So, they are abstracted to form a superclass: 
Superclass=(SIDy,CSy,CMy) (4) 
Here SID is the identifier of the superclass. 
After defining the Superclass, the Classy and 
Classy are written: 
Classy=(CIDy,CSg,CMp) (5) 
Classy=(CIDy,CS¢, CMG) 
Class] and Class» are called subclasses of the 
Superclass. 
Subclass and superclass are related by an is a 
relation. For example, the class building is the 
superclass of the class hotel because a hotel is 
a building. A subclass may also have a further 
classification. The building/hotel generalization 
can be extended with the classes inn, guest house 
and motel etc. While hotel is a subclass of 
building, it can be at the same time a superclass 
of guest house. 
2.2.2 Inheritance In generalization 
hierarchies, some of the properties and methods 
of the subclasses depend upon the structures and 
properties of the superclass(es). Inheritance is 
a tool to define a class in terms of one or more, 
other more general classes. Properties and 
operations which are common for superclass and 
the subclasses are defined only once, and the 
properties and operations of the superclass are 
inherited by all objects of the subclasses. 
Inheritance is the transitive transmission of the 
properties from one superclass to all related 
subclasses, and to their subclasses, etc. But 
subclasses can have additional, specific 
properties and operations which are not shared by 
the superclass. This concept is very powerful, 
because it reduces information redundancy and 
maintains integrity. 
The inheritance can be single or multiple. Single 
inheritance requires that each class has at most 
a single immediate superclass. Figure 1 has shown 
an instance of single inheritance. 
  
building 
| 
residence 
it 
city residence| fural residencd 
  
  
  
  
  
  
  
  
  
  
  
  
  
Fig. 1 An instance of single inheritance 
In multiple inheritance, one subclass has more 
than a single direct superclass, such as the 
subclass hotel may have superclass building and 
superclass business. 
Suppose: 
Class3=(CID3,CSy,CSp, CSc, CMy,CMp, CM) (6) 
Here C34, CSg, CM,, CMp, are in common with two 
other classes. Therefore two superclasses can be 
constructed: 
Superclass;-(SID, ,CS4,CMA) (7) 
774 
Superclassy=(SIDy,CSg,CMp) 
In order to acquire all information and methods, 
Classy must inherit the data and operations from 
Superclass; and Superclass». 
An example from geography shows how multiple 
inheritance often combines two distinct 
hierachies. One hierarchy is determined by the 
separation of artificial and natural 
transportation links, whereas the other hierarchy 
distinguishes water bodies. Classes with 
properties from both hierarchies are channels, 
that are artificial transportation links and 
water bodies, and navigable rivers, whereas ponds 
belong only to one hierachy(Fig. 2) 
      
   
   
transportation links 
artificial. natural | 
transportation transportation 
channel 
   
  
   
Fig. 2 An example of multiple inheritance 
2.3 Association,Aggregation and Propagation 
2.3.1 Association An association relates two or 
more independent objects by considering the 
relation among objects as a higher level set 
object. For example, parcel 1 and parcel 2 all 
belong to Mr. Neilbsen, they can be grouped as 
Neilbsen’s parcel. Parcel 1 and parcel 2 are 
called members of Neilbsen’s parcel. Suppose: 
Objecty=(ID;,S4,Sp,M) (8) 
Objecta=(ID9,S4,Sç,M) 
A new object contains Object, and Object» : 
Object3-(ID3, S4, Object; ,Objecto,M) (9) 
In this case, the Object and Objecto are writen: 
Object1=(IDy ,Sp,M) (10) 
Objectg=(ID9,Sç,M) 
Here Object] and Object, are termed component 
objects. Hence, this abstraction is referred to 
as the member of relation. 
2.3.2 Aggregation A similar abstraction 
mechanism to association is aggregation which 
models composed objects. i.e., objects which 
consist of several other objects. Several objects 
can be combined to form a semantically higher 
level of object where each part has its own 
functionality. The operations and properties of 
an aggregate are not compatible with those of 
parts. For example, the class building is an 
aggregate of all walls, doors, windows and roofs 
which are parts of it. 
There are two different component objects: 
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