1. Object-Oriented Knowledge Representation
Jacques Robin

2. Outline Review of object-oriented concepts
History of object-oriented languages
UML2 as a knowledge representation language

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. History of Object-Oriented Languages
Software Engineering
Programming
Databases
Knowledge
Representation
Distributed
Systems
1965
Simula
Sketchpad
Smalltalk
UML1
Semantic Networks
Frames
Description
Logics
C++
OQL
Java
Frame Logics C#
SQL’99
OCL1
MOF1
OWL
OCL2
UML2
MOF2
Semantic Web
CHORD
SWSL
2006

6. UML as KR Language Class diagram: Activity 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

7. 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-Generalization relationship
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)

8. 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!

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

10. Associations Association: Fields: Navigation:
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
Navigation:
Role if present
Otherwise destination class name
Associations for KR: as many fields as possible!

11. N-ary Associations Single association between N classes
Different from N-1 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

12. 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

13. Aggregations and Compositions
Association with “part-whole” semantics
Associate composite class to its building blocks
Static, definitional characteristic of the “whole” class
Composition:
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

14. 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 inheritance and overriding
Instances of a sub-class must satisfy all the constraints on all its super-classes (principle of substitutability)

15. 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

16. 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

17. Power Types
Generalization set of a super-class defined in terms of a class associated to it
Subclasses of each power type inherits features from the associated class of the super-class that defines the power type
Allows separation of orthogonal concerns
Useful for MDA as a rich modeling element

18. 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

19. 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

20. Simplified MOF Meta-Model of itself
NamedElement
BehaviorallFeature
StructuralFeature
Operation
Parameter *
Property *
Classifier
Feature
TypedElement
Type
ValueSpecification
1..*
Relationship
RedefinableElement *
NamedElement
Element *
InstanceSpecification
Constraint *
Generalization *
Association
Class
AssociationClass
DataType
PrimitiveType
Enumeration
Interface