Grigoris Antoniou

1
Knowledge Representation

• Grigoris Antoniou
• FORTH-ICS, Greece

2
Weeks Objectives

• Get an idea of what Knowledge Representation (KR)
  is about
• Get a taste of the area through a couple of
  concrete languages/systems
• See how KR plays a role in contemporary ICT
  areas Web, pervasive computing
• Get motivated for more?

3
Weeks Outline

1. KR Basics
2. KR on the Web Semantic Web
3. Defeasible Reasoning
4. KR in e-Commerce and Pervasive Computing
5. Summary

4
Part IKnowledge Representation Basics

5
Artificial Intelligence

• The design and study of systems that behave
  intelligently
• Focus on hard problems, often with no, or very
  inefficient full algorithmic solution
• Focus on problems that require reasoning
  (intelligence) and a large amount of knowledge
  about the world
• Critical
• Represent knowledge about the world
• Reason with these representations to obtain
  meaningful answers/solutions

6
Symbolic Knowledge Representation Basic
Assumptions

• Important objects (collections of objects) and
  their relationships are represented explicitly by
  internal symbols
• Symbolic manipulation of internal symbolic
  representations achieves results meaningful in
  the real world.

7
Symbolic Knowledge Representation Basic
Assumptions (2)
Real World
Real World
Map back to real world
Symbolic representation
Symbolic Representation
New conclusions
Manipulation
8
KR Goals

• Find representations that are
• Rich enough to express the important knowledge
  relevant to the problem at hand
• Close to problem at hand compact, natural,
  maintainable
• Amenable to efficient computation

9
Representational Adequacy

• Consider the following facts
• Most children believe in Santa.
• John will have to finish his assignment before he
  can start working on his project.
• Can all be represented as a string! But hard then
  to manipulate and draw conclusions.
• How do we represent these formally in a way that
  can be manipulated in a computer program?

10
Well-defined Syntax Semantics

• Precise syntax what can be expressed in the
  language
• Formal language, unlike natural language
• Prerequisite for precise manipulation through
  computation
• Precise semantics formal meaning of expression

11
Naturalness of Expression

• Also helpful if our representation scheme is
  quite intuitive and natural for human readers!
• Could represent the fact that my car is red using
  the notation
• xyzzy ! Zing
• where xyzzy refers to redness, Zing refers to by
  car, and ! used in some way to assign properties.
  
• But this wouldnt be very helpful...

12
Inferential Adequacy

• Representing knowledge not very interesting
  unless you can use it to make inferences
• Draw new conclusions from existing facts.
• If its raining John never goes out Its
  raining today so...
• Come up with solutions to complex problems, using
  the represented knowledge.
• Inferential adequacy refers to how easy it is to
  draw inferences using represented knowledge.

13
Inferential Efficiency

• You may be able, in principle, to make complex
  deductions, but it may be just too inefficient.
• The basic tradeoff of all KR
• Generally the more complex the possible
  deductions, the less efficient will be the
  reasoning process (in the worst case).
• The eternal quest of KR
• Need representation and inference system
  sufficient for the task, without being hopelessly
  inefficient.

14
Inferential Adequacy (2)

• Representing everything as natural language
  strings has good representational adequacy and
  naturalness, but very poor inferential adequacy.

15
Requirements for KR Languages Summary

• Representational Adequacy
• Clear syntax/semantics
• Inferential adequacy
• Inferential efficiency
• Naturalness
• In practice no one language is perfect, and
  different languages are suitable for different
  problems.

16
Why Reasoning?

• Example
• Patient x is allergic to medication m
• Anybody allergic to medication m is also
  allergic to medication n
• Is it ok to prescribe n for x?
• Reasoning uncovers implicit knowledge not
  represented explicitly
• Beyond database systems technology

17
Syntactic vs Semantic Reasoning

• Semantic reasoning
• Sentences P1,, Pn entail sentence P iff the
  truth of P is implicit in the truth of P1, , Pn
• Or if the world satisfies P1,, Pn then it must
  also satisfy P
• Reasoning usually done by humans
• Syntactic reasoning
• Sentences P1,, Pn infer sentence P iff there is
  a syntactic manipulation of P1,,Pn that results
  in P
• Reasoning done by humans and machines

18
Reasoning Soundness and Completeness

• Sound (syntactic) reasoning
• If P is inferred by P1,, Pn then it is also
  entailed semantically
• Only semantically valid conclusions are drawn
• Complete (syntactic) reasoning
• If P is entailed semantically by P1,, Pn then it
  can also be inferred
• All semantically valid conclusions can be drawn
• Usually interested in sound and complete
  reasoning
• But sometimes we have to give up one for the sake
  of efficiency (usually completeness)

19
Main KR Approaches

• Logic-Based
• Focus on clean, mathematical semantics
  declarativity
• Explainability
• Frames / Semantic Networks / Objects
• Focus on structure of objects
• Rule-based systems
• Focus on efficiency
• A ? B in logic and rule-based systems

20
The Landscape of KR

• Predicate logic (first order logic) and its
  sublanguages
• Logic programming, (pure) Prolog
• Description logics
• Web ontology languages
• Predicate logic (first order logic) extensions
• Modal and epistemic logics
• Temporal logics
• Spatial logics
• Inconsistency-tolerant logics
• Paraconsistency
• Nonmonotonic reasoning

21
The Landscape of KR (2)

• Representing vagueness
• Probabilistic logics
• Bayesian networks
• Markov chains
• Planning and reasoning about action
• Extensions of logic to reason about the
  prerequisites and effects of actions

22
Part IIKR on the Web Semantic Web

23
The Semantic Web

• The Semantic Web vision
• RDF
• OWL
• Rules

24
Todays Web

• Most of todays Web content is suitable for human
  consumption
• Even Web content that is generated automatically
  from databases is usually presented without the
  original structural information found in
  databases
• Typical Web uses today peoples
• seeking and making use of information, searching
  for and getting in touch with other people,
  reviewing catalogs of online stores and ordering
  products by filling out forms

25
Keyword-Based Search Engines

• Current Web activities are not particularly well
  supported by software tools
• Except for keyword-based search engines (e.g.
  Google, AltaVista, Yahoo)
• The Web would not have been the huge success it
  was, were it not for search engines

26
Problems of Keyword-Based Search Engines

• High recall, low precision.
• Low or no recall
• Results are highly sensitive to vocabulary
• Results are single Web pages
• Human involvement is necessary to interpret and
  combine results
• Results of Web searches are not readily
  accessible by other software tools

27
On HTML

• Web content is currently formatted for human
  readers rather than programs
• HTML is the predominant language in which Web
  pages are written (directly or using tools)
• Vocabulary describes presentation

28
An HTML Example

• lth1gtAgilitas Physiotherapy Centrelt/h1gt
• Welcome to the home page of the Agilitas
  Physiotherapy Centre. Do
• you feel pain? Have you had an injury? Let our
  staff Lisa Davenport,
• Kelly Townsend (our lovely secretary) and Steve
  Matthews take care
• of your body and soul.
• lth2gtConsultation hourslt/h2gt
• Mon 11am - 7pmltbrgt
• Tue 11am - 7pmltbrgt
• Wed 3pm - 7pmltbrgt
• Thu 11am - 7pmltbrgt
• Fri 11am - 3pmltpgt
• But note that we do not offer consultation during
  the weeks of the
• lta href". . ."gtState Of Originlt/agt games.

29
Problems with HTML

• Humans have no problem with this
• Machines (software agents) do
• How distinguish therapists from the secretary,
• How determine exact consultation hours
• They would have to follow the link to the State
  Of Origin games to find when they take place.

30
A Better Representation

• ltcompanygt
• lttreatmentOfferedgtPhysiotherapylt/treatmentOffered
  gt
• ltcompanyNamegtAgilitas Physiotherapy
  Centrelt/companyNamegt
• ltstaffgt
• lttherapistgtLisa Davenportlt/therapistgt
• lttherapistgtSteve Matthewslt/therapistgt
• ltsecretarygtKelly Townsendlt/secretarygt
• lt/staffgt
• lt/companygt

31
Semantic Web Technologies

• Explicit Metadata
• Ontologies
• Logic and Inference
• Agents

32
Explicit Metadata

• This representation is far more easily
  processable by machines
• Metadata data about data
• Metadata capture part of the meaning of data
• Semantic Web does not rely on text-based
  manipulation, but rather on machine-processable
  metadata

33
Ontologies

• The term ontology originates from philosophy
• The study of the nature of existence
• Different meaning from computer science
• An ontology is an explicit and formal
  specification of a conceptualization

34
Typical Components of Ontologies

• Terms denote important concepts (classes of
  objects) of the domain
• e.g. professors, staff, students, courses,
  departments
• Relationships between these terms typically
  class hierarchies
• a class C to be a subclass of another class C' if
  every object in C is also included in C'
• e.g. all professors are staff members
• Value restrictions
• e.g. only faculty members can teach courses

35
Example of a Class Hierarchy

36
The Role of Ontologies on the Web

• Ontologies provide a shared understanding of a
  domain semantic interoperability
• overcome differences in terminology
• mappings between ontologies
• Ontologies are useful for the organization and
  navigation of Web sites

37
Typical Ontology Use Case Image Search

• A person searches for photos of an orange ape
• An image collection of animal photographs
  contains snapshots of orang-utans.
• The search engine finds the photos, despite the
  fact that the words orange and ape do not
  appear in annotations

38
Example Semantic Annotation
39
RDF Annotation of A Web Resource
WordNet

ape08.jpg
young
life stage
active agent
chimpanzee
scratching the head
Species ontology
posture
ICONCLASS
40
Ontologies Describe Concepts Used

great ape
geographical range
Africa
subClassOf
chimpanzee
typical habitat
grass lands
rain forest
41
Logic versus Ontologies

• The previous example involves knowledge typically
  found in ontologies
• Logic can be used to uncover ontological
  knowledge that is implicitly given
• It can also help uncover unexpected relationships
  and inconsistencies
• Logic is more general than ontologies
• It can also be used by intelligent agents for
  making decisions and selecting courses of action

42
The Semantic Web Layer Tower
43
Semantic Web Layers

• XML layer
• Syntactic basis
• RDF layer
• RDF basic data model for facts
• RDF Schema simple ontology language
• Ontology layer
• More expressive languages than RDF Schema
• Current Web standard OWL

44
Semantic Web Layers (2)

• Logic layer
• enhance ontology languages further
• application-specific declarative knowledge
• Proof layer
• Proof generation, exchange, validation
• Trust layer
• Digital signatures
• recommendations, rating agencies .

45
The Semantic Web

• The Semantic Web vision
• RDF
• OWL
• Rules

46
Basic Ideas of RDF

• Basic building block object-attribute-value
  triple
• It is called a statement
• Sentence about Billington is such a statement
• RDF has been given a syntax in XML
• This syntax inherits the benefits of XML
• Other syntactic representations of RDF possible

47
Basic Ideas of RDF (2)

• The fundamental concepts of RDF are
• resources
• properties
• statements

48
Resources

• We can think of a resource as an object, a
  thing we want to talk about
• E.g. authors, books, publishers, places, people,
  hotels
• Every resource has a URI, a Universal Resource
  Identifier
• A URI can be
• a URL (Web address) or
• some other kind of unique identifier

49
Properties

• Properties are a special kind of resources
• They describe relations between resources
• E.g. written by, age, title, etc.
• Properties are also identified by URIs
• Advantages of using URIs
• ? global, worldwide, unique naming scheme
• Reduces the homonym problem of distributed data
  representation

50
Statements

• Statements assert the properties of resources
• A statement is an object-attribute-value triple
• It consists of a resource, a property, and a
  value
• Values can be resources or literals
• Literals are atomic values (strings)

51
Three Views of a Statement

• A triple
• A piece of a graph
• A piece of XML code
• Thus an RDF document can be viewed as
• A set of triples
• A graph (semantic net)
• An XML document

52
A Set of Triples as a Semantic Net
53
Basic Ideas of RDF Schema

• RDF is a universal language that lets users
  describe resources in their own vocabularies
• RDF does not assume, nor does it define semantics
  of any particular application domain
• The user can do so in RDF Schema using
• Classes and Properties
• Class Hierarchies and Inheritance
• Property Hierarchies

54
Classes and their Instances

• We must distinguish between
• Concrete things (individual objects) in the
  domain Discrete Maths, David Billington etc.
• Sets of individuals sharing properties called
  classes lecturers, students, courses etc.
• Individual objects that belong to a class are
  referred to as instances of that class
• The relationship between instances and classes in
  RDF is through rdftype

55
Why Classes are Useful

• Impose restrictions on what can be stated in an
  RDF document using the schema
• As in programming languages
• E.g. A1, where A is an array
• Disallow nonsense from being stated

56
Nonsensical Statements disallowed through the Use
of Classes

• Discrete Maths is taught by Concrete Maths
• We want courses to be taught by lecturers only
• Restriction on values of the property is taught
  by (range restriction)
• Room MZH5760 is taught by David Billington
• Only courses can be taught
• This imposes a restriction on the objects to
  which the property can be applied (domain
  restriction)

57
Class Hierarchies

• Classes can be organised in hierarchies
• A is a subclass of B if every instance of A is
  also an instance of B
• Then B is a superclass of A
• A subclass graph need not be a tree
• A class may have multiple superclasses

58
Class Hierarchy Example
59
Inheritance in Class Hierarchies

• Range restriction Courses must be taught by
  academic staff members only
• Michael Maher is a professor
• He inherits the ability to teach from the class
  of academic staff members
• This is done in RDF Schema by fixing the
  semantics of is a subclass of
• It is not up to an application (RDF processing
  software) to interpret is a subclass of

60
Property Hierarchies

• Hierarchical relationships for properties
• E.g., is taught by is a subproperty of
  involves
• If a course C is taught by an academic staff
  member A, then C also involves ?
• The converse is not necessarily true
• E.g., A may be the teacher of the course C, or
• a tutor who marks student homework but does not
  teach C
• P is a subproperty of Q, if Q(x,y) is true
  whenever P(x,y) is true

61
Summary of Basic RDF Functionalities

• Metadata statements
• Instances and classes
• Binary properties
• Class hierarchies
• Property hierarchies
• Domain and range restrictions

62
The Semantic Web

• The Semantic Web vision
• RDF
• OWL
• Rules

63
Reasoning About Knowledge in Ontology Languages

• Class membership
• If x is an instance of a class C, and C is a
  subclass of D, then we can infer that x is an
  instance of D
• Equivalence of classes
• If class A is equivalent to class B, and class B
  is equivalent to class C, then A is equivalent to
  C, too

64
Reasoning About Knowledge in Ontology Languages
(2)

• Consistency
• X instance of classes A and B, but A and B are
  disjoint
• This is an indication of an error in the ontology
• Classification
• Certain property-value pairs are a sufficient
  condition for membership in a class A if an
  individual x satisfies such conditions, we can
  conclude that x must be an instance of A

65
Uses for Reasoning

• Reasoning support is important for
• checking the consistency of the ontology and the
  knowledge
• checking for unintended relationships between
  classes
• automatically classifying instances in classes
• Checks like the preceding ones are valuable for
• designing large ontologies, where multiple
  authors are involved
• integrating and sharing ontologies from various
  sources

66
Reasoning Support for OWL

• Semantics is a prerequisite for reasoning support
• Formal semantics and reasoning support are
  usually provided by
• mapping an ontology language to a known logical
  formalism
• using automated reasoners that already exist for
  those formalisms
• OWL is (partially) mapped on a description logic,
  and makes use of reasoners such as FaCT and RACER
  
• Description logics are a subset of predicate
  logic for which efficient reasoning support is
  possible

67
Limitations of the Expressive Power of RDF Schema

• Local scope of properties
• rdfsrange defines the range of a property (e.g.
  eats) for all classes
• In RDF Schema we cannot declare range
  restrictions that apply to some classes only
• E.g. we cannot say that cows eat only plants,
  while other animals may eat meat, too

68
Limitations of the Expressive Power of RDF Schema
(2)

• Disjointness of classes
• Sometimes we wish to say that classes are
  disjoint (e.g. male and female)
• Boolean combinations of classes
• Sometimes we wish to build new classes by
  combining other classes using union,
  intersection, and complement
• E.g. person is the disjoint union of the classes
  male and female

69
Limitations of the Expressive Power of RDF Schema
(3)

• Cardinality restrictions
• E.g. a person has exactly two parents, a course
  is taught by at least one lecturer
• Special characteristics of properties
• Transitive property (like greater than)
• Unique property (like is mother of)
• A property is the inverse of another property
  (like eats and is eaten by)

70
Three Species of OWL

• W3CsWeb Ontology Working Group defined OWL as
  three different sublanguages
• OWL Full
• OWL DL
• OWL Lite
• Recent modifications have led to OWL2 with new
  sublanguages

71
Summary of Selected Key OWL Functionalities

• Equality of classes and properties
• Important property characteristics transitive,
  functional, inverse
• Union, intersection and compement of classes
• AllValuesFrom(P,D) All values of statements with
  property P must be from class D
• Cardinality constraints

72
The Semantic Web

• The Semantic Web vision
• RDF
• OWL
• Rules

73
Orthogonal Expressivity

• Why consider rules?
• Well established technology, used in the business
  world, natural for many apps
• Orthogonal expressivity
• OWL is based on Description Logic
• Horn logic is orthogonal w.r.t. DL

74
What OWL Cannot Express

• It is impossible to define classes whose
  instances are related to another anonymous
  individual via different property paths.
• E.g. Home workers are those who live and work
  in the same location.
• Easily expressed in Horn logic
• homeWorker(X) -
• work(X,Y),live(X,Z), loc(Y,W), loc(Z,W).

75
What Horn Logic Cannot Express

• Existential quantification
• E.g. All persons have a father.
• Disjunction / union
• E.g. Persons are men or women.
• Negation / complement
• E.g. Men and women are disjoint.

76
RDFS and Horn Logic

• Statement(a,P,b) P(a,b)
• type(a,C) C(a)
• C subClassOf D C(X) ? D(X)
• P subPorpertyOf Q P(X,Y) ? Q(X,Y)
• domain(P,C) P(X,Y) ? C(X)
• range(P,C) P(X,Y) ? C(Y)

77
OWL in Horn Logic

• C sameClassAs D C(X) ? D(X)
• D(X) ? C(X)
• P samePropertyAs Q P(X,Y) ? Q(X,Y)
• Q(X,Y) ? P(X,Y)

78
OWL in Horn Logic (2)

• transitiveProperty(P) P(X,Y), P(Y,Z) ? P(X,Z)
• inverseProperty(P,Q) Q(X,Y) ? P(Y,X)
• P(X,Y) ? Q(Y,X)
• functionalProperty(P) P(X,Y), P(X,Z) ? YZ

79
OWL in Horn Logic (3)

• (C1 ? C2) subClassOf D
• C1(X), C2(X) ? D(X)
• C subClassOf (D1 ? D2)
• C(X) ? D1(X)
• C(X) ? D2(X)

80
OWL in Horn Logic (4)

• (C1? C2) subClassOf D
• C1(X) ? D(X)
• C2(X) ? D(X)
• C subClassOf (D1 ? D2)
• Translation not possible!

81
OWL in Horn Logic (5)

• C subClassOf AllValuesFrom(P,D)
• C(X), P(X,Y) ? D(Y)
• AllValuesFrom(P,D) subClassOf C
• Translation not possible!

82
OWL in Horn Logic (6)

• MinCardinality cannot be translated due to
  existential quantification
• MaxCardinality 1 may be translated if equality is
  allowed
• Complement cannot be translated, in general

83
Part III Defeasible Reasoning

84
Defeasible Reasoning

• Nonmonotonic Reasoning Motivation
• Defeasible Logic Basic Ideas
• Defeasible Logic Properties

85
New Information

• What time do I arrive in Lugano?
• 630pm (by bus from Malpensa)
• New information My flight is delayed by an hour
• New answer 830pm!
• New information has led to the retraction of my
  previous reply nonmonotonic behaviour

86
Incomplete Information

• Why did it happen?
• Actually because I made assumptions (no delay)
  that turned out to be wrong
• I made these assumptions because
• I could not have known in advance certain
  information is incomplete
• Otherwise I would be seen to be strange

87
Incomplete Information on the Web

• Business rules deal with incomplete information
• In the absence of information some assumptions
  have to be made which lead to conclusions not
  supported by classical predicate logic.
• In Web applications other players may not be able
  or willing to provide information.
• Communication problems
• Privacy or security concerns

88
Inconsistent Information

• Classical logics collapse in the face of
  inconsistencies
• Everything can be derived
• But inconsistencies do happen in real settings
• Common when integrating knowledge from various
  Web sources
• Nonmonotonic reasoning is inconsistency tolerant
  reasoning

89
Rules with Exceptions

• Natural representation for policies and business
  rules.
• Priority information is often implicitly or
  explicitly available to resolve conflicts among
  rules.
• Potential applications
• Security policies
• Business rules
• Personalization
• Brokering
• Bargaining, automated agent negotiations

90
Defeasible Reasoning

• Nonmonotonic Reasoning Motivation
• Defeasible Logic Basic Ideas
• Defeasible Logic Properties

91
Defeasible Logics

• Rule-based, without disjunction.
• Classical negation is used in the heads and
  bodies of rules
• Negation-as-failure is not used but can be
  emulated
• Rules may support conflicting conclusions.
• Skeptical Conflicting rules do not fire.
• Consistency is preserved.
• Priorities on rules may be used to resolve some
  conflicts among rules.

92
Example 1

• R1 ? a
• a provable?

93
Example 1

• R1 ? a a
• Yes (of course)

94
Example 2

• R1 ? a
• R2 ? ?a
• a provable?

95
Example 2

• R1 ? a -a
• R2 ? ?a -?a
• No! (sceptical)

96
Example 3

• R1 ? a
• R2 ? ?a
• R1gtR2
• a provable?

97
Example 3

• R1 ? a a
• R2 ? ?a -?a
• R1gtR2
• Yes!

98
Example 4

• R1 a ? b
• R2 ? ?b
• R1gtR2
• b provable?

99
Example 4

• R1 a ? b -a
• R2 ? ?b ?b
• R1gtR2 -b
• No, quite the opposite.

100
Example 5

• R1 ? a
• R2 ? ?a
• R3 a ? b
• R4 ?a ? b
• b provable?

101
Example 5

• R1 ? a -a
• R2 ? ?a -?a
• R3 a ? b -b
• R4 ?a ? b
• No (no floating conclusions)

102
Example 6

• R1 ? a
• R2 ? ?a
• R3 a ? b
• R4 ? ?b
• ?b provable?

103
Example 6

• R1 ? a -a
• R2 ? ?a -b
• R3 a ? b ?b
• R4 ? ?b
• Yes (no propagation of ambiguity)

104
Example 7

• R1 ? a
• R2 ? ?a
• R3 a ? b
• R4 ?a ? ?b
• R1gtR2
• R4gtR3
• b or ?b provable?

105
Example 7

• R1 ? a a
• R2 ? ?a -?a
• R3 a ? b -?b
• R4 ?a ? ?b b
• R1gtR2
• R4gtR3
• b (sequence of conflict resolution important)

106
Example 8

• R1 a ? e
• R2 b ? e
• R3 c ? ?e
• R4 d ? ?e
• a b c d
• R1gtR3
• e provable?

107
Example 8

• R1 a ? e a
• R2 b ? e b
• R3 c ? ?e c
• R4 d ? ?e d
• a b c d -e
• R1gtR3 -?e
• No (not inferior attack by R4)

108
Example 9 (Team Defeat)

• R1 a ? e a
• R2 b ? e b
• R3 c ? ?e c
• R4 d ? ?e d
• a b c d e
• R1gtR3
• R2gtR4

109
Defeasible Reasoning

• Nonmonotonic Reasoning Motivation
• Defeasible Logic Basic Ideas
• Defeasible Logic Properties

110
Important Properties

• Consistency A and ?A cannot be both derived,
  unless they are already known as certain
  knowledge (facts)
• Coherence A and A cannot be derived from the
  same knowledge base.
• Complexity Defeasible logic has linear
  complexity.

111
Semantic Characterization

• Defeasible logic is defined as a proof theory. A
  more abstract characterization is desirable.
• Argumentation semantics More abstract definition
  of meaning in terms of arguments (reasoning
  chains) and their mutual interactions.
• Proof theory is sound and complete w.r.t. this
  semantics

112
Connection to Logic Programming

• Based on the translation of defeasible theories
  into logic programs through the well-studied
  meta-program of
• Antoniou G., Billington D., Governatori G., Maher
  M.J, "A Flexible Framework for Defeasible
  Logics", Proc. AAAI/IAAI 2000, AAAI/MIT Press,
  pp. 405-410.

113
The Meta-Program

• definitely(X) - fact(X).
• definitely(X) -
• strict(R,X, Y1,...,Yn),
• definitely(Y1),...,definitely(Yn).
• defeasibly(X) - definitely(X).
• defeasibly(X) -
• not definitely(?X),
• supportive_rule(R,X, Y1,...,Yn),
• defeasibly(Y1),...,defeasibly(Yn),
• not overruled(R,X).

114
The Meta-Program (2)

• overruled(R,X) -
• rule(S,?X,U1,...,Un),
• defeasibly(U1),...,defeasibly(Un),
• not defeated(S, ?X).
• defeated(S,?X) -
• sup(T,S),
• supportive rule(T,X, V1,...,Vn),
• defeasibly(V1),...,defeasibly(Vn).

115
The Meta-Program (3)

• supportive_rule(Name,Head,Body)-
• strict(Name,Head,Body).
• supportive_rule(Name,Head,Body)-
• defeasible(Name,Head,Body).
• rule(Name,Head,Body)-
• supportive_rule(Name,Head,Body).
• rule(Name,Head,Body)-
• defeater(Name,Head,Body).

116
Part IV Applications of Defeasible Reasoning

117
Applications

• Semantic brokering
• Electronic auctions
• Pervasive computing / ambient intelligence

118
Motivation

• 1st generation e-commerce (present)
• Buyers and sellers are humans
• Catalogue of well-defined commodities
• Fixed price purchases by means of credit card
  transaction
• 2nd generation e-commerce (future)
• Buyers and sellers are software agents

119
Background Theory Brokering

• Brokering or matchmaking process that requires a
  host to take a query and to return all
  advertisements which satisfy the requirements
  specified in the query
• Advertisements
• Preferences
• Brokering Engine
• Brokering engine uses a specific technique and
  performs the matching of preferences with
  advertisements

120
Suitability of Defeasible Logic

• Formal language with well-understood meaning, a
  proof theory, model semantics, and argumentation
  semantics
• It is predictable ,explainable and has linear
  complexity
• Sceptical formalism. It does not support
  contradictory conclusions

121
Suitability of Defeasible Logic (2)

• Natural representation of important features
• Rules with exceptions
• Priorities for expressing user preferences

122
An Apartment Renting Example

• Apartments and their properties are the
  advertisements
• The renters requirements and preferences are
  expressed in defeasible logic

123
User Requirements Preferences

1. Carlos is looking for an apartment of at least
   45m2 with at least 2 bedrooms. If it is on the
   3rd floor or higher, the house must have an
   elevator. Also, pet animals must be allowed.
2. Carlos is willing to pay 300 for a centrally
   located 45m2 apartment, and 250 for a similar
   flat in the suburbs. In addition, he is willing
   to pay an extra 5 per m2 for a larger apartment,
   and 2 per m2 for a garden.
3. He is unable to pay more than 400 in total. If
   given the choice, he would go for the cheapest
   option. His 2nd priority is the presence of a
   garden lowest priority is additional space.

124
Predicates Used in Formalization

• size(x,y), where y is the size of apartment x (in
  m2)
• bedrooms(x,y), where apartment x has y bedrooms
• price(x,y), where y is the price for x
• floor(x,y), where apartment x is on the y-th
  floor
• gardenSize(x,y), where apartment x has a garden
  of size y
• lift(x), meaning that there is an elevator in the
  house of x
• pets(x), meaning that pets are allowed in x
• central(x), meaning that x is centrally located

125
Predicates Used (2)

• acceptable(x), meaning that flat x satisfies
  Carloss requirements
• offer(x,y), meaning that Carlos is willing to pay
  y for flat x

126
Formalization of Requirements

• r1 gt acceptable(X)
• r2 bedrooms(X,Y), Y lt 2 gt acceptable(X)
• r3 size(X,Y), Y lt 45 gt acceptable(X)
• r4 pets(X) gt acceptable(X)
• r5 floor(X,Y), Y gt 2, lift(X) gt acceptable(X)
• r6 price(X,Y), Y gt 400 gt acceptable(X)
• r2 gt r1, r3 gt r1, r4 gt r1, r5 gt r1, r6 gt r1

127
Formalization of Requirements (2)

• r7 size(X,Y), Y 45, garden(X,Z), central(X) gt
  offer(X, 300 2Z 5(Y-45))
• r8 size(X,Y), Y 45, garden(X,Z),central(X) gt
  offer(X, 250 2Z 5(Y-45))
• r9 offer(X,Y), price(X,Z), Y lt Z gt
  acceptable(X)
• r9 gt r1

128
A Sample Collection of Apartments
App Bed Size Cent Floor Lift Pets Gard Price
a1 1 50 yes 1 no yes 0 300
a2 2 45 yes 0 no yes 0 335
a3 2 65 no 2 no yes 0 350
a4 2 55 no 1 yes no 15 330
a5 3 55 yes 0 no yes 15 350
a6 2 60 yes 3 no no 0 370
a7 3 65 yes 1 no yes 12 375
129
Results of User Requirements

• Apartment a1 is not acceptable because it has one
  bedroom only (rule r2).
• Apartments a4 and a6 are unacceptable because
  pets are not allowed (rule r4).
• Apartment a2 is unacceptable because it costs
  more than the 300 Carlos is willing to pay
  (rules r7 r9).
• The rest, a3, a5 and a7, are acceptable.

130
Formalization of User Preferences

• r10 acceptable(X), price(X,Z),
  not(acceptable(Y),
• Y ? X, price(Y,W), W lt Z) gt cheapest(X)
• r11 cheapest(X), gardenSize(X,Z),
  not(cheapest(Y), Y ? X, gardenSize(Y,W), W lt Z)
  gt largestGarden(X)
• r12 largestGarden(X), size(X,Z),
  not(largestGarden(Y), Y ? X,
• size(Y,W), W lt Z) gt rent(X)

131
Results of User Preferences

• Apartments a3 and a5 are the cheapest acceptable
  apartments (rule r10)
• a5 is selected because it has larger garden than
  a3 (rules r11 and r12)

132
Applications

• Semantic brokering
• Electronic auctions
• Pervasive computing / ambient intelligence

133
Auction Strategies

• English Auction
• One of the most popular one-to-many negotiation
  mechanisms
• Simplest form multi-party single-issue
  negotiation
• Popular in Internet trading

134
English Auction Principles

• Seller sets reservation price, which may or may
  not be announced to the bidders
• Seller sets timing constraint,
• firm deadline, as maximum duration between two
  successive bids, or both
• Potential buyers then issue increasingly higher
  bids, with increment threshold

135
English Auction Principles (2)

• Auction stops when the timing constraint is
  violated
• i.e. either the deadline is reached, or no bid
  registered for longer than the established
  maximum duration.
• The last bidder then buys the item at the price
  of the last bid
• If no bid above reservation price, the item is
  not sold

136
Auction Broker

• Standard in online trading communities
• Registers the parameters of the auction
• Publishes them
• Processes incoming bids
• Continuously makes accessible the auction's status

137
A Sample Bidder Strategy

• Mark wishes to participate in the auction of an
  item. He doesn't know exactly how much the item
  is worth, but he thinks that its value lies
  somewhere within two bounds L and U. He is keen
  not to over-value the item, so he decides to
  assume at the beginning of the auction that the
  item is worth L, and to eventually increase his
  valuation whenever one of the following two
  situations occurs (a) at least 3 bids above his
  current valuation have been registered, or (b)
  somebody has bid more than 20 of his current
  valuation.

138
A Sample Bidder Strategy (2)

• As soon as one of these conditions is met, Mark
  will raise his valuation by the minimum possible
  amount that allows him to stay in the auction.
  However, he will never accept to valuate the item
  above U. As it is usual in the case of English
  auctions, Mark will start by bidding some minimum
  amount (i.e. the reservation price), and if
  needed, he will subsequently overbid the other
  participants' bids by the minimum increment, as
  long as the resulting bid is less than his
  current valuation. In the eventuality where the
  auction's deadline is too close and that he does
  not hold the current highest bid, he will bid his
  current valuation instead of just overbidding by
  the minimum increment.

139
Predicates Functions for Auction Description

• min_increment denotes the minimum mount by which
  the bidders are allowed to overbid
• initial_bid denotes the minimum amount of the
  first acceptable bid. (reservation price may be
  higher, but unknown to bidders)
• time_remaining(T) provides the time remaining
  before the end of the auction
• highest_quote(N) provides the current highest bid
  
• quotes_above(X, N) holds if N bids above amount X
  have been registered.

140
Predicates Functions for Bidding Strategy

• time_threshold is the duration to the deadline,
  below which Mark estimates that he should bid his
  valuation instead of just overbidding by the
  minimum increment
• significant_bidders is the number of bidders that
  should bid above Mark's current valuation before
  he considers raising it
• significant_increment is the amount (expressed as
  a percentage), that another bidder should bid
  above Mark's current valuation before he
  considers raising it (in working example it is
  0,2)

141
Predicates Functions for Bidding Strategy (2)

• max_valuation is self-explainable
• submit_bid(X) states that a bid of amount X
  should be submitted
• valuation(X) gives the current valuation while
  pre_valuation(X) gives the valuation that was
  valid at the end of the previous activation of
  the reasoning module
• my_bid(X) gives the amount of the last accepted
  bid issued by the bidder. At the beginning of the
  auction my_bid(0) holds

142
Formalization of Bidding Strategy

• r1 my_bid(X), highest_quote(Y), valuation(Z),
• X lt Y, Y min_increment lt Z,
• time_remaining(T), T gt time_threshold
• ? submit_bid(Y min_increment)
• If there is enough time remaining and the
  agent's current bid is not the highest one, it
  should be increased by the minimum increment,
  provided that the current valuation allows so.

143
Formalization of Bidding Strategy (2)

• r2 my_bid(X), highest_quote(Y), valuation(Z),
• X lt Y, Y min_increment lt Z,
• time_remaining(T), T ? time_threshold
• ? submit_bid(Z)
• If the deadline is close and the bidder does not
  hold the item, a bid of the amount of the current
  valuation should be submitted immediately.

144
Formalization of Bidding Strategy (3)

• r3 pre_valuation(X) ? valuation(X)
• r4 pre_valuation(X), quotes_above(X, N),
• N ? significant_bidders, highest_quote(Y)
• ? valuation(Y min_increment)
• r5 pre_valuation(X), highest_quote(Y),
• Y gt (1 significant_increment) ? X
• ? valuation(Y min_increment)
• r6 Y gt max_valuation gt ?valuation(Y)
• r4 gt r3, r5 gt r3

145
Formalization of Bidding Strategy (4)

• Conflicting literals
• C(submit_bid(x)) ? submit_bid(y) y ? x
• C(new_valuation(x))
• ? new_valuation(y) y ? x

146
Formalization of Bidding Strategy (5)

• Rules r3 through r6 allow to derive the valuation
• r4 and r5 model the two conditions under which
  the valuation should be raised
• r6 is a defeater modeling the fact that the
  bidder is under no circumstances willing to
  valuate the item above a given amount.

147
Modularity of the Formalization

• Suppose user wants to modify the strategy
• raise the valuation if the reservation price has
  not been met and the highest bid is above my
  current valuation
• Just add the rule
• r7 reservation_not_met, valuation(X),
• highest_quote(Y), Y gt X ?
• valuation(Y min_increment)
• r7 gt r3

148
Modularity of the Formalization (2)

• We dont have to worry whether the reservation
  price is greater than the bidders maximum
  valuation or not.

149
Applications

• Semantic brokering
• Electronic auctions
• Pervasive computing / ambient intelligence

150
Context in Ambient Intelligence

• Aim of AmI systems
• right information to the right users, at the
  right time, in the right place, and on the right
  device
• thorough knowledge and understanding of context
• Context in Ambient Intelligence
• .. any information that can be used to
  characterize the situation of an entity. An
  entity is a person, place or object that is
  considered relevant to the interaction between a
  user and application, including the user and
  application themselves.. Dey and Abowd, 1999

151
Contextual Reasoning in Ambient Intelligence

• Challenges
• Imperfect nature of the available context
  information
• Unknown, ambiguous, imprecise, erroneous
• Special characteristics of ambient environments
• Highly dynamic and open environments
• Distributed context knowledge
• Unreliable and restricted wireless communications
• Limitations of current AmI systems
• No formal model for reasoning with imperfect
  context
• Centralized architectures ? No support for
  distributed reasoning

152
Motivating AmI Scenario
Dr. Amber is located in the RA201 university
classroom reading his e-mails on his laptop. It
is Tuesday, the time is 7.50 p.m., and he has
just finished with a lecture for course CS566.
His context-aware mobile phone receives an
incoming call, but it is not in silent mode.

• Dr. Ambers phone is configured to take decisions
  about whether it should ring in case of incoming
  calls based on its context and Dr. Ambers
  preferences
• The phone should ring, unless it is in silent
  mode or Dr. Amber is busy with some important
  activity.
• A lecture at the university is one such important
  activity.

153
Motivating AmI Scenario
class
RA201
one person detected
no class activity
154
Scenario Characteristics

• Assumptions
• each agent aware of the type and quality of
  imported knowledge
• each agent has some computing and reasoning
  capabilities
• each agent willing to disclose part of its local
  knowledge
• Challenges
• context is incomplete, imprecise, ambiguous
• restricted computing capabilities
• light communication load for making quick
  decisions

155
Multi-Context Systems

• Definition
• Logical formalizations of distributed context
  theories connected through a set of mapping
  rules, which enable information flow between
  different contexts
• Context a logical theory that models local
  context knowledge
• Challenges
• Heterogeneity of local context theories
• Inconsistencies caused by the interaction of
  contexts through the mappings

156
Global Inconsistency in MCS
Context A
k
k
Context C
Context B
157
Modeling the AmI scenario

• Local facts and rules
  Phone (P1)
• r11l ? incoming_call
• r12l ? normal_mode
• r13l incoming_call, normal_mode,
  important_activity ? ring
• r14l lecture ? important_activity
• Mapping rules
• r15m scheduled(CS566)2, location(RA201)3
  ? lecture
• r16m class_activity4 ? lecture
• Preference relation
• T1 P3, P4, P2

158
Modeling the AmI scenario

• Laptop (P2)
• r21l ? day(Tuesday)
• r22l ? time(19.50)
• r23l day(Tuesday), time(X), 19.00 lt X lt
  20.00 ? scheduled(CS566)
• Localization Service(P3)
• r41l ? location(RA201)
• Classroom Manager (P4)
• r41l ? projector(off)
• r42m ? detected(X)5, Xlt2, projector(off) ?
  class_activity
• Person Detection Service(P5)
• r51l ? detected(1)

159
Future Work

• Overlapping vocabularies
• Access control privacy mechanisms
• More applications in the Ambient Intelligence and
  Semantic Web domains
• Run on small devices
• Efficient reasoning is well-suited for real-world
  and real-time applications

160
Part V Summary

161
Summary

• KR is about difficult problems that cannot be
  solved directly algorithmically
• Or offers advantages in terms of transparency,
  modularity and explanation
• KR is a multi-faceted area
• Always seeking a balance between expressive power
  and manageable computational complexity
• KR in contemporary ICT areas
• Web
• Ambient Intelligence

162
References

• The standard textbook on Knowledge
  Representation
• R. Brachman and H. Levesque. Knowledge
  Representation and Reasoning. Morgan Kaufmann
  2004
• The standard textbook on the Semantic Web
• G. Antoniou and F. van Harmelen. A Semantic Web
  Primer, 2nd ed. MIT Press 2008
• www.semanticwebprimer.org
• A useful page on the semantic web
• www.semanticweb.org

163
References (2)

• A textbook on nonmonotonic reasoning
• G. Antoniou. Nonmonotonic Reasoning. MIT Press
  1997
• A paper on defeasible logics
• G. Antoniou, D. Billington, G. Governatori and M.
  Maher. Representation Results for Defeasible
  Logic. ACM Transactions on Computational Logic
  2,2 (2001) 255-287 http//eprint.uq.edu.au/archiv
  e/00002222/01/tocl.pdf

164
References (3)

• A paper on brokering based on defeasible
  reasoning
• G. Antoniou, T. Skylogiannis, A. Bikakis, M.
  Doerr, N. Bassiliades. DR-BROKERING A semantic
  brokering system. Knowledge-Based Systems 20(1)
  61-72 (2007)
• lpis.csd.auth.gr/publications/EEE05-a.pdf
• A paper on defeasible reasoning in ambient
  intelligence
• A. Bikakis, G. Antoniou, P. Hasssapis. Strategies
  for Contextual Reasoning with Conflicts in
  Ambient Intelligence. Knowledge and Information
  Systems (forthcoming)