LOGICAL CALCULUS AND HILBERT-HUANG ALGEBRA

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Since the discovery of Hilbert logic and Hilbert-Huang Algebra by James Kuodo Huang (AKA Kuodo J. Huang) in 2005, the meaning of "Logic calculus or logical calculus" has become a new theory and technology. Hilbert logic system can be any useful extension of boolean logic systems in which fundamental theory of logic can be proven. As a matter of fact, it is the first proven mathematical theory to build reliable computerized systems or theoretical systems.

Calculus (numerical calculus) has become a standard mathematical course for science students in colleges for a long time. Every college student of natural science has to take Calculus related courses. There are two mathematicians to be credited to discover the Calculus. One is Isaac Newton who is also to be known as physicist. The other one is Gottfried Leibniz who is also known to be a logician. Because both Gottfried Leibniz and Isaac Newton discovered the fundamental theorem of calculus. All scientists have calculated their own integrals using fundamental theorem of calculus for a long time. We define this calculus to be numerical calculus or number calculus. Logical calculus began with the discovery of Boolean algebra by an English mathematician George Boole in 1854. The discovery of the fundamental theorems of logic was only very recently by James Kuodo Huang in 2005 and published in 2006. James Kuodo Huang discovered Hilbert-Huang algebra which is an extension of Boolean algebra so that the fundamental theorem of logic can be proven. In other words James Kuodo Huang is the one who has discovered and has proven the Fundamental Theorems of Logic. We define logical calculus to be logical calculus in Hilbert logic theory. Furthermore James Kuodo Huang had also defined logical integral, science integral, and engineering integral in his Hilbert logic theory. He also had given examples of logic integrals, science integrals and engineering integrals in the following journals below.

Dr. James Kuodo Huang had pointed out that many scientists and mathematicians, especially David Hilbert and his followers, had developed a lot of theories which had made him develope his Hilbert logic theory becoming easier.

The most useful applications of Huang's "Hilbert logic theory" are two-valued Hilbert logic theories. Dr. James Kuodo Huang had given and had proven three basic two-valued Hilbert logic theories associated with their correspondent Hilbert-Huang algebras. Most of the applications of Hilbert-Huang logic to mathematics, sciences, and engineering can be starting from there on. We have to acknowledge that "Hilbert logic theories" developed by James Kuodo Huang is one of the best and useful theories to the applications for mathematics, sciences, and engineering to build reliable systems (where the systems can be either computerized application systems or theoretical systems).