The stable logic analysis model of a complex system or a steady multilateral system with two non-compatibility relations has been used in medicine, physical, finance, intelligent control and automation. Its main purpose is to investigate the structure of stable logic analysis corresponding to a general complex system.

Two stable logic analysis models of complex systems have been investigated, the causal model with compatibility relations, the causal model with non-compatibility relations. This article focuses on the causal model with non-compatibility relations.

Zhang’s theories, multilateral matrix theory [1] and multilateral system theory [2], give a new and strong mathematical reasoning method from macro (Global) analysis to micro (Local) analysis. He and his colleagues have made some mathematical models and methods of reasoning [3- 18], which make the mathematical reasoning of Traditional Chinese Science (TCS, or Oriental Science) possible [14] based on “Yin Yang Wu Xing”(阴阳五行) Theory [19]. This paper will use steady multilateral systems to demonstrate the treatment principle of Traditional Chinese Medicine (TCM): “Real disease is to rush down his son but virtual disease is to fill his mother”(实则泻其子, 虚则补其母) and “Strong inhibition of the same time, support the weak”(抑强扶弱).

The article proceeds as follows: Section 2 contains basic concepts and main theorems of steady multilateral systems while both intervention rule and self-protection rule based on the multilateral systems are demonstrated in Section 3. Some discussions are given in Section 4 and conclusions are drawn in Section 5.

In the real world, we are enlightened from some concepts and phenomena such as “biosphere”, “food chain”, “ecological balance” etc. With research and practice, by using the theory of multilateral matrices [1] and analyzing the conditions of symmetry [1,3] and orthogonality [4-6,13,18] what a stable system must satisfy, in particular, with analyzing the basic conditions what a stable working procedure of good product quality must satisfy [12,18], we are inspired and find some rules and methods, then present the logic model of analyzing stability of complex systems [8-11]-steady multilateral systems [14,15]. There are a number of essential reasoning methods based on the stable logic analysis model, such as “transition reasoning”, “atavism reasoning”, “genetic reasoning”, etc.

The fundamental issues of any complex system are the problems of stability. But for many stable problems, the usual methods in Western science can not be used (see [20]). In this case, however, many methods in TCS can be always done.

For example, it is will known that Western medicine is in the microscopic approach to disease and always make directly medical treatments on disease organs. By Theorems 3.1, 3.2, 3.3 and 3.4 in this paper, it can be found that the method always destroys the original human being’s balance and has none beneficial to human’s immunity. Western medicine can produce pollution to human’s body, having strong side effects. Excessively using medicine can easily paralysis the human’s immunity, which AIDS is a product of Western medicine. Using medicine too little can easily produce the medical and drug resistance problem.

But TCM studies the world in the macro point of view and always makes indirectly medical treatments on disease organs. By Theorems 3.1, 3.2, 3.3 and 3.4 in this paper, it can be found that the method’s target is in order to maintain the original balance of human being and in order to enhance the immunity. TCM believes that each medicine have one-third of drug. She never encourages patients to use medicine in long term. TCM has over 5000-year history. It almost has not side effects or medical and drug resistance problem.

The mainly difference between TCS and Western Science is that Western science only considers Axiom (or Hypothesis) but TCS doesn’t. The key to intelligent control and automation should be to study the issues of nonAxiom (or non-Hypothesis). This paper’s drawbacks are just in order to solve these problems. The ideas are due to TCS.

1) What is “Stable”? Western Science defined it as “A price or rate which changes only slowly, opposite of volatile.” But in TCS, it is specifically defined as that there is at least a causal chain (defined in (1) of Section 2.5) in a system such that the system can be survival. The definition given in TCS, for a relatively stable complex system, is most essential. If there is not the chain or circle, then will be some elements without causes or some elements without results in the system. Thus, this system is to be in the state of finding its results or causes, and there is not any stability to say.

Liao, et al. [20] has proved that for the problems of stability, many methods in Western Science can not work. Such as analysis of variance (ANOVA), regression analysis, non-five index method, etc. But a lot of methods due to TCS can be used to solve the stable center of any high-dimensional function. Such as, the global sensitivity analysis based on ANOVA [21], the Global-Local algorithm [12] and the procedure of searching zero effects [22], etc. The works were received the prestigious Science Advance First-Degree Prize of China Army in 2006.

2) What is “complex system”? Western Science defined it as “Consisting of many diverse and autonomous but interrelated and interdependent components or parts linked through many (dense) interconnections. Complex systems cannot be described by a single rule and their characteristics are not reducible to one level of descripon. They exhibit properties that emerge from the interaction of their parts and which cannot be predicted from the properties of the parts”. But in TCS, it is specifically defined as a system which has at least one non-compatibility relation in a logic analysis model of a system— multilateral system [2,15] (Defined in Section 2.4).

It is will known that the body of human is a complex system. But in Western Medicine, the existence of both side effects or medical and drug resistance problems proves it non-reasonable to some extent. But in TCM, there exist a lot of good methods to solve the problems of human body, such as theories of “Wu Yun Liu Qi”(五运六气, environment of energy), “Jing Luo”(经络, meridian/ hannel system),” “Zang Xiang”(藏象 or 脏腑, Zang Fu organ), etc. We [7-12,14-17] want to study the complex system by using these methods in TCS instead of the ones in Western science, such as “emergence”, “control”, “model”, “distribution”, and so on. It is because the methods in Western science only involved the compatibility relations under one Axiom system, and only concern how to attain the energy of complex system through study or observations at the position of standing on our own but do not show how to afford the energy for the complex system through logic or practice.

3) What is “Science”? Western science defined it as “knowledge attained through study or practice” but TCS only considers it specifically and carefully as “knowledge about energy attained and afford”. Only to know how to attain energy at the position of standing on our own but not to know how to afford energy is not a complete “Science”. What can kill the “Science” is need to know and need to protect it as more as possible. One can do by logic or practice but only by observations.

For example [14], Western Medicine is different from TCM because the TCM has a concept of Chi (or Qi, 气) as a form of energy. It is believed that this energy exists in all things (living and non-living) including air, water, food and sunlight. Chi is said to be the unseen vital force that nourishes one’s body and sustains one’s life. It is also believed that an individual is born with an original amount of Chi at the beginning of one’s life and as one grows and lives, one acquires Chi from eating and drinking, from breathing the surrounding air and also from living in one’s environment. And the one also affords Chi for the human body’s Meridian/hannel system and Zang Fu organ which form a parasitic system of human, called the second physiological system of human. The second system of human controls the first physiological system (anatomy system) of human. An individual would become ill or dies if one’s Chi in the body is imbalanced or exhausted. The concept is summarized as the energy theory of multilateral systems (Defined in Section 3.1). But there do not exist these concepts in Western science.

4) What is “Axiom”? Western Science considers it as “Hypothesis” but TCS considers it specifically and carefully as “Tao(Yin and Yang)”(道(阴和阳)), anything can be decomposed into two parts which have two kinds of opposite relations), or “You Sheng Yu Wu”(有生于无, anything is born by nothing), or “Bu Yan Shi Jiao”(不言施教, teaching cannot be made by suppose).

Lao Tzu, was one of the earliest philosopher in the Chinese history, who describes the marvel of Tao as an evolving force that operates throughout the universe. Tao is the first cause of the universe. Lao Tzu said that Tao is ‘the way’ and he emphasized this in the first verse of his Tao Teh Ching [23] that: “道可道, 非常道, 名可名, 非常名, 无名天地之始, 有名万物之母 (老子道德经, 第一章)”.

Translated as:

“The Tao that can be said is not the everlasting Tao.

If a name can be named, it is not the everlasting name.

That which has no name is the origin of heaven and earth;

That which has a name is the mother of all things”.

(Lao Tzu’s Tao Teh Ching, Verse.1) [24].

Therefore Tao is always without a name and that it is the origin of heaven and earth. Tao can also be said to be the “Absolute” that it can be said to be the movement and a stillness without a beginning, Yin and Yang (also known as Tai Chi in Figure 4) are things that can be said to be without a beginning.

The Tai Chi (Ultimate Principle of Existence) involved “The two dynamic powers” (the white space represents the Yang and the black space represents the Yin) exists in equilibrium and from which a coordinated and vigorous force is produced. This classic symbol for Yin and Yang appears like a pair of fish swimming in a circle around

each other; the tail of one is formed from the head of the other. Here, we can see that Yin-Yang are born out of each other and are transformed into each other. Each of the Yin-Yang contains the seed of the other; there is a tiny seed circle of dark Yin contained in the white part of Yang, as there is a seed circle of white Yang contained in the darkness of Yin. Tao is the force, which flows through all lives. Each person is to nurture the breathing or what is also known as the integral life force (“Chi” or “Qi”) that has been given to him/her. Unlike Western thinking, time is not linear but cyclical. And overall, each and every Taoism believer’s goal is to align him(her)self, by having a balance (the perfect sense of balance is embodied in the idea of Yin Yang) or being harmonious with the Tao.

In the universe, there should always be a balance of nature. Yin (female) and Yang (male) are always at work, and there should be a good balance between them; and hence the avoidance of extremes. This is indeed what the concept of TCS, which is anchored in Taoism roots, is summarized as the multilateral systems (Defined in Section 2.4) (see [2,14]).

5) What is “reasoning”? Western Science considers it as the reasoning under one Axiom system such that only compatibility relation reasoning researched on. But TCS mainly researches the reasoning among many Axiom systems in nature (or do not consider any Axiom system or see it nothing, or “You Sheng Yu Wu”(有生于无), anything is born by nothing) and mainly considers the noncompatibility relations between different Axioms. The noncompatibility relations are more important than compatibility relations if they are considered at same time. Lao Tzu reputed the condition of reasoning to be “Bu Zi Sheng”(不自生, not their own definition, then their reasoning and research ).

We have seen simple example of reasoning. If we know: Robins are birds. All birds have wings (Axiom). Then if we ask: Do robins have wings? “Yes”. Some reasoning (albeit very simple) has to go on answer the question. But, in TCS, one believes that Robins which are birds may be not to have wings. The one believes that the Axiom system may be not true because the Axiom is our Hypothesis or observations and there may be other Axiom system in which birds have not wings. The one mainly considers the relationship between the birds and its energies.

In general, any multilateral system (defined in Section 2.4) is a reasoning model in TCS because it is defined by a set, which is independent of the reasoning procedure, and not defined by the reasoning itself. But in Western science, almost all reasoning is defined by itself, for example, by one Axiom system obtained by observations. In other words, it is born by itself.

6) What is “causal model”? Western science defined it as “Estimating approach based on the assumption that future-value of a variable is a mathematical function of the values of other variable(s). Used where sufficient his torical data is available, and the relationship (correlation) between the dependent variable to be forecasted and associated independent variable(s) is well known”. But TCS mainly researches the causal model among many Axiom systems in Nature and mainly considers the causal model of non-compatibility relations which is more important than ones of compatibility relations if they are considered at same time. In other words, TCS mainly considers the causal among three relations, such as “Yang” relation: the neighboring relations, as beneficial, harmony, obedient, loving, etc.; “Yin” relation: alternate relations, as harmful, conflict, ruinous, killing, etc.; as well as a general equivalent category, “Tong Lei”(同类): the compatibility relation but seeing it as an equivalent relation, as similarly, family, brother, under the same Axiom system, etc.

Zhang, et al. [2,8-11] first consider the stable structure of the logic model with causal effects between two noncompatibility relations which is similar to the theory of “Yin Yang Wu Xing” in TCS. The concept of causal model has been further explained and extended to construct the generalized causal model—multilateral system (Defined in Section 2.4) in this paper. There exists none the idea in Western science.

7) What is “symmetry”? The outstanding mathematician Hermann Weil highly evaluated the role of symmetry in modern science: “Symmetry, as though is wide or narrow we did not perceive this word, there is the idea, with the help of which a man attempted to explain and to create the order, beauty and perfection”. But in TCS, it is simply defined as the neighboring relations (Defined in Section 2.2).

Global sensitivity analysis in symmetry has been first considered in [1]. Any high-dimensional function can be decomposed into a sum of some symmetrical functions based on the systems of orthogonal idempotents [3] such that these symmetrical functions are orthogonal one another [21]. The methods due to TCS can be also used to solve the causal problems of the neighboring relations (Defined in Section 2.2), such as global sensitivity analysis in symmetry based on ANOVA [1,21], Global-Local Algorithm in symmetry [1,12] and procedure of searching zero effects in symmetry [22], and so on. But there exists none the idea in Western science.

8) What is “orthogonal”? Western science defined it as “In geometry, orthogonal means ‘involving right angles’ (from Greek ortho, meaning right, and gon meaning angled). The term has been extended to general use, meaning the characteristic of being independent (relative to something else). It also can mean: non-redundant, nonoverlapping, or irrelevant. In computer terminology, something—such as a programming language or a data object—is orthogonal if it can be used without consideration as to how its use will affect something else”. But in TCS, it is simply defined as the alternate relations (Defined in Section 2.2).

Global sensitivity analysis in orthogonality has been also first considered in [1]. Any function with high-dimensional variable can be decomposed into a sum of functions with low-dimensional variable such that these functions are orthogonal one another. The methods due to TCS can be used to solve the causal problems of the alternate relations, such as Global sensitivity analysis in orthogonality based on ANOVA [1,21], Global-Local algorithm in orthogonality [1,12] and procedure of searching zero effects in orthogonality [22], and so on.

Western science studied the global sensitivity analysis in orthogonality by using the methods of Monte Carlo and quasi-Monte Carlo algorithms. Wang et al. [18] have proved that the method of using orthogonal arrays is more optimal than those in Western science. The procedure in [18] is due to the theories of the “Yi Jing”(《易经》), the “Ming Xiang”(命相) and the “Fend Shui”(风水) of China.

Construction of orthogonal arrays in Western science is always to use the theory of group. But in TCS, the images concept of Lao Tzu is considered as the origin or beginning of anything. Similarly to the images of Tao, many new concepts have been found, such as, matrix images [4], generalized difference matrices [25] and generalized orthogonal arrays [26] (orthogonal balance block design [1], or balance block orthogonal arrays [27]), and so on. Many new constructing methods of orthogonal arrays have been obtained, such as add, subtract, multiply, divide and replace. They are composed of five classes [4-6,12,13] by the idea of “Wu Xing”. We believe they are all ones because by Theorem 2.5 all complex system can be decomposed into five classes with non-compatibility relations. The works were received the prestigious Innovative Teaching and Technology First-Degree Prize of China in 2010.

9) What is “Intelligent”? Western science defined it as “Intelligence is the system’s level of performance in reaching its objectives”. But in TCS, it is simply defined as the system’s level of performance in order to know the laws or images of the Tao.

In TCS, the intelligent knowledge mainly is due to the Tao Teh Ching and the “Yi Jing”. The Tao Teh Ching is a logic model and the “Yi Jing” is a reasoning model. Zhang [1] first studies the mathematical logic reasoning structure of Tao Teh Ching, called theory of multilateral systems [2] (Defined in Section 2.4) and the mathematical algorithm reasoning structure of “Yi Jing”, called theory of multilateral matrices [1]. Based on these, many new procedures which are due to TCS have been obtained, such as, the global sensitivity analysis based on ANOVA [21], Global-Local algorithm [12] and procedure of searching zero effects [22], and so on. Both the multilateral matrices and the multilateral systems are the foundation for studying the intelligent knowledge in TCS.

10) What is “Control”? Western science defined it as “Management process in which the (1) actual performance is compared with planned performance, (2) difference between the two is measured, (3) causes contributing to the difference are identified, and (4) corrective action is taken to eliminate or minimize the difference”. But in TCS, it is simply defined as the intervention (making a treatment) on a complex system (Defined in Section 3.2).

In Chinese, the control concept is mainly due to the theory of “Yin Yang Wu Xing”, which doesn’t consider the function model to control but control by using five indexes:

Wood (), fire, earth, metal and water, where there exist two kinds of opposite non-compatibility relations among the five subsets. Zhang, et al. [7] have studied the statistical estimating methods of the five indexes and Zhang [12] has given the proofs of the theory and obtained a lot of algorithms from Global to Local controlling by using the five indexes, called GL algorithm. Luo et al. [28] has further explained its applications in the turning point analysis of finance time series. Treatment principle of intervention (Defined in Section 3) in this paper is the foundation for controlling.

11) What is “Automation”? The dictionary defines automation as “the technique of making an apparatus, a process, or a system operate automatically.” But in TCS, it is specifically and carefully defined that one can establish a system such that it can run naturally only by using the capability of self-protection of the system (Defined in Section 3.3), i.e., it is wu wei er wu bu wei (无为而无不为)-by doing nothing, everything is done.

In Chinese, the automation concept is mainly due to the Taoism believer’s idea. The idea is to set a causal circle (circle of Tao) on a system, i.e.wood) fireearthmetal waterwood···where there exist two kinds of opposite non-compatibility relations among the five subsets. Any nature system of objects has its energy and its capability of self-protection. If one wants to obtain the system’s energy, the system’s capability of self-protection will work. If the one can establish a causal circle above on the system such that it can run naturally only by using the nature force of a causal circle or the capability of self-protection, the one may be doing nothing but everything is done. The method is called “Tao Fa Zi Ran”(道法自然, imitation of Nature).

In order to implement above idea, we must test first the structure of computer’s language whether it satisfies the circle’s conditions or not and make a causal circle above. Zhang et al. [29] have studied the structure of SAS language and found it satisfying the circle’s conditions to some extent. A lot of computer automated program templates have given in [29], such as automated modeling (zero component search), automated simulation, GL algorithm, automated prediction, automatic calculation, etc. The intervention rule and self-protection rule in this paper are the foundation of these methods.

This work shows how to treat the diseases of a steady multilateral system and three methods are presented.

If only one subsystem falls ill, mainly the treatment method should be to intervene it indirectly for case: the capability coefficient of intervention reaction, according to the treatment principle of “Real disease is to rush down his son but virtual disease is to fill his mother”. The intervention method directly can be used in case but should be used as little as possible.

If two subsystems with the neighboring relation encounter sick, the treatment method should be intervene them directly also according to the treatment principle of “Real disease is to rush down his son but virtual disease is to fill his mother”.

If two subsystems with the alternate relation encounter sick, the treatment method should be intervene them directly also according to the treatment principle of “Strong inhibition of the same time, support the weak”.

Other properties of steady multilateral systems, such as balanced, orderly nature, and so on, will be discussed in the next articles.

This article has been repeatedly invited as reports, such as People’s University of China in medical meetings, Shanxi University, Xuchang College, and so on. The work was supported by Specialized Research Fund for the Doctoral Program of Higher Education of Ministry of Education of China (Grant No.44k55050).