Created on March 1, 2013, 6:51 p.m. by Hevok & updated by Hevok on May 2, 2013, 4:38 p.m.
Ontologies need to be represented. For this, first of all one has to identify Classes. Classes are sets of Things. They represent Concepts. They can be either concrete specific Objects of the real World or they can be Abstract Concepts. The individuals populating these Classes share certain attributes. So the have something in common and they therefore form a Class. For instance, the Class of all Students, or the Class of Professors or even more general the Class of all Persons/Humans. The Attributes describe the Class and can be given by name-value Pairs for example. Then one can describe this classes in a more formal or informal way. For an Ontology is more important to make a formal Description. Ontologies require formal specifications. Informal means that it is only given in natural language of which the Problem is that Natural Language can not be correctly be understood by Machines, therefore one has to give a more formal definition. One can have a informal description but in the end one has to come back to Logic.
The address contains the name, title, and place of residence of the person addressed.
Address:
Classes, Relations and Instances
Classes itself are related to other Classes. For example the Classes of Professors and Students are both subclasses of the Person. A Professor is a Person and a Student is also a Person. ON the other hand a Student has one or more Addresses. The Class Person is related to the Class of all Addresses by and has an Relation (to address here). A Professor gives a Lecture and a Student visits a Lecture. So these two Classes are connected to the same Class Lecture, but by a different Relation. The Lecture is a subclass of all the Courses that are available at the University.
A formal definition what are Classes is can be given by Set Theory.
Formal Definition:
Sets m1,...mn
Relations R u m1 x ... m2
When the Classes are represented as Sets (from m = 1 to m = n), then a Relation R is defined as a Subset of the Cartesian Product of all these Sets.
In the end all the Relations can be specified as Class Attributes, but the Attribute Values are other Classes.
One can define more Knowledge besides Classes and the Relations among those Classes as one can but further knowledge on those Relations. The Relations and Attributes can be constrained. One can determine which Values are allowed and which are not allowed, what make Sense and what does not make Sense.
Given the Class Person, Woman and Men Both Woman and Man are subclasses of Person, but on the other hand one Individual can only be a Woman or a Man. A man can not on the same time be an Entity of the other Class Woman. These two classes are disjoint which means when one does an Intersection between woman and man then the result should be an empty Set. This is a Constrain that one can put between two Classes. The relation cans say that no individual can be at the same time be in both of these Classes.
On the other hand one can put number Restrictions. For instance, there is one to one Relation (1:1) between a Person and a Student on the other hand a person can have more than one address which is a one to n Relation (1:n).
These constraints are more Knowledge and Semantics that can be put on Relations or specific Attributes.
With Classes, Relations and Constraints, put together one can form Statements and Assertions. So one can make a logical Statement. A special Case of this Statements are Axioms. An Axiom is Knowledge that can not be expressed simply with the Help of Other existing Components. So one need these Axioms to make Sense, but it is not part of the formal Definition of the basic Sets of Constructs of Classes or Relations. It is something like a Rule. For example it is not possible to lecture two Courses at the same time, because than one has to be two Persons which is not possible.
Classes are sets of Individuals. Individuals can be Member of a Class. Individuals may include concrete Objects like People, Animals, Robots or anything else as well as Abstract Objects like Numbers and Words and even Abstract Concepts like Love or Revenge.
For example given a Class Seminar and a Specific Instance of this Class which is a Seminar and also one has specific Attributes or Relations to Attributes that means it takes place at a specific Time and is located at a specific Location. This is an Instance, Instances populate the Classes and they populate the Ontology. -takes place at-> Friday 10.00 am Course <-is subclass of- Seminar <-is a- Seminar Constructing a Digital Decipher Machine -is located at-> Chat Room number 5
This is only the basics and the Conceptional model. Different Ontology types and ontology examples need to be created. They following question need to be addressed How to represent knowledge with the Help of Logic? This is very important one need this formal model and the Logic to make Calculations and to be able to make automatic way so Inductions or Deductions, which means that one is able to draw Conclusions and one can make implicit knowledge, that is given somewhere in a knowledge base, explicit and one can deduce now knowledge.
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