ObjectOriented Knowledge Representation

1
Object-OrientedKnowledge Representation

• Jacques Robin

2
Outline

• Object-oriented languages
• Review key concepts of object-orientation
• History of OO languages
• Motivation for OO software engineering and
  knowledge representation
• First generation OOKR languages
• Semantic networks
• Semantic networks x Classical First-Order Logic
  (CFOL)
• Frames
• Frames x Semantic Networks
• Frames x CFOL

• UML
• The variety of UML diagrams
• Class diagrams
• Object diagrams
• Meta-knowledge representation and MOF
• The UML meta-model
• Activity diagrams
• UML x Semantic networks
• UML x Frames
• Limitations of UML Diagrams

3
Review of Key Object-Orientation Concepts

• Class (or concept, or category) abstract
  representation of a set of individuals with
  common structural and/or behavioral properties
• A class defines a complex type
• Object (or individual, or instance) individual
  instance of a given class
• An object conforms to the complex type defined by
  its class
• An object is created by instantiating its class
  (constructor method)
• Each object has a unique identifier (oid) that
  distinguishes it from other instances of the same
  class sharing the same properties
• The structural properties of a class are a set of
  attributes (also called fields or slots), which
  value is constrained to be of a certain subset of
  types (primitive types or classes)
• The structural properties of an object are
  specific values for these attributes within the
  ranges defined by its class
• The behavioral properties of a class are a set of
  operations (also called methods, procedures,
  deamons or functions) that its instances can
  execute
• The signature of a class is the set of type
  constraints on its attributes and on the
  parameters and return value of its operations
• The properties of a class have various
  visibilities such as public, protected and
  private allowing their encapsulation
• Classes are organized in a generalization
  (specialization) hierarchy
• Properties are inherited down the hierarchy from
  a class to its subclasses and its objects

4
Inheritance

• Allows concise knowledge representation through
  reuse of specifications and implementations among
  classes and objects down a specialization
  hierarchy
• Types of inheritance
• Structural inheritance
• Attribute signature inheritance (constraint
  inheritance)
• Value inheritance
• Behavioral inheritance
• Operation signature inheritance (constraint
  inheritance)
• Operation code inheritance
• Inheritance multiplicity
• Simple inheritance (each class restricted to
  having a single super-class, and each object
  restricted to belong to a single class)
• Multiple inheritance of different properties from
  different sources
• Multiple inheritance of same property from
  different sources
• Inheritance monotonicity
• Monotonic inheritance simple without overriding
• Non-monotonic inheritance with overriding,
  logically equivalent to default reasoning,
  semantics beyond Classicial First-Order Logic

5
A Brief History of OO Languages
Software Engineering
Distributed Systems
Programming
Knowledge Representation
Databases
1965
Semantic Networks
Semantic Web
2006
6
Motivation for OO in Software Engineering

• Improved productivity, quality, legibility and
  maintainability in developing software artifacts
• Software reuse instead of rewriting or cut and
  paste
• More intuitive
• Divide software in abstract entities and
  relations that directly match common cognitive
  abstraction of modeled domain
• Easy to learn
• Unifying notation
• Single representation paradigm for all software
  process stages
• Single, unified modeling language (UML)

7
Initial Motivation for OOin Knowledge
Representation

• Reasoning at the level of categories
• Inheritance as reasoning task
• Representing structural knowledge with a notation
  that is more intuitive than formal logic
• Easier to acquire, understand, maintain, etc.
• Reasoning about classifying instances into
  categories and inheritance can internally reuse a
  logic-based theorem prover, but in a way that is
  transparent, hidden from the domain expert
• Benefits of software engineering carrying over to
  knowledge (base) engineering

8
Categories

• The organization of objects in categories is a
  vital part of knowledge representation
• Most human reasoning occurs at the abstract
  level of general categories (intentional
  knowledge), rather than at the level of
  individual objects (extensional knowledge)
• Partial information
• coming for example from the sensors of an agent,
  
• about an object can be sufficient to classify it
  into a set of fixed categories
• about which general knowledge has been
  formalized
• The missing information
• needed for example for an agent to make a
  decision about how to handle the object or
  predict its behavior
• about the object can then be derived from the
  properties of the category
• Complex taxomonies involving generalization and
  composition relationships among categories form a
  rich network of abstract knowlege onto which to
  base the reasoning of an agent

9
Properties of Categories

• Disjointness
• No common elements
• Ex. male and female
• Exhaustive decomposition
• Covers the entire set of entities in the
  represented domain
• Ex. an animal that is not male, must be female
• Partition
• Exhaustive decomposition into disjoint categories
• Counter-example citizenships
• Composition
• A category of objects has another category of
  objects as one of its constituing parts
• Ex. A state is part of federal nation, a chapter
  is part of a book

10
Semantic Networks

• Category-oriented knowledge visual modeling
• Each category and instance is represented by a
  network node
• Each relationship between categories and
  instances is represented by a network link
• Special subsetOf and partOf relationships among
  categories
• Special memberOf relationship between a category
  and its instances
• Early semantic networks had single isa
  relationship that did not distinguish between
  subsetOf and memberOf
• Efficient algorithms to derive instance
  properties from their category
• By value inheritance
• By link path query

11
Semantic Networks Examples

• Network with four categories and four instances

• Network with N-ary relationship reified as a
  category instance

12
Semantic Networks x CFOL Examples

• (?P, person(P) ? mammal(P)) ?
• (?P, fenalePerson(P) ? person(P)) ?
• (?P, malePerson(P) ? person(P)) ?
• (?P, person(P)
• ? (?M hasMother(P,M) ? femalePerson(M)))
• (?P, person(P), ?abnormal(P,person,legNumber)
  ? legNumber(P,2)) ?
• femalePerson(mary) ? malePerson(john) ?
• sister(mary,john) ? malePerson(john) ?
• abnormal(john,person,legNumber) ?
  legNumber(john,1)
• fly(shankar,newYork,newDelhi,yesterday)

13
Early Semantic Networks

• Shortcut the formalization level of knowledge
  representation
• Directly mapped the graphical, knowledge level to
  the user-hidden programming code, implementation
  level
• Inference engines implemented reasoning that was
  unsound with semantic networks defined by most
  users, due to lack of
• Well-defined semantics for non-monotonic
  inheritance and reification ofN-ary
  relationships as categories
• Distinction between categories and instances

14
Late Semantic Networks

• Incorporated ever increasing types of links to
  get back expressive power close to that of CFOL
• Lost visual modeling simplicity and intuitiveness
• Remaining limitations
• Inheritance and link navigation sole inference
  services
• No construct to represent behavioral knowledge
• No construct to represent behavioral knowledge,
  state changes, events and time
• Currently obsolete, superseded by Description
  Logics
• Most recent DL engines use CFOL theorem proving
  techniques instead of graph traversal techniques
  to reason correctly and efficiently

15
Frames

• A frame has a name as its identification and
  describes a complex category or instance using a
  set of attributes (called slots)
• A frame system is a hierarchical organized set of
  frames.
• An evolution of semantic networks
• They also implement monotonic and non-monotonic
  inheritance
• Nodes are replaced by frames
• Edges are replaced by attributes (slots)
• Procedures may be attached to the slots of a
  frame to
• Represent behavioral knowledge
• Implement other forms of reasoning than mere
  inheritance
• Provide a knowledge acquisition user-interface
• Provide a reasoning explanation user-interface

16
Frames

• Categories (classes) and instances (objects)
  represented by Frames
• A frame is composed by slots
• A slot is composed by facets
• Facets may be
• Value specification (known or by default)
• Constraint over value (type, cardinality)
• Procedures (triggers for when the slot is
  acessed, modified or necessary to derive some
  fact during reasoning)
• Frames hierarchically organized with multiple
  inheritance of slots
• Inheritance is complex (without no formal
  definition) due to the variety of facets and
  interactions
• Reasoning is implemented comgining inheritance
  and triggers
• Frames used for
• Knowledge representation
• Inference engine implementation
• Knowledge acquisition interface implementation
• Reasoning explanation interface implementation
• Frames are always an extension of some host
  programming language (Lisp, C, Prolog, etc.)

17
Frames example
Frame Course in KB University Slot enrolls
Type Student Cardinality.Min 2
Cardinality.Max 30 Slot taughtby Type
(UNION GradStudent
Professor) Cardinality.Min 1
Cardinality.Max 1
Frame BasCourse in KB University Is-a Course
Slot taughtby Type Professor
Frame Professor in KB University Slot degree
Default PhD.
Frame Student in KB University
Frame AdvCourse in KB University Is-a Course
Slot enrolls Type (INTERSECTION
GradStudent (NOT
Undergrad)) Cardinality.Max 20
Frame GradStudent in KB University Is-a
Student Slot degree Default Bachelor
Frame Undergrad in KB University Is-a Student
18
Frames x CFOL Example
Frame Course in KB University Slot enrolls
Type Student Cardinality.Min 2
Cardinality.Max 30 Slot taughtBy Type
(UNION GradStudent
Professor) Cardinality.Min 1
Cardinality.Max 1
Frame Professor in KB University Slot degree
Default PhD.

• partOf(course,kbUniversity) ? fsfv(course,enrolls,
  type,student) ? fsfv(course,enrolls,minCard,2) ?
  fsfv(course,enrolls,maxCard,30) ?
• fsfv(course,taughtBy,type,courseTaughtByType) ?
  ((courseTaughtByType gradStudent) ?
  (courseTaughtByType professor)) ?
  fsfv(course,taughtBy,minCard,1) ?
  fsfv(course,taughtBy,maxCard,1)
  ?partOf(advCourse,kbUniversity) ?
  isa(advCourse,course) ?
• fsfv(advCourse,enrolls,type,advCourseEnrollsType)
  ?includes(advCourseEnrollsType,gradStudent)
  ?excludes(advCourseEnrollsType,undergradStudent)
  ?
• partOf(professor,kbUniversity) ?
  fsfv(professor,degree,default,phd)
• Missing formulas axiomatizing in CFOL the
  semantics of partOf, isa and all the slots
  (minCard,maxCard,type, default, etc)

Frame AdvCourse in KB University Is-a Course
Slot enrolls Type (INTERSECTION
GradStudent (NOT
Undergrad)) Cardinality.Max 20
19
Frames limitations

• Non-declarative behavior knowledge representation
  as host programming language code as prevents
  direct acquisition from domain expert
• No formal semantics
• No distinction between categories and instances
• Ad-hoc implementation of deduction and abduction
  usually inefficient as compared to logic-based
  ones
• There are no inductive inference engines for
  frame learning
• Lacks key reuse-oriented facilities of modern OO
  programming languages such as visibility,
  interfaces, components, etc.

20
UML as KR Language

• Class diagram
• Modern, well-founded version of semantic
  networks
• Activity diagram
• Modern, well-founded version of flow charts
• Graphical syntax for procedures
• Class diagrams Activity diagrams
• Graphical syntax of expressive power
  approximately equivalent to that of Frames
• Strengths
• Universal standard, well-thought, well-known and
  well-tooled (CASE)
• Facilitates convergence between software and
  knowledge engineering
• Limitations
• Lack of full UML compilers to executable
  languages
• Lack of inference engine to automatically
  reasoning with knowlege represented only as UML
  models
• No mathematically defined formal semantics yet
• Thus
• Only useful at the knowledge level
• Need to be used in conjunction with other
  language(s) that provide the formalization and/or
  implementation level

21
UML Class Diagram

• Categories represented as classes (nodes)
• Classes encapsulates
• Primitive type properties, attributes
• Behaviors, operations
• Relationships between classes represented as
  associations (edges)
• Special associations for
• Specialization relationship (reciprocal of isa)
• partOf relationship (aggregation and
  compositions)
• Reified relationships represented as association
  classes
• Role names and cardinality constraints on
  associations
• Many other logical constraints built-in class
  diagram syntax
• Arbitrary logical constraints relating any part
  of the class diagram using Object Constraint
  Language (OCL, cf. next lecture)

22
Classes Attributes

• Common characteristics of the class members
• Fields (slots)
• Base or derived
• Visibility (public, protected, private)
• Name
• Type (Primitive Built-In or Used-Defined
  Enumerations)
• Initial default value
• Property
• Object attributes different value for each
  object
• Class attributes same value for all objects
• Attributes for KR as many fields as possible!

23
Classes Operations

• Common signature of services provided by the
  class members
• Fields
• Visibility
• Name
• Input parameter
• Direction
• Name
• Type
• Multiplicity
• Default value
• Property
• Return type
• Property
• Object methods called on objects
• Class methods called to manipulate class
  attributes
• Operations for KR as many fields as possible!

24
Associations

• Association
• Generic relation between N classifiers
• Fields
• One or two Names
• Navigation direction
• Two Ends, each with
• One Multiplicity Range (default 1)
• Zero to One role
• Zero to one Qualifier
• Qualifier needed to distinguish different
  instances of a one-to-many or many-to-many
  association
• Navigation
• Role if present
• Otherwise destination class name
• Associations for KR as many fields as possible!

25
Association Classes

• Class connected to an association and not to any
  of its ends
• Allows associating properties and behaviors to an
  association
• One object of the association class for each link
  of the connected association
• A one-to-many or many-to-many association class
  cannot be substituted by a simple class and a
  pair of simple associations
• Example
• Ca has objects A1, A2, A3, A4
• Cb has objects B1, B2, B3, B4
• Extent of association class Cc between Ca and Cb
  with multiplicity at both ends has necessarily
  16 instances
• Class Cc associated to Ca through association
  Aca and to Cb through association Acb could have
  only 4 instances

Difference with ?
4
Elevator control
Queue
Elevator
26
Ternary Associations

• Single association between 3 classes
• Different from two binary associations
• Different from one binary association class
• Example
• Ca has objects A1, A2
• Cb has objects B1, B2
• Cc has objects C1, C2
• No link in the ternary association Ca-Cb-Cc
  corresponding to pair of links A1-B1, B2-C1

27
Aggregation Associations

• Association with part-whole semantics
• Associate composite class to its building blocks
• Static, definitional characteristic of the
  whole class
• In contrast to composite structure diagrams that
  model dynamic, configuration characteristic of
  the containing class
• Shared aggregation
• Many-to-many aggregation

28
Composition Associations

• Special case of one-to-one or one-to-many
  aggregation where part(s) cannot exist(s) without
  the unique whole
• Deletion of the whole must therefore always be
  followed by automatic deletion of the parts

29
Class generalizations

• Taxonomic relation between a class and one of its
  more general direct super-class
• Special case of generalization between any two
  classifiers
• Several generalizations form a taxonomic tree
  free of generalization cycles
• Sub-classifier inherits the features from all its
  direct super-classifiers
• Private attributes and operations not accessible
  from sub-classes
• Protected attributes and operations accessible
  from sub-classes but not from associated classes
• UML generalizations allow multiple
  inheritanceand overriding
• Instances of a sub-class must satisfy all the
  constraints on all its super-classes (principle
  of substitutability)

30
Abstract Classes

• Class that cannot be instantiated
• Only purpose factor gradual refinements of
  common and distinct structures and behaviors down
  a taxonomic hierarchy
• Abstract operation common signatures of distinct
  implementations specified in subclasses
• Supports polymorphism generic call signature to
  distinct operations, with automatic dispatch to
  the implementation appropriate to each specific
  call instance

31
Generalization Sets

• Subclass set that can be labeled as
• complete or incomplete
• overlapping or disjoint
• Complete and disjoint generalization sets form a
  partition of the super-class
• Sub-subclass can specialize members of two
  overlapping generalization sets

32
UML Object Diagrams

• Object Diagram contains
• Specific (named) or generic (named after role,
  unnamed) instances of classes
• Possibly several instances of the same class
• Specific instances of associations (links) among
  objects
• Possibly several instances of the same
  association
• Illustrates specific instantiation patterns of
  associated class diagram

33
UML x Semantic Networks Example

• Semantic Network

• Corresponding Class Diagram

34
UML x Semantic Networks Example
sisterOf
0..2
Legs
hasMother
sisterOf
johnmalePerson
maryfemalePerson
Legs
Missing OCL constraint defining semantics of
sisterOf association has derived from
hasMother(an hasFather) associations
hasMother
hasMother
femalePerson
35
UML x Frames Example
Frame Course in KB University Slot enrolls
Type Student Cardinality.Min 2
Cardinality.Max 30 Slot taughtBy Type
(UNION GradStudent
Professor) Cardinality.Min 1
Cardinality.Max 1
KBUniversity
1..
1..
0..20
Frame AdvCourse in KB University Is-a Course
Slot enrolls Type (INTERSECTION
GradStudent (NOT
Undergrad)) Cardinality.Max 20
enrolls
Course
Student
1..
taughtBy
AdvCourse
BasCourse
Frame BasCourse in KB University Is-a Course
Slot taughtBy Type Professor
Lecturer
Undergrad
Frame Student in KB University
Frame GradStudent in KB University Is-a
Student Slot degree Default Bachelor
Frame type constraint in red best modeled as OCL
constraints
Frame Undergrad in KB University Is-a Student
Frame Professor in KB University Slot degree
Default PhD.
36
Comparison Table
37
Meta-Object Facility (MOF)

• Structural meta-knowledge representation language
• Reuses UML class diagrams to specify, in an
  object-oriented way, the abstract syntax of
  computational languages
• Advantages over BNF grammars
• Visual clarity
• Abstract
• Terminals with internal structure and behaviors
• Richer variety of relation semantics among
  non-terminals specialization, aggregation,
  composition and simple associations instead of
  merely linearization order
• Reuse through inheritance, package import and
  package merge
• A MOF specification of the abstract syntax of a
  language L is called a meta-model of L

38
Relationship between MOF and UML
UML2 Infrastructure
...
Constructs
Associations ...
merge
Application
models
merge
metamodels
metamodels
metamodels
39
Simplified MOF Meta-Model of itself
Relationship
NamedElement
Classifier
Element
1..

Generalization
TypedElement
Type
Constraint
RedefinableElement
Association
redefined
ValueSpecification

Classifier
Feature
Class
AssociationClass
BehaviorallFeature
Operation
Parameter

Property

StrcuturalFeature
InstanceSpecification
40
Simplified MOF Meta-Model of itself
41
MOF Meta-Model ofEarly Semantic Networks
? OOP/OOSE Classes Objects

• OOP/OOSE
• attributes
• other associations

? OOSE aggregation composition associations
? OOP/OOSE subclass instance relationships
Node
Link


IS-A
PART-OF
Attribute Specification
Single Value Specification
Multiple Value Specification
42
MOF Meta-Model of Frames
? OOP/OOSE Classes Objects

• OOP/OOSE
• Attributes
• Associations

No corresponding concepts in OOP/OOSE
? OOP/OOSE Methods Activities
? OOSEConstraints
? OOP/OOSE subclass instance relationships
IS-A

Frame
Slot
Facet
Host Language Procedure


Procedural Attachment
Constraint
Value Specification
Cardinality Constraint
Single Value Specification
Min Int Max Int
Multiple Value Specification
Type Constraint
Input Parameter
Return Value
43
Simplified MOFMeta-Model of UML Classifiers
Type
Classifier
Feature
generalizes
Class
Interface
Association
DataType
StructuralFeature
BehavioralFeature
Parameter
AssociationClass
PrimitiveType
Enumeration
Operation
Constraint
Property
Boolean
Integer
String
Real
AssociationEnd
Attribute
44
Simplified MOF Meta-Modelof UML Relations
Relation
Association
Generalization
Dependency
AssociationClass
Aggregation
QualifiedAssociation
GeneralizationSet
Realization
Composition
PowerType