Chapter 12: Ontologies and Knowledge Representation

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Chapter 12 Ontologies and Knowledge
Representation
PRINCIPLES OF DATA INTEGRATION
ANHAI DOAN ALON HALEVY ZACHARY IVES
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Outline

• Introduction to Knowledge Representation and its
  relevance to data integration
• Description Logics a family of KR languages
• The Semantic Web and its languages

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Knowledge Representation

• Knowledge representation (KR) focuses on more
  expressive languages that database schemata and
  integrity constraints
• Designed for artificial intelligence applications
  (e.g., natural language understanding, planning)
  where complex relationships exist between
  objects.
• KR uses ontologies to represent relationships
  between elements in a knowledge base.
• KR is relevant to data integration because
  relationships between data sources can be
  complex.
• The use of KR in data integration was
  investigated since the early days of the field.

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KR in Data Integration Example
Mediated schema ontology with classes and
relationships
Data sources S1 has comedies and S2 documentaries
S3 movies with at least two awards S4 comedies
with at least one Oscar
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Example Part 1
S1 is relevant to Q1 because Comedy is a subclass
of Movie (by subsumption)
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Example Part 2
S2 is irrelevant to Q2 because Comedy and
Documentary are declared disjoint.
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Example Part 3(a)
S3 is relevant to Q3 because movies with two
awards will definitely satisfy the second
subgoal.
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Example Part 3(b)
S4 is relevant to Q3 because oscar is a
sub-property of award.
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Outline

• Introduction to Knowledge Representation and its
  relevance to data integration
• Description Logics a family of KR languages
• The Semantic Web and its languages

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Description Logics Introduction

• Description Logics are a subset of first-order
  logic
• Only unary predicates (called concepts) and
  binary predicates (called roles, properties).
• Knowledge bases are composed of
• T-box defining the concepts and the roles
• A-box including ground facts about individuals
• Complex concepts are defined by concept
  descriptions
• The expressive power of the language is
  determined by the set of constructors in the
  grammar of concept descriptions
• Complex roles can also be defined via constructors

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T-Boxes

• Can include statements of the form
• A is a base concept and C can be a concept
  description.
• Example grammar for concept descriptions see
  next slide.

(it should really be a square inclusion)
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An example Grammar for Concept Descriptions.
C,D are complex concepts. A is a base concept.
Many other constructors possible union,
existential quantification, equality on role
paths,
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Example Terminology
a1 Italians are people (really. Dont
laugh!) a2 Comedies are movies a3 Comedies are
disjoint from documentaries a4 Movies have at
most one director a5 Award movies are those that
have at least one award a6 Italian hits are
award movies whose director is Italian
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Abox the Ground Facts

• A set of assertions of the form C(a), or R(a,b)
• b is called an R-filler of a.
• C and R can be concept descriptions
• Akin to asserting that a tuple is in a view
  rather than in base relations
• Below, we state that LaStrada is an Italian hit,
  were not given the director or the award it won.

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Semantics of Description Logics

• Semantics are based on interpretations.
• Given a knowledge base ?, the models of ? are the
  interpretations that are consistent ?s T-box and
  A-box.
• Any fact that is true in all models of ? are said
  to be entailed by ?.

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Interpretations Formally

• An interpretation I contains a non-empty domain
  of objects, OI .
• I assigns an object aI in to every constant a in
  the A-box.
• We make the unique names assumption a?b implies
  that aI?bI
• I assigns CI , a subset of OI, to every concept C
  
• I assigns a binary relation RI, a subset of OI x
  OI to every role R.

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Extensions of Complex Expressions
The extensions of concept and role descriptions
are given by the following equations. (S denotes
the cardinality of the set S).
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Conditions on Models

• An interpretation of ? is a model if the
  following conditions hold

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Example Interpretation
Assume an interpretation with the identity
mapping on individuals in the knowledge base and
a few extra elements (Director1, Award1, Actor2,
). The following interpretation is a model
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Example Interpretation

• Notes
• We do not know the director of LaStrada or its
  award.
• Removing LifeIsBeautiful from Comedy would make
  it a non-model.
• Adding another director would also make it a
  non-model.

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Inference in Description Logics

• This is where all the action is coming up with
  efficient algorithms for inference and
  understanding the complexity of the problems.
• Subsumption (only for the T-box)
• A concept C is said to be subsumed by concept D
  w.r.t. a T-box T, if in every model, I, of T,
• Examples

is subsumed by
is subsumed by
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Query answering with DLs

• The simple case instance checking
• Does ? entail C(a) or R(a,b)? i.e., does
  C(a)/R(a,b) hold in every model of ??
• The more general problem is query answering. Find
  the answers to a conjunctive query
• where g1,, gn can be concept and/or role names.

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Semantics of Conjunctive Queries

• Compute the answer to Q in every model of ?
• Any tuple that is in the intersection of the
  answers is entailed by ?.
• This should remind you of the semantics of
  certain answers!
• Lets look at a few examples.

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Query Answering Example 1

• Consider the Q1 over the following A-box
• Applying Q1 directly to the A-box would yield no
  answers (award would not be matched)
• However, ItalianHits(LifeIsBeautiful) implies
  that LifeIsBeautiful won at least one award.
• Hence, LifeIsBeautiful should be in the answer!

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Query Answering Example 2

• Consider Q2
• With the following A-box
• Comedy(LaFunivia), director(LaFunivia,Antonioni),
  Italian(Antonioni)
• Neither conjunctive query will yield an answer
  because we know nothing about awards.
• However, we can reason by cases that the
  following is entailed by Q2.

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End of Example 2

• Ok, we have
• But thats not enough to infer that LaFunivia
  should be in the answer.
• However, we also know that movies have at most
  one director, so
• Hence, LaFunivia is an answer to Q2.

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Comparing DLs to OODB

• Object-oriented databases
• Also focus on unary and binary relations
• OODBs are more focused on modeling the physical
  aspects of objects and their properties
• An object can only belong to a single (most
  specific) class.
• Description logics are about knowledge and
  complex relationships
• Class membership can be inferred
• An individual can belong to multiple classes.

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Comparing DLs to Relational Views

• In principle, concept descriptions are view
  definitions
• Relational views employ selection, projection,
  join, union and apply to more than unary and
  binary relations.
• DLs universal quantification, number
  restrictions, intersection,
• Subsumption query containment
• Universal quantification and number restrictions
  would require negation in conjunctive queries.
  Hence containment would be undecidable
• In DLs you can put facts directly in views
  (i.e., complex concept).

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Outline

• Introduction to Knowledge Representation and its
  relevance to data integration
• Description Logics a family of KR languages
• The Semantic Web and its languages

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The Semantic Web

• Basic idea annotate content on Web pages with
  semantics
• Specify that a web page is about a restaurant,
  where the address appears on the page, and what
  are the menu items.
• On a page with restaurant reviews, mark the
  restaurants with a global identifier so the
  review and restaurant data can be fused.
• Without these annotations, systems need to infer
  this correlations and are often wrong.

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Languages, Languages

• RDF Resource Description Framework
• Language for marking up data
• Triples with a few cool features
• RDF Schema (RDFS) basic schema for RDF documents
• OWL Web Ontology Language. Comes in multiple
  flavors
• Owl-Lite
• Owl-DL, Owl-Full
• All these languages are influenced by KR
  formalisms (some more and some less)

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RDF Basics

• RDF triples are statements about resources
• They are of the form
• (subject, predicate, value)
• Names can get long (because they can be URLs), so
  we often use qnames (qualified names)
• ex instead of http//www.example.org/

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RDF as a Graph
Uniform Resource Identifiers available beyond a
single data set.
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Uniform Resource Identifiers

• In a typical database, identifiers are used only
  internally. They have no meaning outside the
  database.
• RDF uses URIs for subjects, predicates and
  optionally for values
• Hence, multiple data sets can refer to the same
  identifier.
• Key benefit for data integration!
• Note this does not entail standardization!
• Youre free to invent your own, but youre
  encouraged to reuse existing URIs so your data
  meshes well with others

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Blank Nodes
Blank node
You can assign IDs to blank nodes, but they are
internal to a document.
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Reification

• Reification is a way of stating statements about
  statements
• Provenance, uncertainty, date asserted,
• To reify, make the statement itself into a
  resource
• Once reified, you can state its properties

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RDF Schema

• Enables declaring classes, subclass hierarchies,
  membership in a class, and restrictions on
  domains and ranges of classes.
• Important a class can be an instance of another
  class!

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RDFS Declaring Properties

• RDFS you can declare sub-properties, domains and
  ranges of properties.

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OWL Web Ontology Language

• Languages based on description logics but without
  the unique-names assumption
• sameAs and differentFrom specify whether two
  individuals are the same/different.
• OWL-Lite intersection, number restrictions (but
  only with 0 or 1), universal and existential
  quantification on properties.
• OWL-DL union, complement, disjointness, number
  restrictions, enumeration (Sunday, Monday..),
  hasValue (filler for property value), and more.
• OWL-Full OWL-DL reification.

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SparQL Querying RDF

• Language based on matching of triples
• Borrows ideas from conjunctive queries and XQuery

Result
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SparQL The Construct Clause
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Summary of Chapter 12

• Knowledge Representation enables modeling complex
  relationships between classes and objects.
• The languages of the Semantic Web apply these
  ideas to the Web context and with URIs.
• The constant challenge the tradeoff between
  expressive power and computational complexity of
  reasoning
• Question to ponder Can we live with a fast
  reasoning algorithm that misses some derivations
  occasionally?