variable)o E.g., Person, Lawer ⊔ Doctor
Roles (binary predicates/formulae with two free variables)
o E.g., hasChildIndividuals (constants)
o E.g., John, Mary
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Description Logics (Syntax)Description languages
Defining complex concepts: sets of individuals
Defining complex roles: binary relations on individuals
Complex concepts are built byAtomic concepts: Tissue, HeartConstructors: Tissue⊓part-of.Heart
Complex roles are built byAtomic roles: part-of, has-locationConstructors: HasFatherˉ
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Heart is a muscular organ that is part of the circulatory system
Heart⊑MuscularOrgan⊓part-of.CirculatorySystem
Example
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Description Logics (Semantics)
Interpretation: I=(I,.I) Domain: I
Assignment function .I
individual names, class names and property names...
• .I
• aI • CI
• RI
•Δ• II • IC
• IR
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Description Logics (Cont.)
Interpretation: I=(I,.I)
Construct Syntax Example Semantics
Atomic concept A Heart AI I
Atomic role R part-of RI I I
Negation C Heart I \ CI
Conjunction C ⊓ D Lawyer⊓Doctor CI∩DI
Value restriction R.C part-of.Wood {a|b. (a,b) RI, b CI}
… … … …
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Description Logics (Ontology)
TBox T: defining terminology of application domain Inclusion assertion on concept :C ⊑ D
Inclusion assertion on roles: R ⊑ S
ABox A: stating facts about a specific “world” membership assertion: C(a) or R(a,b)
Pericardium ⊑ Tissue ⊓ part-of.Heart
Part-of ⊑ has-location
HappyMan(Bob), HasChild(Bob, Mary)
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Given an interpretation ISemantics of TBox axioms
I ⊨ C ⊑ D if CI DI
I ⊨ R ⊑ S if RI SI
Semantics of ABox assertionsI ⊨ C(a) if aI CI I ⊨ R(a,b) if (aI,bI) RI
Description Logics(Semantics)
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Model of an ontology O=<T, A>I is a model of O if it satisfies all axioms
in T and all assertions in AConcept satisfiability
Concept C is satisfiable in O if CI is nonempty for some model I of O
Ontology Entailment:O ⊨ iff I⊨ for all models I of O
Description Logics(Semantics)
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RDF is a flexible data model for Semantic Web
RDF Schema provides simple inference capability
OWL allows more expressive representation of knowledge but is hard to scale to Web data
Semantic technologies have been adopted by major companies such as Google, Yahoo and Facebook
Conclusion
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Reasoning Task: Classification
DiseaseHeartDiseaseMiocardial_Infarction⊑⊑
⊑
心肌梗塞 心脏病 疾病
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Example
Endocardium ⊑ Tissue cont-in.HeartWall ⊓ ∃ ⊓ ∃ cont-in.HeartValve
HeartWall ⊑ BodyWall part-of.Heart⊓∃
HeartValve ⊑ BodyValve part-of.Heart⊓∃
Endocarditis ⊑ Inflammation⊓ ∃ has-loc.Endocardium
Inflammation ⊑ Disease act-on.Tissue⊓∃
HeartDisease has-⊓∃loc.HeartValve
⊑ CriticalDisease
HeartDisease ⊑ Disease has-loc.Heart⊓∃
Endocarditis⊑HeartDisease
Endocarditis⊑CriticalDisease
Role of Classificationa) Enrich ontologyb) Query writtingc) Check satisfiability of KB
Reasoning Task: Classification
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Endocarditis⊑HeartDisease
Meningitis⊑HeartDisease
HeartDisease Disease⊑ ⊓ has-loc.Heart∃
Meningitis⊑ has-loc.Heart∃
Endocarditis ⊑ has-loc.Heart∃
Classification
Justification
Justification
Through classification, we have“Meningitis⊑ has-loc.Heart”∃ After finding justification, we found“Meningitis⊑HeartDisease” is
wrong
Repair KB using justifications
Reasoning Task: Finding Justification
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Suppose we have the following query “ 心脏病患者有哪些?”
This query can be used for medical statistics
Reasoning Task: Query Rewritting
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王红
心内膜炎
心脏病
冠心病心肌梗塞
李明… …
We know“ 王红” is 心内膜炎患者, we should include her as 心脏病患者
List(X) :- Endocarditis(X) ⋁ Miocardial_Infarction(X) ⋁ Coronary_disease(X).
Reasoning Task: Query Rewritting
Suppose we have the following ontology
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Inconsistency may occur during ontology construction One source of inconsistency comes from disjoint axioms
心脏病
脑科疾病
心内膜炎
• ⊑
• ⊑
!
Reasoning Task: Checking Inconsistency
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Mining disjoint Concepts : Association rule mining, Inductive logic programming
In Zhishi.me, hudong: 大豆食心虫 not only belongs to animal but also contains in plant
In Zhishi.me, there are 50 common instances between animal and plant
• 植物
• 花
• 玫瑰
• 蔷薇
• 农作物
• 玉米
• 小麦
• 动物• 哺乳动物• 老
虎• 狮
子
RDF Data
Mining Axioms 植物 disjoint 动物
花 disjoint 农作物植物 disjoint 哺乳动物
……
Disjointness Axioms
Reasoning Task: Checking Inconsistency
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In Dbpedia, we find 42153 disjointness axioms by mining axioms algorithm
Reasoning Task: Checking Inconsistency
Number of Common individuals Pairs of disjoint classes
[1,10) 317
[10,100] 27
[100,1000) 7
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Detecting noisy type assertion
Experiment result of detecting noisy type assertion in DBpedia
Reasoning Task: Checking Inconsistency
Disjoint concepts with common instance
Classifier
Place(pope) errorPerson(Dibra ) error
…Place(Xbox_Music) and
Person(Xbox_Music) error
Noisy type assertion detection
< pope Place Person>< Dibra Place Person >
…< Xbox_Music Place Person >
Classifier Precision Recall F1-Measure
J48 93.6% 93.6% 93.6%
J48(boost) 95.6% 95.6% 95.6%
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Reasoning with Large Scale Imprecise Knowledge on the Semantic Web
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Motivation More and more semantic data are published and
linkedSemantic data are inherently imprecise
Data extraction may result in imprecisionData linking may result in imprecision Reasoning with large imprecise semantic data
Schema of the data may also be imprecise Schema inductionOntology enrichment Reasoning with large imprecise ontologies
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•
Background: Fuzzy pD*
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•
Background: Fuzzy pD*
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MapReduce
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• Mapper1
• Mapper2
Reducer1
(I)
Reducer2
(love)
Reducer3
(you)
Reducer4
(like)
I love you love
I likeyou
<I , 1>
<love , 1>
<you , 1>
<love , 1>
<I , 1>
<like , 1>
<you , 1>
<I , 2>
<love , 2>
<you , 2>
<like , 1>
Example
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Challenges
Ordering the rule applicationsBad orders will generate more non-BDB fuzzy triples
The shortest path calculationSome rules essentially calculates the all-pair shortest paths
Sameas rulesCanonical representation technique is not applicable to handle the semantics of vague sameas triples
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Ordering the rule applications
Control flow of the reasoning algorithms
•
•
New fuzzy triples derived?
New fuzzy triples derived?
New fuzzy triples derived?
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Shortest path calculation
•
•
•
•
•
•
•
•
•
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Sameas rules
•
Vague sameas triples
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Dataset Weighted DBPedia core ontology wpdLUBM 1000, 2000, 4000, 8000
Cluster 25 machine with at most 75 mapper/reducer slots
Setting
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#units 128 64 32 16 8 4 2
Time(sec.) 122.653 136.861 146.393 170.859 282.802 446.917 822.269
Speedup 6.70 6.01 5.62 4.81 2.91 1.84 1.00
Dataset: Weighted DBPedia core ontology
Results:
Experiment
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Scalability over number of units
Experiment
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Reasoning on fuzzy-EL+
R2
Classfication rules for fuzzy-EL+
∃performAs.ComplicationHeart_ComplicationMiocardial_Infarction⊑(1.0)⊑(0.2)
⊑(0.2)
心肌梗塞 心脏附近并发症 具有并发症表现的疾病
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Challenges and methods
Transforming rule-applying to an operation on tables The rules are given by operations on sets. It is more straightforward to treat them as operations on tables, in other words, relation algebra
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Handling multi-way join
• •
MapReduce can handle a 2-way join in one job.
Challenges and methods
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Evaluation on Galen
• EL-Galen• 8nodes, 16 units
Concepts Roles GCI RI
47,840 1,892 87,594 1,947
1. 82
3. 32 4. 45
5. 53
10. 63
0.00
2.00
4.00
6.00
8.00
10. 00
12. 00
0 2 4 6 8 10
hour
number of copi es
Scal abi l i t y Test 2
• Scalability test 1: The system’s performance speeds up linearly to the increase of number of units• Scalability test 2: The cost time increases linearly to the number of copies of the input ontology
1. 82 2. 02
2. 80
4. 09
0.000.501.001.502.002.503.003.504.004.50
0.0000 0.2000 0.4000 0.6000
hours
1/ number of uni t s
Scal abi l i t y Test 1
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Evaluation on Snomed-CT
• Snomed-CTConcepts Roles GCI RI
836,612 77 1,438,948 23
• Scalability test : The cost time increases linearly to the number of copies of the Snomed-CT
0.5 1 1.5 2 2.5 3 3.50
5
10
15
20
25
30
the number of copies
hours
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Conclusion and Discussion Ontology reasoning plays an important role for KG
Detecting logical inconsistency and repair knowledge bases (improve the quality of the knowledge)
Extend knowledge bases ( materialization, classification) Query rewritting and extension
Reasoning in KG need meta-reasoning Variety of knowledge: terminological knowledge, rule, probabilistic
knowledge ect. Challenging problems
Current work is mainly based on MapReduce and Hadoop, thus suffers from the problem of efficiency and dynamics
Only lightweight ontology languages, such as RDFS, OWL 2 RL are supported
Reasoning with imprecise knowledge is not well discussed