Chapter Five 5.3 of Concept Algebra |
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Chapter Five 5.3 of Concept Algebra Shilong Wu, April 15, 2008
Chapter 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Chapter 3 3.1 3.2 3.3Chapter 4 4.0 4.1 4.2Chapter 5 Foundation of Solving Concept Equation5.1 Solving Concept Equation of General Form 5.2 Normal Model of Concept Equation 5.3 Least Solution Theorem and Most Solution Theorem in Normal Equation 5.4 Solving Concept Equation in Normal Model
In the procedure of building up and studying the Wu algebra <2><3><4>, I found the General Wu algebra <4> could be to express the relationship among the concepts completely. And the new propositions can be calculated from known concept expressions. So the General Wu algebra renames the Concept algebra.
The concept algebra is to research the relationship among the concepts these are abstraction of the objects. So we also can say the concept algebra is to research the relationship of the objects. However the concept is also the least element of the judgment. And the category is a concept after classifying the objects. So the concept is the same base of the Set and the Logic. As we know the basic relation between two objects A and B is “A is B”, “A is not B”, “A includes B”, “A does not include B”, “A relates with B” and “A does not relate with B” and so on. The concept is the description of the object, so the relations among the concepts also have the similar relation of the objects. For example “concept A is same as concept B” can be expressed as following expression on the concept algebra A <=> B Here the operation <=> that is one operation on concept algebra can be explained as “be”, “equal to” or “be the same as”. The operation !<=> that also is one operation on concept algebra is dual operation of <=> can be explained as “be not”, “equal to in complement of”. For example “concept A equals to in complement of B” can be expressed as A !<=> B …… The following post is Chapter Five 5.3 of concept algebra (or General Wu Algebra). Any questions touch me, please.
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