Download - Ontologies Reasoning Components Agents Simulations Object-Oriented Knowledge Representation Jacques Robin

OntologiesReasoningComponentsAgentsSimulations

Object-OrientedObject-OrientedKnowledge RepresentationKnowledge Representation

Jacques Robin

OutlineOutline

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

Review of Key Review of Key Object-Orientation ConceptsObject-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

InheritanceInheritance

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

Software Engineering DistributedSystems

A Brief History of OO LanguagesA Brief History of OO LanguagesProgramming Knowledge

RepresentationDatabases

Simula

Sketchpad

Java

C#

Semantic Networks

DescriptionLogics

Frame Logics

SQL’99

Frames

Smalltalk

1965

2006

C++

OQL

UML1

OCL1MOF1

OCL2UML2MOF2

Semantic Web

OWL

SWSL

CHORD

Motivation for OO Motivation for OO in Software Engineeringin 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)

Initial Motivation for OOInitial Motivation for OOin Knowledge Representationin 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

CategoriesCategories

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

Properties of CategoriesProperties 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

Semantic NetworksSemantic 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

Semantic Networks: ExamplesSemantic Networks: Examples

Network with four categories and four instances

Network with N-ary relationship reified as a category instance

Semantic Networks x CFOL: Semantic Networks x CFOL: ExamplesExamples

(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)

Early Semantic NetworksEarly 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

Late Semantic NetworksLate 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

FramesFrames

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

FramesFrames

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.)

Frames: exampleFrames: 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: 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: 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

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 UniversityFrame: Student in KB University

Frame: GradStudent in KB University Is-a: Student Slot: degree Default: Bachelor


Frame: Undergrad in KB University Is-a: Student


Frames x CFOL: ExampleFrames x CFOL: Example

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: 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






Frames: limitationsFrames: 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.

UML as KR LanguageUML 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

UML Class DiagramUML 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)

Classes: AttributesClasses: 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!

Classes: OperationsClasses: 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!

AssociationsAssociations

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!

Association ClassesAssociation 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

Elevatorcontrol

Queue Elevator

Difference with: ?

4

Ternary AssociationsTernary 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

Aggregation AssociationsAggregation 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

Composition AssociationsComposition 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

Class generalizationsClass 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 inheritance

and overriding Instances of a sub-class must

satisfy all the constraints on all its super-classes (principle of substitutability)

Abstract ClassesAbstract 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

Generalization SetsGeneralization 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

UML Object DiagramsUML 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

UML x Semantic Networks: ExampleUML x Semantic Networks: Example

Semantic Network Corresponding Class Diagram

UML x Semantic Networks: ExampleUML x Semantic Networks: Example

Mammals

femalePerson

gender = female

malePerson

gender = male

Person

gender: gendershasMother

Legs0..2

sisterOf

john:malePerson :Legsmary:femalePersonsisterOf

:femalePerson

hasMother hasMother

Missing: OCL constraint defining semantics of sisterOf association has derived from hasMother(an hasFather) associations

<<enumeration>>Gendersfemalemale

transsexual





Frame: BasCourse in KB University Is-a: Course Slot: taughtBy Type: Professor

Frame: BasCourse in KB University Is-a: Course Slot: taughtBy Type: Professor



Frame: Student in KB UniversityFrame: Student in KB University





UML x Frames: ExampleUML x Frames: Example

KBUniversity

CourseStudent

AdvCourse BasCourse

<<enumeration>>Degreesbachelormaster

phd

Professor

degree = phd

GradStudent

degree = bachelor

1..*

0..20

1..*

Lecturer

taughtBy

enrolls

1..*

Undergrad

Frame type constraint in red best modeled as OCL constraints

Comparison TableComparison Table

Intuitive

Graphical

Syntax

Well-Founded

ConstructsExpressivity KR Layer

Formal

Semantics

Available

Inference

Engines

Standard

Widely Used

Semantic Networks

Y N StructuralKnowledge

ImplementationN Y N

Frames N NStructural

Behavioral as Code

Knowledge +/- Implementation

N Y N

UML2(w/ OCL)

Y Y

Structural

Behavioral as Model

Temporal

Knowledge N N Y

CFOL N Y

Structural

( unintuitively )

Behavioral through Logic Programming

Temporal through

Axiomatization

Knowledge +/-

FormalizationY Y +/-

Meta-Object Facility (MOF)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

Relationship between MOF and UMLRelationship between MOF and UML

...

UML2 Infrastructure

ClassesAttributes

TypesPackages

...

Basic

Associations...

Constructs

...

UML2 Superstructure

ActivitiesActionsStates

Transitions...

Behavioral

ComponentsPorts

...

Structural

merge

merge

...

MOF

Reflection metamodelsmetamodels

metamodels

Applicationmodels

Classifier

Simplified MOF Meta-Model of itselfSimplified MOF Meta-Model of itself

Element Relationship1..*

Generalization

NamedElement

TypedElementType Constraint

Feature

BehaviorallFeature

RedefinableElement

redefined

*

Operation Parameter

Classifier

*

Association

StrcuturalFeature

Class

Property

AssociationClass

*

ValueSpecification

*

InstanceSpecification

Simplified MOF Meta-Model of itselfSimplified MOF Meta-Model of itself

InstanceSpecification

Parameter*

Generalization

*

AssociationClass

AssociationClass

DataType

PrimitiveType Enumeration

Interface*

1..*Relationship

Relationship

NamedElement

Constraint

*

TypedElementType

Property

ValueSpecification

Classifier

Feature Classifier

RedefinableElement

*

Element

*

NamedElement

BehaviorallFeature StructuralFeature

Operation

*

MOF Meta-Model ofMOF Meta-Model ofEarly Semantic NetworksEarly Semantic Networks

Node Link

SingleValue

Specification

MultipleValue

Specification

AttributeSpecification

*

<<enum>>Certainty

Level

KnownDefault

OOP/OOSE

Classes& Objects

OOP/OOSEattributes& other

associations

*

IS-A PART-OF

OOSEaggregation & composition associations

OOP/OOSEsubclass & instance

relationships

MOF Meta-Model of FramesMOF Meta-Model of Frames

Frame Slot Facet

SingleValue

Specification

TypeConstraint

MultipleValue

Specification

CardinalityConstraint

ProceduralAttachment

InputParameter

ReturnValue

HostLanguageProcedure

* *

ConstraintValue

Specification

*

<<enum>>Certainty

Level

KnownDefault

Min: IntMax: Int

MissingReadWrite

<<enum>>Trigger

OOP/OOSE

Classes& Objects

OOP/OOSEAttributes

& Associations

No corresponding

concepts in OOP/OOSE

OOP/OOSEMethods

& Activities

OOSEConstrain

ts

IS-A

OOP/OOSEsubclass & instance

relationships

Simplified MOFSimplified MOFMeta-Model of UML ClassifiersMeta-Model of UML Classifiers

Classifier

Type

ClassInterface Association

AssociationClass

DataType

PrimitiveType Enumeration

Feature

StructuralFeature BehavioralFeature Parameter

Operation ConstraintProperty

Boolean Integer String AssociationEnd AttributeReal

generalizes

Simplified MOF Meta-ModelSimplified MOF Meta-Modelof UML Relationsof UML Relations

Association

AssociationClass

Generalization

Aggregation

Composition

Relation

Dependency

RealizationQualifiedAssociation GeneralizationSet

PowerType

Download - Ontologies Reasoning Components Agents Simulations Object-Oriented Knowledge Representation Jacques Robin

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