Introduction of Knowledge Graphs

Introduction to Knowledge Graphs
Jeff Z. Pan
School of Informatics, University of Edinburgh
Slides available online: https://www.slideshare.net/jeffpan_sw/introduction-of-
knowledge-graphs
Copyright © 2021 Jeff Z. Pan

Outline
We will cover:
• Foundation of Knowledge Graph
• What is Knowledge Graph
• Applications
• Standards: RDF, OWL, SPARQL
• Some key research topics
• Knowledge Graph Construction
• Knowledge Graph Reasoning
• Knowledge Graph Querying, etc
2

• Term coined by Google
• Knowledge Graph (KG): KB of inter-
connected entities defined by a schema
• Three levels of knowledge
• Entity
• Triple (unit of a multi-relational graph)
• Schema (defining the vocabulary)
3
Knowledge Graph
[Photo: https://www.w3.org/TR/rdf11-primer/ ]

• Key benefits
• Find the right thing
• Get the best summary
• Go deeper and broader
Knowledge Graph @ Google
[ Introducing the Knowledge Graph: things, not strings (Amit Singhal)]
4
Taj Mahal
Matt Groening
Marie Curie

• Knowledge Graph for Alexa
• Billions of entities
• Combining heterogeneous knowledge sources
• provide answers to customer queries
Knowledge Graph @ Amazon’s Alexa
[How Alexa keeps getting smarter (Amazon Staff)]
5

Knowledge Graph @ Alibaba’s Search &
Recommendation Engines
[Learn How a Knowledge Graph Can Improve Your Online Shopping Experience (Zhu Muhua et al.)]
• Key benefits
• Structured data
• Detecting noise in data
• Connected data
• Enable deep data cognition
6

Knowledge Graph @ MS’ Office 365
[Beyond Office 365 – knowledge graphs, Microsoft Graph & AI! (Landqvist and Molnar)]
• Key benefits
• Enterprise KG provides
connected data supporting
people at work
• Personalised search
7

• Question: Is Knowledge Graph invented by Google?
• Answer: No, there has been a long tradition on research
graph form of knowledge
8
Origin of Knowledge Graph
8

Semantic Networks
• Proposed by Richens and
Quillian (independently, 1950s-
60s) to analysis the meaning of
words in sentences
• memory like structure to store
and access knowledge by
machines
• Basic notations:
• Nodes: to represent objects,
concepts, or situations
• Arcs: to represent relationships
9

Pros/Cons of Semantic Networks
• Easy to follow hierarchy
• Easy to trace association
• Flexible
• No well defined syntax
• No formal semantics
• Not expressive enough to define meaning of
labels
• Inefficient
• Many were later addressed by KL-ONE
languages, later known as Description Logics
(underpinning of the W3C OWL standard)
10

Knowledge Graph: Going Beyond Semantic Network
• Resource Description Framework (RDF, W3C standard
for Knowledge Graph)
• with formal syntax, such as meta-properties like rdf:type
and rdfs:subClassOf
• with formal semantics
• NOT able to define classes though (that’s why OWL is
needed)
• Large open KGs: Dbpedia, Yago, Freebase (2006)
• data sub-graph
• [dbr:Barack_Obama rdf:type dbo:President .]
• [dbr:Barack_Obama dbo:birthPlace dbr:Hawaii .]
• [dbr:Barack_Obama dbo:spouse dbr:Michelle_Obama .]
• Schema sub-graph
• dbo:President ⊑ dbo:Politician
• dbo:spouse ⊑ dbo:spouse－ (symmetricObjectProperty in
OWL)
11

Knowledge Graph: Going Beyond Semantic Network
• Key KG Standards:
• KG standard: RDF
• KG schema standard: OWL, based on Description
Logics (DL)
• KG query language standard: SPARQL
• An example knowledge graph in DL:
• ABox (data): tom:Koala, (tom,tim):friend,(tom,e1):eat
• TBox (schema / ontology): Koala ⊑ ∀eat.Plant
• This KB infers that e1:Plant
• Expressiveness: mainly based on TBox
12
tom
e1
Koala
eat
Plant
tim
friend
12

¡ Infer implicit knowledge from explicit knowledge
13
Reasoning
13

Outline
We will cover:
• Applications
14

DBpedia Knowledge Graph: Construction
15
• Mapping Wikipedia template
elements to elements in DBPedia
elements
• Mappings are created in a
community-driven process
• Example: suppose we consider
some wikipedia pages about
actors
• {{TemplateMapping
• | mapToClass = Actor
• | mappings =
• {{ PropertyMapping | templateProperty =
name | ontologyProperty = foaf:name }}
• {{ PropertyMapping | templateProperty =
birth_place | ontologyProperty = birthPlace
}} }}
15

• Exmaple (continued)
• dbpedia:Vince_Vaughn rdf:type
dbpedia-owl:Actor .
• dbpedia:Vince_Vaughn foaf:name
"Vince Vaughn"@en .
• dbpedia:Vince_Vaughn dbpedia-
owl:birthPlace dbpedia:Minneapolis .
DBpedia Knowledge Graph: Construction
16

CURIOS: Constructing KG via CMS
• A page template contains
• a page title
• a set of fields, for displaying literal
value
• a set of relations, i.e. links to other
pages
• Mapping between CMS entities
and ontology entities
• template ó (browsing) class
• field ó datatype properties
• relation ó object properties
[Reasoning Driven Configuration of Linked Data Content Management Systems (Taylor et al.)]
17

Consistency Checking for Schema Updates
Domain ontology
LDCMS configuration (in php)
18
[Reasoning Driven Configuration of Linked Data Content Management Systems (Taylor et al.)]

Knowledge Graph Construction from (Web) Tables
StockTicker Name GICS Sector
AMZN Amazon …
GOOG Alphabet …
Basic_Info
Stock URL CEO Name Country
AMZN www.amazon.com Jeff Bezos USA
Background_Info
Ticker Date Income ($) Liabilities
AMZN 06/01/2018 177.86 billion ...
Finance_Result
Foreign Key
• (Web) Table understanding
• Extraction of Web tables: HTML tables, attribute-value pairs (such as info box),
entity lists
• Alignment with KG schema
• Column type prediction
• Table enhancement
Basic_Info
Background_Info
background_info
name
ceo_name
Finance_Result
finance_result
xsd:int
income
xsd:string
xsd:string
[Credit: J Chen]
[Ten Years of Web Tables (Cafarella et al.)]
19

NELL: Never Ending Language Learner
20
• Goals
• Extract information from Web texts to
construct KB
• Learn to read better than before
• Inputs
• schema with 800 types and relations
• 10 - 20 seed examples for each
• Output: continuously growing KB
• Key methods
• Coupled Pattern Learner(CPL)
• Coupled SEAL(CSEAL)
• Coupled Morphological Classifier(CMC)
• Rule Learner(RL)
[Toward an Architecture for Never-Ending Language Learning (Carlson et al.)]
20

Open vs Closed Domain KG Construction
21
• Two types of knowledge graphs
• Closed domain knowledge graphs: with closed vocabulary, such as DBpedia and NELL
• Open domain knowledge graphs: with open vocabulary, such as the old fashioned
semantic networks
• Question: if we know Google bought YouTube, how could we make use of
such knowledge in NL form to answer questions like “Who owns YouTube?”
• Entailment graphs are needed for supporting the textual entailment
: company-1 buy company-2 |= company-1 own company-2
• These are meaning postulates, such as (buy sub-relation own)
• From Description Logic’s perspective, they are schema (rdfs:subPropertyOf) axioms
• Two major approaches
• Unsupervised methods: using machine reading (covering 100K relations)
• Supervised methods: using pre-trained language models (such as RoBERTa)
[Building and Interrogating Knowledge Graphs in Natural Language (Mark Steedman)]
21

Outline
We will cover:
• Applications
22

OWL Profiles and Reasoning
• OWL 2 has three tractable (with low
computational complexity ) profiles
• OWL 2 EL: schema reasoning, instance
reasoning and query answering
• Potentially huge TBox
• OWL 2 QL: query answering
• OWL 2 RL: the “rule fragment” of OWL 2
• Unions of any of the two profiles are
no longer tractable
23

EL (the core of OWL 2 EL)
• EL Class Description
• existential restriction: $r.C
• conjunction: C ⊓ D
• the top class: ⊤
• not including: value restriction "r.C, disjunction C ⊔ D, the
bottom class ^
• EL Axioms
• GCI: C ⊑ D
• Normal forms for EL
• A ⊑ B
• A1 ⊓ A2 ⊑ B
• A ⊑ $r.B
• $r.A ⊑ B
• where A, A1, A2, B are either named class in Sig(T) or the top
class ⊤
24

EL Reasoning: Normalisation
• Input axiom
• $r.A ⊓ $r.$s.A ⊑ A ⊓ B
• Normalisation
1. $r.A ⊓ $r.$s.A ⊑A0, A0 ⊑ A ⊓ B (NF0)
2. $r.A ⊑ A1, A1 ⊓ $r.$s.A ⊑ A0 (NF1l)
3. $r.$s.A ⊑ A2, A1 ⊓ A2 ⊑ A0 (NF1r)
4. $s.A ⊑ A3, $r.A3 ⊑ A2 (NF2)
5. A0 ⊑ A, A0 ⊑ B (NF4)
[credit: F Baader]
25

EL Reasoning: Subsumption Checking
1. Extend the KB with {A’ ⊑ A ⊓ C, $r.B ⊑ B’}, which is normalised as {A’ ⊑ A, A’ ⊑ C, $r.B ⊑ B’} (NF4)
2. A ⊑A, B ⊑B, A’ ⊑A’, B’ ⊑B’, B1 ⊑B1, B2 ⊑B2, C ⊑ C (CR1)
3. A ⊑ ⊤, A’ ⊑ ⊤ B1 ⊑ ⊤, B2 ⊑ ⊤, C ⊑ ⊤, B ⊑ ⊤, B’ ⊑ ⊤ (CR2)
4. A ⊑ ⊤, ⊤ ⊑ B => A ⊑ B (CR3)
5. B1 ⊑ ⊤, ⊤ ⊑ B => B1 ⊑ B (CR3)
6. B2 ⊑ ⊤, ⊤ ⊑ B => B2 ⊑ B (CR3)
7. C ⊑ ⊤, ⊤ ⊑ B => C ⊑ B (CR3)
8. A ⊑ $r.A, A ⊑ B, $r.B ⊑ B1 => A ⊑ B1 (CR5)
9. A ⊑ $r.A, A ⊑ B, $r.B ⊑ B’ => A ⊑ B’ (CR5)
10. A’ ⊑A, A ⊑B’ =>A’ ⊑B’ (CR3)
11. Since A’ ⊑B’ holds, we have A ⊓ C ⊑ $r.B
Question: Check if A ⊓ C ⊑ $r.B holds
[credit: F Baader] 26

27
Design of OWL 2: Approximate Reasoning
27

• Reasoning Task: TBox classification
• Step 1: Represent non-OWL2-EL concepts with
fresh named concepts
• K ⊑ ∀eat.P is replaced by K ⊑ X1, X1 ≡ ∀eat.P
• Step 2: Maintain semantic relations for these
named concepts
• complementary relations
• cardinality relations
• Step 3: Additional tractable completion Rules (on top of
the EL ones), e.g.
• Handling complement
• E.g. P ⊑ V => ¬V ⊑ ¬P
ALL
eat P
K
V
ALL
H Some
eat nP
K
nV
Some H
P V
X1 X2
28
• K ⊑ ∀eat.P, P ⊑ V, ∀eat.V ⊑ H
Approximate Reasoning: OWL 2 DL => OWL 2 EL
[Tractable approximate deduction for OWL (Pan et al.)]
28

Approximate Reasoning: OWL 2 DL => OWL 2 EL
• The above algorithm is for schema reasoning
• Data+Schema reasoning requires further optimisation
(due to the large number of unnecessary negated
nominals)
Ontology Reasoner Evaluation
(ORE 2014):
• A competition for sound and
complete reasoners
• TrOWL (3rd place in OWL 2
DL ABox materialisation) is
an approximate reasoner
• Even getting 99.99% of the
reasoning results is not
counted
• only 100% counted
29
29
[Tractable approximate deduction for OWL (Pan et al.)]

Knowledge Graph: Going Beyond Description Logic KBs
• Observation: Approximate reasoning (mode 1) so far tend to
replace complex schema with (faithful) simpler schema
• Questions:
• Q1: What happens if we do not have schema at all, how do
we define approximate reasoning (mode 2) to deal with the
knowledge incompleteness issue?
• Q2: Would it make sense to apply these two kinds of
approximate reasoning (modes 1 and 2) when schema is
available?
30
30

Knowledge Graph Embeddings
• Embedding entities and relationships of
multi-relational data in low-dimensional
vector spaces
• Use the embedding model for tasks like
link prediction, or rule extraction
• KGE model is fully expressive
• if given any ground truth,
• there exists an assignment of values
to the embeddings of the entities and
relations that
• accurately separates the correct
triples from incorrect ones
• TransE and DistMult are not fully
expressive but ComplEx and SimplE are
• Bilinear models (inc. ComplEx and
SimplE) cannot strictly represent
relation subsumption rules
[image credit: ampligraph.org]
31
[see also From Knowledge Graph Embedding to Ontology Embedding? An Analysisof the Compatibility
between Vector Space Representations and Rules (Gutierrez-Basulto and Schockaert)]

Fake News Detection with Knowledge Graph
• Fake news detection based on KG: given a set of news triples g and a
background knowledge graph G
• true if g U G is consistent
• fake otherwise
● The embedding model M of entities and relations in G obtained by
minimising a global loss function involving all entities and relations
● Bias based on model M can be used for approximate reasoning
32
FAKE "Hillary Clinton and her State department were actively arming Islamic
jihadists, which includes ISIS…"
(Hillary Clinton, arm, Islamic jihadists)
TRUE “Hillary Clinton-led State Department had approved weapon shipments to
Libya during the intervention in 2011, and that those weapons had later ended up
in the hands of jihadists”
(Hillary Clinton, have approved weapon shipments to, Libya)
(https://www.cnbc.com/2016/12/30/read-all-about-it-the-biggest-fake-news-stories-of-2016.html)
[Content based Fake News Detection Using Knowledge Graphs (Pan et al.)]
32

Evaluation of KG Embeddings
• Partial gold standard: some entities and relations are selected for manual
annotation
• Pros: usually good quality
• Cons: Costly and only applicable to those with simple schema (if schema is used)
• Silver standard: the KG is assumed to be perfect and used as a test dataset,
widely used for KG completion
• Pros: not expensive to get
• Cons: KGs are not perfect and thus quality is not as good as partial gold standard
• Experimental results suggest KGE based KG completion methods are not
impressive when schema aware correctness is considered, despite good
performance reported in sliver standard based evaluations
Silver S TransE STransE DistMult ComplEx
WN18
Hit@1
8.9% - 72.8% 93.6%
WN18
Hit@10
93.4% 93.4% 93.6% 94.7%
FB15k
Hit@1
23.1% - 54.6% 59.9%
FB15k
Hit@10
64.1% 79.7% 82.4% 84.0%
[Pattern-Based Reasoning to Investigate the Correctness of Knowledge Graphs (Wiharja et al.)]
33

Iterative Schema Aware KG Completion
• Hypothesis: Different kinds of KG completion methods might complement each other
[Wiharja et al., 2021]
• Idea: combine three types of triple producers (Embedding based, Rule learning based
and Materialisation based) with approximate consistency checking
• To run in an iterative manner, one after another until stopping condition triggered
• The notion of completeness is replaced by the notion of coverage
• Findings:
• Combinations work well if start with R- or M- based producers
• Different methods completement each other
• Can produce 20-40 times of schema correct triples
[Schema aware iterative Knowledge Graph completion (Wiharja et al.)]
34

Outline
We will cover:
• Applications
35

Knowledge Graph Querying with SPARQL
• SPARQL is the standard query language of and standard protocol for querying KGs
•
•
ABOX
G
TBOX
9hasMother v Mother
9hasMother v Child
9hasP arent v P arent
9hasP arent v Child
Mother v P arent
hasMother v hasP arent
...
S P O
:Mother rdfs:subClassOf :Parent
:hasMother rdfs:subPropertyOf :hasParent
:hasMother rdfs:range :Mother
:hasParent rdfs:domain :Child
:hasParent rdfs:range :Parent
...
S P O
:marie :hasMother :maria_t
:marie :hasParent :maria_t
SELECT ?X ?P ?S WHERE {
?X :hasParent ?P . ?X :hasSpouse ?S .
?P a RulerOfAustria . ?S a :RulerOfFrance .
} ABOX-materialized
S P O
:marie :hasMother :maria_t
:marie a :Child
:marie :hasParent :maria_t
:maria_t a :Mother
:maria_t a :Parent
[credit: A Polleres]
36

• Some key challenges:
• User queries are in NL, thus semantic
parsing is needed
• How to combine embedding with logical
operators for answering complex queries
17/08/2021
Question Answering over Knowledge Graphs
38

Knowledge Graphs as Bridge between Human and AI Systems
• Human intelligence (e.g. to understand image)
• Perception: Dogs, happy ,letters, numbers, red
• Knowledge: Dog year, Spring Festival, red for
celebration
• Reasoning: 2018 is a dog year, best wish for
Spring Festival
• How knowledge graphs help:
• Richer Input for Machine Learning
• Explain Machine Learning
• Meta Learning: Guide learning with
knowledge
Question : What is this device used for?
Question : Which food seen here has a
country for the first part of its name?
Question : What sport is this? Question : Is this television broken or working?
39

• Knowledge Graph (or Big Knowledge), Big Data and Deep Learning
are key drivers of AI
• unique technology for both reasoning and learning
• reduce the need of large, labelled datasets, facilitate transfer learning and
explain-ability
• encode domain, task and application knowledge that would be costly to
learning from data alone
• facilitate the upgrade of AI from perceptual intelligence to cognitive
intelligence
KGs have become the epicentre of the AI hyperbole
[Photo : https://www.w3.org/TR/rdf11-primer/ ] 40

Thank you!
Jeff Z. Pan
@jpansw
http://knowledge-representation.org/j.z.pan/

Introduction of Knowledge Graphs

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