Object-Oriented Knowledge Representation

1
Object-OrientedKnowledge Representation

• Jacques Robin
• CIn-UFPE

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
• Frames
• Comparison with Classical First-Order Logic
  (CFOL)
• UML
• The variety of UML diagrams
• Class diagrams
• Object diagrams
• Meta-knowledge representation and MOF

• Ontologies
• What is an ontology?
• Elements of an ontology
• Services provided by an ontology
• The pluridisciplinary origin of ontological
  engineering
• Typology of ontologies
• Sub-fields and general issues in ontological
  engineering
• OCL
• What is OCL?
• Motivating examples
• OCL expression contexts
• The link between the OCL and UML metamodels
• The OCL metamodel
• OCL Types
• Inheritance and encapsulation in OCL
• Local variale definitions
• The OCL operator library
• OCL vs. UML
• OCL vs. Java

3
Review of Key Object-Orientation Concepts

• Class (or concept, or category) abstract
  represention 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 possess a unique identifier (oid)
  that distinguish it from other instance of the
  same class sharing the same properties
• The structural properties of a class are a set of
  attributes (also called fields or slots) names,
  each one 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 or
  functions) that its instance can execute
• The signature of a class is the set of
  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
  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 especifications and implementations
  among classes and objects down a generalization
  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 superclass, 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
Distributed System
Programming
Knowledge Representation
Databases
Software Engineering
1965
Today
Simula
Semantic Networks
Sketchpad
Smalltalk
Frames
Today
C
OQL
Next lecture
Advanced AI courses
UML1.0
Description Logics
SQL99
Java
OCL
Advanced AI coursed
Today
Frame Logics
MOF
Advanced AI courses
C
Semantic Web Languages
UML2.0
Today
2005
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

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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. Brazil is part of South America, a chapter
  is part of a book

10
Semantic Networks

• Knowledge visual modeling category-oriented
• Each category and object is represented by a
  newtwork node
• Each relationship between categories is
  represented by a network link
• Special hierarchical relationships is-a
  (inheritance) and part-of
• Efficient algorithms for deriving object
  properties, according to category conformance
• Derivation by value inheritance
• Derivation by link path query

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Semantic Networks - Example
Logical assertion n-ary Fly
Semantic network with four objects and four
categories
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Abstract Syntax of semantic networks in UML
? OOP/OOSE Classes Objects

• OOP/OOSE
• attributes
• other associations

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


Attribute Specification
IS-A
PART-OF
Single Value Specification
Multiple Value Specification
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Semantic Networks vs. Classical First-Order Logic
(CFOL) intentional knowledge

• Mary ?FemalePersons
• SisterOf (Mary, John)
• ?x x ?Persons ? x ? Mammals
• ?x x ?Persons ? ?y HasMother (x, y) ? y ?
  FemalePersons
• ?x x ?Persons ? Legs (x, 2)
• Note that this property has only status of
  default knowledge, since it can be overrided at
  the instance level to represent exceptions such
  as John
• Default knowledge reasoning is non-monotonic and
  as such cannot be represented in CFOL

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Semantic Networks vs. CFOL extensional knowledge

• Fly (Shankar, NewYork, NewDelhi, Yesterday)

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Semantic Networks - limitations

• Main Limitations
• Incomplete to implement the majority of
  intelligent systems
• No well founded declarative semantics (shortcut
  from konwledge level to implementation level
  without using logical formalism)
• Frames try to overcome first limitation
• Description logics try to overcome second
  limitation
• Other Limitations
• Search in large semantic networks may be very
  inefficient
• Nodes and links definitions are not homogenous
• Inheritance may cause difficulties while handling
  exceptions
• There can be conflicts between inherited features
• Behavior and procedural knowledge is difficult to
  represent sequence and time are not defined
• Less expressive than first-order logic There
  are no quantifiers

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Frames

• A frame has a name as its identification and
  describes a complex object using a set of
  attributes
• A Frame System is a hierarchical organized set of
  frames.
• They are an evolution of semantic networks
• Nodes are replaced by frames
• Edges are replaced by attributes (slots)
• They implement monotonic reasoning (ex,
  inheritance without overriding) and non-monotonic
  (ex, inheritance with overriding)
• Procedures may be attached to a frame
• They describe knowledge or some procedure related
  to an attribute.

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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.)

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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
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Abstract Syntax for Frames im UML
? 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
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Frames limitations

• Non-declarative Behavior Knowledge prevents
  direct codification from domain expert
• No formal semantic
• Implementation ad-hoc of deduction e adbduction,
  usually inefficient
• There are no inductive inference engines for
  frame learning
• It does not include encapsulation concepts nor
  components from moder OO programming languages

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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

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UML Classifiers Simplified Meta-Model
Type
Classifier
Feature
generalizes
Class
Interface
Association
DataType
StructuralFeature
BehavioralFeature
Parameter
AssociationClass
PrimitiveType
Enumeration
Operation
Constraint
Property
Boolean
Integer
String
Real
AssociationEnd
Attribute
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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!

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UML Relations Simplified Meta-Model
Relation
Association
Generalization
Dependency
AssociationClass
Aggregation
QualifiedAssociation
GeneralizationSet
Realization
Composition
PowerType
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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!

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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
27
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

28
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

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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

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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)

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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

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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

33
Objects and Links

• 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

34
UML x Semantic Networks Example

• Semantic Network

• Corresponding Class Diagram

35
UML x Semantic Network Example

• Semantic Network

• Corresponding Class Diagram

36
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
Frame Student in KB University
Frame GradStudent in KB University Is-a
Student Slot degree Default Bachelor
Frame Undergrad in KB University Is-a Student
Frame Professor in KB University Slot degree
Default PhD.
Frame AdvCourse in KB University Is-a Course
Slot enrolls Type (INTERSECTION
GradStudent (NOT
Undergrad)) Cardinality.Max 20
Frame BasCourse in KB University Is-a Course
Slot taughtby Type Professor
37
UML Unified Modeling Language

• UML advantages as knowledge representation
  language
• Standard notation and edition tools
• Well-defined Links composition, agreggation,
  inheritance, ...
• It works at the knowledge level
• Graphical easy modeling

38
Comparison Table
Semantic Networks Frames UML OCL Predicate Logic
Originated field IA IA SE IA
Inference engine for automated reasoning Yes Yes No Yes
Complete well founded formal declarative semantics No No No Yes
Knowledge Representation Structural Struc. Declar. Bheavior. Procedural Struct. Declar. Behavior. Procedu-ral Struct. Declar.
Easy visual syntax Yes No Yes No
39
O que é uma ontologia?

• Definição especificação (semi-)formal explícita
  de uma concepção compartilhada
• Concepção modelo das entidades, relações,
  axiomas e regras de algum domínio
• Formal
• processável por máquina
• permitindo raciocínio automático
• com semântica lógica formal
• Compartilhada por uma comunidade, permitindo
  entendimento
• Conceitos de computação relacionados
• Base de conhecimento reutilizável
• Esquema de banco de dados

40
Elementos de uma ontologia

• Hierarquia de conceitos
• entidades
• cada entidade definida por conjunto de pares
  atributo-valor
• correspondem
• as classes dos modelos orientado a objetos
• as entidades do modelo relacional
• aos termos do modelo lógico
• atributos propriedades x atributos relações
• preenchidos por valores atômicas (tipos
  primitivos) x por outros conceitos
• Status epistemológico do valor
• Exatamente conhecida, default, probabilista
• relações
• sem hierarquia x em hierarquia paralela a
  hierarquia de entidades
• correspondem
• associações, agregações e atributos dos modelos
  OO cujos valores são objetos
• as relações do modelo relacional
• aos predicados do modelo lógico

41
Elementos de uma ontologia

• Restrições
• sobre valores possíveis dos atributos dos
  conceitos
• correspondem
• as assinaturas de classes em modelos OO
• as axiomas universalmente quantificados em
  modelos lógicos
• as restrições de integridade nos esquema de BD
• Regras dedutivas
• sobre atributos de (conjunto de) conceitos
• permitem inferência automática da existência de
  instâncias de conceitos a partir da existência de
  outras instâncias
• correspondem
• as regras dos sistemas especialistas e
  programação em lógica
• aos métodos dos modelos OO
• as visões em BD

42
Elementos de uma ontologia

• Instâncias de conceitos
• definição de entidade e relações específicos
  (indivíduos)
• correspondem
• aos fatos de sistemas especialistas e programação
  em lógica
• aos objetos dos modelos OO
• aos dados dos BD

43
Serviços suportados por uma ontologia

• Consultas e manipulação
• correspondem
• métodos de acesso a valor e de reflexão em
  linguagens OO
• consultas de interrogação e manipulação em BD
• ask, tell e retract das bases de conhecimento
• sobre conceitos
• Quais são as entidades E relacionadas a entidade
  0 via relações r1, r2?
• Quais são as relações R mais gerais que r1?
• Definição d de entidade E é consistente com o
  resto da ontologia?
• sobre instâncias
• um indivíduo I com propriedades P1, ..., Pn é
  instância de quais conceitos?
• Raciocínio automático
• geralmente dedutivo

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Origem e motivação para ontologias
Gerenciamento do Conhecimento em
Organizações desde 90
Integração de Dados desde 95
Ontologias
Engenharia de Software requisitos e reuso desde
90
Filosofia desde 350 A.C.
Sistemas Multi-agentes desde 95
Recuperação de Informação na Web desde 00
45
Tipologia das ontologias

• Especialista modela um domínio particular
  restrito
• Geral
• modela o conhecimento de senso comum
  compartilhado por todos os seres humanos
• parte de mais alto nível, reutilizável em vários
  domínios
• Conceitual fundamentada na capacidade de
  raciocinar
• Lingüística fundamenta no vocabulário de uma(s)
  língua(s)
• De meta-dados especializada na descrição de
  recursos on-line, no entanto sobre qualquer
  domínio
• De tarefas e métodos modela procedimentos e
  comportamentos abstratos no lugar de entidades ou
  relações

46
(No Transcript)
47
Sub-problemas de modelagem de uma ontologia geral

• Categorias e conjuntos
• Medidas
• Objetos compostos
• Tempo
• Espaço
• Mudanças
• Eventos e processos
• Objetos físicos
• Substâncias
• Objetos mentais e crenças

48
Problemática geral e questões sobre ontologias

• Divisão
• como delimito as classes e os atributos?
• quais são as distinções que trazem valor
  agregado?
• Escopo
• qual conhecimento incluir?
• qual a fronteira do meu domínio?
• Granularidade
• até que nível de detalhe modelar os domínio?
• problema da ramificação?
• Validação
• como avalio a qualidade do modelo?
• como escolho entre várias modelagem alternativas
  (as vezes propostas por pessoas diferentes)?
• como identificar aspectos importantes que estão
  faltando?

49
Problemática geral e questões sobre ontologias

• Muito difícil responder a essas perguntas porque
• Almejados reuso e relativa independência de
  aplicação impedem ser guiado completamente pelos
  requisitos de uma aplicação restrita
• Para ontologias gerais de senso comum pior devido
  a imensidão em largura e profundidade do
  conhecimento a modelar
• Metodologias ainda incipientes
• Methontology
• Sensus http//www.isi.edu/natural-language/resour
  ces/sensus.html
• No entanto, já existe tentativa de padronização
  http//suo.ieee.org/
• http//www.fipa.org/

50
What is OCL? Definition and Role

• A textual specification language to adorn UML
  and MOF diagrams and make them far more
  semantically precise and detailed
• OCL2 integral part of the UML2 standard
• OCL complements UML2 diagrams to make UML2
• A domain ontology language that is
  self-sufficient at the knowledge level to
  completely specify both structure and behaviors
• A complete input for the automated generation of
  a formal specification at the formalization level
  to be verified by theorem provers
• A complete input for the automated generation of
  source code at the implementation level to be
  executed by a deployment platform
• OCL complements MOF2 diagrams to make MOF2
• An object-oriented declarative abstract syntax
  and semantics specification language that is
  self-sufficient at the meta-knowledge/meta-modelin
  g level
• OCL forms the basis of model transformation
  languages
• such as Atlas Transformation Language (ATL) or
  Query-View-Transform (QVT)
• which declaratively specify through rewrite
  transformation rules the automated generation of
  formal specifications and implementations from a
  knowledge level ontology
• OCL expressions are reused in the left-hand side
  and right-hand side of such rules
• To specify objects to match in the source
  ontology of the transformation
• To specify objects to create in the target
  formal specification or code of the transformation

51
What is OCL?Characteristics

• Formal language with well-defined semantics
  based on set theory and first-order predicate
  logic, yet free of mathematical notation and thus
  friendly to mainstream programmers
• Object-oriented functional language
  constructors syntactically combined using
  functional nesting and object-oriented navigation
  in expressions that take objects and/or object
  collections as parameters and evaluates to an
  object and/or an object collection as return
  value
• Strongly typed language where all expression and
  sub-expression has a well-defined type that can
  be an UML primitive data type, a UML model
  classifier or a collection of these
• Semantics of an expression defined by its type
  mapping
• Declarative language that specifies what
  properties the software under construction must
  satisfy, not how it shall satisfy them
• Side effect free language that cannot alter
  model elements, but only specify relations
  between them (some possibly new but not created
  by OCL expressions)
• Pure specification language that cannot alone
  execute nor program models but only describe them
• Both a constraint and query language for UML
  models and MOF meta-models

52
What is OCL?How does it complement UML?

• Structural adornments
• Specify complex invariant constraints (value,
  multiplicity, type, etc) between multiple
  attributes and associations
• Specify deductive rules to define derived
  attributes, associations and classes from
  primitive ones
• Disambiguates association cycles
• Behavioral adornments
• Specify operation pre-conditions
• Specify write operation post-conditions
• Specify read/query operation bodies
• Specify read/query operation initial/default
  value

53
OCL Motivating Examples

• Diagram 1 allows Flight with unlimited number of
  passengers
• No way using UML only to express restriction that
  the number of passengers is limited to the number
  of seats of the Airplane used for the Flight
• Similarly, diagram 2 allows
• A Person to Mortgage the house of another Person
• A Mortgage start date to be after its end date
• Two Persons to share same social security number
• A Person with insufficient income to Mortgage a
  house

1
2
54
OCL Motivating Examples
context Flightinv passengers -gt size()
lt plane.numberOfSeats
1
context Personinv PersonallInstances() -gt
isUnique(socSecNr) context PersongetMortgage(su
mMoney,securityHouse) pre self.mortgages.monthl
yPayment -gt sum() lt self.salary 0.3
context Mortgage inv security.owner
borrower inv startDate lt endDate
2
55
OCL Expression Contexts
56
OCL Contexts Default Value and Query
Specifications

• Initial values
• context LoyaltyAccountpoints integer init
  0
• context LoyaltyAccounttransactions
  Set(Transaction) init Set
• Query operations
• context LoyaltyAccountgetCustomerName()
  Stringbody Membership.card.owner.name
• context LoyaltyProgramgetServices()
  Set(Services)body partner.deliveredServices
  -gt asSet()

57
OCL ContextsSpecifying Invariants on Attributes

• The context of an invariant constraint is a class
• When it occurs as navigation path prefix, the
  self keyword can be omitted
• context Customer inv self.name Edward
• context Customer inv name Edward
• Invariants can be named
• context Customer inv myInvariant23
  self.name Edward
• context LoyaltyAccountinv oneOwner
  transaction.card.owner -gt asSet() -gt size()
  1
• In some context self keyword is required
• context Membershipinv participants.cards.Members
  hip.includes(self)

58
OCL Contexts Invariants for Disambiguating
Association Cycles and Plural Multiplicity

• Cycles of association with plural multiplicity
  are often underconstrained by class diagrams,
  thus not reflecting actual modeled domain
  semantics
• In the real world a person cannot use the house
  of another person as security for a mortgage
• context Personinv mortgages.security.owner -gt
  forall(onwnerPerson owner self)

59
Association Navigation

• Association navigation
• context Transaction def getCustomer()Custome
  r self.card.owner
• Attribute access
• context Transaction def getCustomerName()Str
  ing self.card.owner.name
• Abbreviation of collect operator that creates
  new collection from existing one, for example
  result of navigating association with plural
  multiplicity
• context LoyaltyAccount inv transactions -gt
  collect(points) -gt exists(pInteger
  p500)
• context LoyaltyAccount inv
  transactions.points -gt
  exists(pInteger p500)
• Use target class name to navigate roleless
  association
• context LoyaltyProgram inv levels -gt
  includesAll(Membership.currentLevel)
• Call UML model and OCL library operations

60
Generalization Navigation

• OCL constraint to limit points earned from
  single service to 10,000
• Cannot be correctly specified using association
  navigation
• context ProgramPartner inv totalPoints
  deliveredServices.transactions
  .points -gt sum() lt 10,000
• adds both Earning and Burning points
• Operator oclIsTypeOf allows hybrid navigation
  following associations and specialization links
• context ProgramPartner inv totalPoints
  deliveredServices.transactions -gt
  select(oclIsTypeOf(Earning)) .points -gt
  sum() lt 10,000

61
OCL Contexts Specifying Attribute Derivation
Rules

• context CustomerCardprintedName
• derive owner.title.concat(
  ).concat(owner.name)
• context TransactionReportLine String derive
  self.date transaction.date
• ...
• context TransactionReport inv dates lines.date
  -gt forAll(d d.isBefore(until) and
  d.isAfter(from))
• ...

62
OCL ContextsSpecifying Pre and Post Conditions

• context LoyaltyAccountisEmpty() Booleanpre
  -- nonepost result (points 0)
• Keyword _at_pre used to refer in post-condition to
  the value of a property before the execution of
  the operation
• context LoyaltyProgramenroll(cCustomer)pre
  c.name ltgt post participants
  participants_at_pre -gt including(c)
• Keyword oclIsNew used to specify creation of a
  new instance (objects or primitive data)
• context LoyaltyProgramenrollAndCreateCustomer(n
  String,dDate)Customerpost result.oclIsNew()
  and result.name n and
  result.dateOfBirth d and participant
  -gt includes(result)
• oclIsNew only specifies that the operation
  created the new instance, but not how it did it
  which cannot be expressed in OCL

63
Links BetweenOCL and UML Meta-Models
64
The OCL Expressions Meta-Model
65
The OCL Types Meta-Model
66
OCL Types

• Value Types
• UML primitive types (including user-defined
  enumerations)
• OCL collection types (even of user-defined
  classifiers ?)
• Their instances never change value
• ex, Integer instance 1 cannot be changed to
  instance 2, nor can string instance Lew
  Alcindor be changed to string instance Kareem
  Abdul-Jabbar, nor can enumeration Grade instance
  A can be changed to enumeration instance C.
• Object types UML classifiers
• Their instances can change value, i.e., the
  Person instance p1 can have its name attribute
  Lew Alcindor changed to Kareem Abdul-Jabbar
  yet remain the same instance p1
• OclAny
• Most generic OCL type, subsuming all others
• General reflective operations are defined for
  this type and inherited by all other OCL types

67
OCL Types

• Primitive data types (from UML) boolean,
  string, integer, real
• Type conformance rules
• t1 conforms to t2 if t1 lt t2 in type hierarchy
• t1 collection(t2) conforms to t3
  collection(t4) if t2 conforms to t4
• integer lt real
• Type casting
• Operation oclAsType(s) can be invoked on an
  expression of type g to recast it as a type s
• s must conform to g
• OclVoid
• Undefined value (similar to null values of SQL)
• Tested by oclIsUndefined operation of OclAny type

68
OCL Types Collections

• Collection constants can be specified in
  extension
• Set1, 2, 5, 88, Setapple, orange,
  strawberry
• OrderedSetblack, brown, red, orange,
  yellow, green, blue, purple
• Sequence1, 3, 45, 2, 3, Bag1, 3, 4, 3, 5
• Sequence of consecutive integers can be
  specified in intension
• Sequence1..4 Sequence1,2,3,4
• Collection operations are called using -gt
  instead of .
• Collection operations have value types
• They do not alter their input only output a new
  collection which may contain copies of some input
  elements
• Most collections operations return flattened
  collections
• ex, flattenSet1,2,Set3,Set4,5
  Set1,2,3,4,5
• Operation collectNested must be used to preserve
  embedded sub-structures
• Navigating through several associations with
  plural multiplicity results in a bag

69
OCL Semantics Encapsulation and Inheritance

• By default, OCL expressions ignore attribute
  visibility
• i.e., an expression that access a private
  attribute from another class is not syntactically
  rejected
• OCL constraints are inherited down the
  classifier hierarchy
• OCL constraints redefined down the classifier
  hierarchy must follow substituability principle
• Invariants and post-condition can only become
  more restrictive
• Preconditions can only become less restrictive

• Examples violating substituability principle
• context Stove inv temperature lt 200
• context ElectricStove inv temperature lt 300
• context Stoveopen()
• pre status StoveStateoff
• post status StoveStateoff and isOpen
• context ElectricStoveopen()
• pre status StoveStateoff and temperature
  lt 100
• post isOpen

70
OCL Expressions Local Variables

• Let constructor allows creation of aliases for
  recurring sub-expressions
• context CustomerCard
• inv let correctDate Boolean
  validFrom.isBefore(Datenow) and
  goodThru.isAfter(Datenow)
• in if valid then correctDate false
  else correctDate true endif
• Syntactic sugar that improves constraint
  legibility

71
OCL Library Generic Operators

• Operators that apply to expressions of any type
• Defined at the top-level of OclAny

72
OCL Library Primitive Type Operators

• Boolean host, parameter and return type boolean
• Unary not
• Binary or, and, xor, , ltgt, implies
• Ternary if-then-else
• Arithmetic host and parameters integer or real
• Comparison (return type boolean) , ltgt, lt, gt
  lt, gt,
• Operations (return type integer or real) , -,
  , /, mod, div, abs, max, min, round, floor
• String host string
• Comparison (return type boolean) , ltgt
• Operation concat(String), size(), toLower(),
  toUpper(), substring(ninteger,minteger)

73
OCL Library Generic Collection Operators
74
OCL Library Syntax of Loop Operators

• Loop operators (aka. iterator operations, aka.
  iterators)
• Common characteristics
• They are all hosted by an OCL expression of type
  collection
• They all take an OCL expression as input
  parameter (called the body of the loop)
• They optionally take as second parameter an
  iterator variable
• The return type of the body expression and the
  type of the iterator variable must conform to the
  type of the host collections elements
• Loop operators iterate over the elements of the
  host collection, applying the body expression to
  each one of them
• Distinguishing characteristics
• How they combine the body expression application
  into a new result collection

75
OCL LibrarySpecialized Collection Operators
76
Example of OCL Expressions with Loop Operators

• context LoyaltyProgram inv self.Membership.accou
  nt -gt isUnique(acc LoyaltyAccount
  acc.number)
• context LoyaltyProgram inv Membership.account
  -gt isUnique(acc acc.number)
• context LoyaltyProgram inv Membership.account
  -gt isUnique(number)
• Iterator variable clarifies that number refers
  to the number attribute of each collection
  element and not to the number of elements in the
  collection
• Loop expressions with reference to the iterator
  requires an iterator variable
• context ProgramPartner inv
  self.programs.parters -gt
  select(pProgramPartner p.self)

77
OCL Constraints vs. UML Constraints
context ClassicalGuitar inv strings-gt forAll(s
s.oclIsType(plasticStrings))
context ElectricGuitar inv strings -gt forAll(s
\ s.oclIsType(MetalStrings))
context ClassicGuitar inv strings -gt
forAll(type StringTypeplastic)
context Guitar inv type GuitarTypeclassic
implies strings -gt forAll(type
StringTypeplastic inv type
GuitarTypeclassic implies strings -gt
forAll(type StringTypeplastic
context ElectricGuitar inv strings -gt
forAll(type StringTypemetal)
78
OCL vs. Java

• Declarative specification of operation
  post-conditions in OCL is far more concise than
  corresponding implementation in mainstream
  imperative OO language such as Java
• This is due mainly to OCLs powerful collection
  operators
• Example OCL expression self.parters -gt
  select(deliveredServices -gt forAll(pointsEarned
  0))
• Corresponding Java code
• Iterator it this.getPartners().iterator()
• Set selectResult new HashSet()
• while( it.hasNext() )
• ProgramPartner p (ProgramPartner) it.next()
• Iterator services p.getDeliveredServices().ite
  rator()
• boolean forAllresult true
• while( services.hasNext() )
• Service s (Service) services.next()
• forAllResult forAllResult
  (s.getPointsEarned() 0)
• if ( forAllResult )
• selectResult.add(p)
• return result