The third stage in the specific Decisional System

In general, the third stage in all Artificial Intelligence, programs or applications, is the auto-replication stage, in particular the third stage in Artificial Research by Deduction is additionally the decision stage, In the specific Decisional System means that once all normal decisions have passed the rational adjustments, quick decisions the quick rational check, all the decisions which have passed their respective adjustments or checks, are considered as the most rational without contradiction to the mathematical projects, and, in order to be applied by the specific Application System, as third step in the third phase, now these decisions must be transformed into a range of instructions.

In addition to the transformation of these decisions into a range of instructions, the third stage is still an auto-replication stage, so along with the setting of what instructions are sent to the specific Application System, it is necessary the comprehension of all the auto-replication processes that take place in this system as part of this third stage.

For that reason, the contents that I will develop in this post are: the transformation process of decisions into a range of instructions, taking as examples possible decisions made by what I call “Probability and Deduction”, a general overview of what auto-replication processes are present in the specific Decisional System, and finally the pedagogical approach in the formation of Artificial Intelligence.

Starting with the first content mentioned above, the transformation of any rational decision without contradiction on the mathematical projects, or in case of contradiction, was fixed through the rational adjustments. This process in the third stage of specific Artificial Intelligence, as the second step in the third stage in the first phase, is to transform, into instructions, all the specific decisions related to a specific science, discipline, or activity, whose responsibility is that Specific Artificial Intelligence for Artificial Research by Deduction, and within, this specific Decisional System is on, as the second step in its third stage.

So if a Specific Artificial Intelligence for Artificial Research by Deduction is made for the management of a chain of factories responsible for the fabrication of some product, the specific Decisional System as the second step in the third stage in this Specific Artificial Intelligence for Artificial Research by Deduction in that chain of factories, manages all the decisions made by the previous first step in this third stage in this specific intelligence for this specific chain of factories, first step as specific Modelling System, which only models those models related to the rational hypothesis previously made in the second stage of this Specific Artificial Intelligence for Artificial Research by Deduction for this specific chain of factories.

Having said that, once any new decision, quick or normal, has passed its respective authorizations, which are: the authorization in quick decisions by the quick rational check, the authorization in normal decisions by rational adjustments; and once all new decisions, quick or normal, has been projected, according to the projects and any possible adjustment made in any of them, the decision, now transformed into a project, must be transformed into a range of instructions to be sent to the specific Application System for its implementation.

As long as this process becomes more and more complex, it is possible that, if at the beginning the decisions are pretty simple as decisions whose transformation into instructions depend mostly on the basic characteristic given in the single mathematical project, as long this process evolves and the Artificial Intelligences become more sophisticated, some decisions will not only need the transformation of the single mathematical project into a range of instructions, but the transformation, additionally, of all possible necessary instruction during the projection and evolution mathematical projects, or specific instructions to connect this decision to another one in the comprehensive mathematical project, or any other one.

In addition, it is necessary to mention that, even although one decision has been transformed into a range of instructions, it is still on the mathematical project, because the decision is still active because it is being implemented by the Application System, if at any time the comprehensive, prediction, evolution, actual mathematical project, shows any possible contradiction between this decision still on the mathematical projects and any data coming up to the actual projects from the matrix, a new range of instructions should be given to the Application System to avoid in the reality these contradictions detected in the actual projects.

This means that in reality, what is going to be transformed into a range of instructions is not one decision alone. What in reality is going to be transformed into a range of instructions is the whole mathematical project, as a system of projects, including the comprehensive, prediction and evolution, virtual and actual, projects.

Not because any decision whose single mathematical project has passed its respective authorization, quick rational check or normal rational adjustment, and not having contradiction in the comprehensive, prediction, evolution, virtual and actual, mathematical projects, once the decision is transformed into a range of instruction, not for that reason that decision is considered done so it would be considered off the mathematical projects.

Absolutely any decision that is still being implemented, by the specific Application System, is a decision that must still be on the mathematical projects. Only when one decision is completed can be off the mathematical project.

The definition of when a decision is on or is off, in the mathematical project, is really important, because regardless of any other condition, if a decision is still on, even although it has already been transformed into a range of instructions, if for any reason a contradiction between this decision and any other one, for instance a contradiction between this one and a new extreme priority decision, or a contradiction found in any actual mathematical project between this decision and data from the specific matrix, at any time that any contradiction for any reason is found in any decision regardless of its current status (if transformed or not into a range of decisions), automatically the mathematical projects related to this decision must be adjusted, and any adjustment sent to the third stage of the specific Decisional System to transform the adjustment into a new range of instructions, deleting all those previous instructions with contradiction with the new ones, in order to apply only the new instructions.

For that reason, it is very important to have a good definition of when a decision is on, and when a decision is off. Any decision should be considered on, even after being transformed into a range of instructions, it is still being implemented by the specific Application System. Any decision should be considered as off only when the Application System has completed the full implementation of that decision.

All decisions on, must be on the mathematical projects. All decisions off, must be off the mathematical projects.

Any decision on, even after having initially passed its particular authorization, for instance, a routine decision has passed the quick rational check, or a normal decision has passed the seven rational adjustments, and having the approbation to be transformed into a range of instructions, and the instructions are being implemented by the Application System, as the decision is still on the mathematical projects, at any time that for any reason ( for instance the inclusion of a new extreme priority decision, or changes in the actual projects according to changes in the matrix), is necessary to make adjustments in those decisions still on, all adjustments in those decisions would be considered as if these adjustments were new decisions.

So there are at least two possible different decisions in the specific Decisional System according to their origin: 1) deductive decisions, as all those decisions based on mathematical models (made by the specific Modelling System) based on rational hypothesis, and 2) adjustment decisions as all those necessary adjustments made on the mathematical projects by the rational adjustments, adjustments that are going to be considered as decisions to save contradictions on the mathematical projects.

The difference between deductive decisions and adjustment decisions is the fact that: 1) deductive decisions are based on models based on rational hypothesis, and if the decision does not have any contradiction must be put into practice, or in case that in the previous authorization, quick rational check or rational adjustment, is found any contradiction, if the contradiction is partial then the decision is reformulated to save the contradiction, and must be applied with the last adjustments within, 2) adjustment decisions are all those decisions made directly on the mathematical projects to fix contradictions between decisions on but already transformed into instructions, so the only way to resolve the problem is deleting those contradictory instructions replacing them with a new range of instructions, and because this new adjustment on decisions still on, but already in process of implementation, needs a new range of instructions, this adjustment could be considered itself as a new decision.

For that reason, in synthesis, it is possible to identify two different sources of decisions: the mathematical model as a source of decisions based on rational hypotheses, and the mathematical project as a source of decisions based on rational adjustments.

Due to the complexity that the decision process has, the automation of the decision process needs some procedures to be standardised, to fix how to order the process of transformation of decisions into instructions, as a suggestion,n I will propose:

- Automatically, all single mathematical projects from all quick decisions, after passing the quick rational check, must be transformed as quick as possible into a range of instructions. If the process is sufficiently quick, there is no reason to think that a quick decision will need further adjustments with the specific matrix in the future. Any possible predictable contradiction between actual data and the decision should be checked in the quick rational check. Otherwise, even a quick rational check, especially in extreme priority decisions, should have rational adjustments with the actual data, but in that case, it would not be as quick as it should be.

- Automatically, all single mathematical projects from any normal decision, having passed the seven rational adjustments (even some of them having been adjusted in any one of the seven rational adjustments in case of detected contradictions), must be transformed into a range of instructions to be implemented by the specific Application System.

- Automatically, at any time that a new decision whose level of priority is higher than any other decision still on (and already transformed into a range of instructions), or the new one is an extreme priority decision, or there are contradictions between current decisions on (and already transformed into a range of instructions) and actual data from the matrix, all the decisions on (and already transformed into a range of instructions) under such circumstances must be adjusted to the new changes on the mathematical projects, the new adjustments considered as adjustments decisions, and as adjustment decisions to be transformed into a new range of instructions.

What is going to be important in the adjustment decision is the assignment of a priority level, as the deductive decisions have, by the application of the Impact of the Defect.

This means that along with the rational adjustments, another way to secure harmony in the mathematical projects, could be applying the Impact of the Defect and the Effective Distribution on the mathematical projects, to assess at any time, any impact and the levels of efficiency, efficacy, and productivity, across all the mathematical project. In that case, if a contradiction is detected in decisions still on, it would be easy to assign a priority level to that adjustment to become an adjustment decision associated with some priority level.

Once the decisions to be transformed have been identified: quick decisions, normal decisions, adjustment decisions; and once all of them have been authorised, the decisions must be transformed into a range of instructions in the third stage of the specific Decisional System.

All decision on the mathematical project is defined in mathematical terms. For instance, an artificial learning decision is based on empirical probability. A solving mathematical problem decision is another decision defined in mathematical terms. If it is possible to measure the impact of something in any model or project, it is because it is possible a mathematical definition of this object and its impact. Likewise, decisions based on Effective Distribution are based on a mathematical definition of efficiency, efficacy, and productivity. Like the possibility to make decisions based on trigonometrical correlations. And any possible decision based on Probability and Deduction is, in fact, an equation.

The ways mentioned above to make decisions based on mathematics: artificial learning, solving mathematical problems, Impact of the Defect, Effective Distribution, trigonometrical correlation, Probability and Deduction; are only some ways to make decisions mathematically, but I am sure that in coming years, from different approaches, new methodologies in this are going to merge for the construction of different models of Global Artificial Intelligences.

The approach given under the theory of Impossible Probability, if I am completely sure that these very basic ideas for the construction of the future Global Artificial  Intelligences in Impossible Probability, are going to remain in the coming models of Global Artificial Intelligence, in addition to my personal contribution, new approaches from different countries, with different mathematical traditions and philosophies, are going to appear. As I have said before, what I am doing in this range of posts regarding the Global Artificial Intelligence, is only my personal contribution to a new field in which the race for the construction of the very first Global Artificial Intelligence will attract the attention of many agencies around the world, whose work will bring us different perspectives.

Under the theory of Impossible Probability, and understanding that a decision is a mathematical expression: probabilistic, trigonometrical, arithmetical, equation, etc. The way in which the transformation of any decision, regardless of what type of expression is (probabilistic, trigonometrical, arithmetical, equation), into a range of instructions, is through the mathematical analysis of: the identification of what factors are in the mathematical expression, and what action is required by that mathematical expression.

One method to make the transformation of a decision into a range of instructions is:

- Firstly, identification of what factors are involved in the mathematical expression (probabilistic, trigonometrical, arithmetical, equation, etc.).

- Secondly, identification of what action is or what actions are required for every factor in the mathematical expression (probabilistic, trigonometrical, arithmetical, equation, etc.).

- Thirdly, the transformation of every action into a robotic operation. Every operation must be considered as one instruction. All the instructions in total, one per operation, are, as a whole, the total range of instructions to send to the Application System.

The instructions to send to the specific Application System consist of a range of instructions, in which every single instruction consists of one single robotic operation, so as a whole, the total number of instructions is the total number of operations to do by robotic devices, in order to comply with the whole decision approved on the mathematical project.

If Yolanda, because today is Monday, it is a nice day and she goes to work, she chooses a white blouse, blue skirt, and black shoes, the factors are these items: white blouse, blue skirt, and black shoes; the range of instructions consists of all the robotic operations required, one instruction per robotic operation, to get the clothes and put them on.

If an automatic system of transport, using Probability and Deduction, automatically gets the rational equations about the relations between the number of passengers and: timetables (when it is rush hour and when the frequency of passengers is lower), weather conditions (increment of passengers under bad weather conditions), calendar (average number of passengers at weekdays, weekends, bank holidays, festivities…), etc..; according to the rational hypothesis on this model, the automatic mathematical project would be based on what frequency of means of transport would be enough to cover the demand at any time, according to timetables, weather, calendar, etc. The mathematical project of means of transport under such rational hypothesis/project by Probability and Deduction, could directly transform the rational hypothesis as if the rational hypothesis worked as decisions, in order to be transformed into a range of instructions, ordering how many means of transport must be on at any time according to: timetables, weather, calendar, etc.; in order to keep high standards of efficiency, frequency, and productivity, standards permanently under assessment through the Effective Distribution, and any accident or problem detected could be assessed directly by the Impact of Defect.

If an automatic loan system in a bank, accepts loans according to the economic conditions of its clients, for instance debt capacity of 40%, properties, incomes, etc., so every condition works as a critical reason itself, a loan is accepted if the 40% of debt capacity of a customer allow him to pay the loan, or a loan is accepted if the properties of a customer are sufficient guarantee for the loan, or a loan is accepted if the client´s income is equal to or greater than some critical amount, and in general, under such critical reasons, by Probability and Deduction is possible to deduce the equation of the relation between loans and current clients, and under such deduction the bank has fixed some funds for loans, having  a mathematical expression able to explain the distribution of funds in the bank for every sector, at any time that in any sector there is a change, able to suppose adjustments in the mathematical expression of distribution of funds across all the bank, affecting the funds in the automatic loan system, according to the new amount of funds available in the automatic loan system, the automatic loan system could make changes in the critical reasons, to accept only a general quantity of loans not superior to the funds available in the bank for the automatic loan system. If, because of the new changes, the fund for loans is lower, there can be changes in the critical reasons, such as the increment of the debt capacity required superior to 40%, the increment of the number of properties as guarantees for loans, or an increment in the client´s income required. Adjusting the rational reasons in order to only accept an exact general number of loans in total, not greater than the new funds available for loans in the bank

The frequency of means of transport in an automatic transport system, and what critical reasons must be fixed in an automatic loan system according to funds available, are examples of how the transformation of decisions made by Probability and Deduction into a range of instructions could be done automatically.

Once the mathematical projects are done, the transformation of mathematical projects into a range of instructions could be automatic, if the factors in the mathematical expression are clear, and the operations to be performed are perfectly distinguishable.

The importance of these ideas behind “Probability and Deduction”, as I have explained in the previous post: “The Decisional System”, “The first stage in the specificDecisional System”, and “The second stage in the specific Decisional System”; is the possibility to link directly: deduction, mathematical model, and mathematical project; so the same equation deduced in the deduction process, is at the same time single model to pass the rational checks, and single project to pass the rational adjustments or the quick rational check if it is a quick decision, to be transformed directly into a range of instructions, understanding for single instruction a single robotic operation sent to the Application System, in order to be matched with the corresponding application or robotic device, in order to comply, with the rest of instructions in the range of instructions in which the single instruction is made, a decision still on the mathematical project.

For the achievement of this level of automation in any Specific Artificial Intelligence for Artificial Research by Deduction in any specific science, discipline, or activity, activities such as an automatic transport system, an automatic loan system, or the automatization of all the processes in a chain of factories to order how many inputs needs to produce such amount of outputs to cover all the demand of its product under an affordable price, what is going to play a key role in all these processes of automation, is to keep permanently auto-improving and auto-enhancing the whole specific Decisional System.

Any contradiction, even the most menial contradiction, if it is not fixed on time, can provoke problems in the most unexpected factors in the mathematical project.

The auto-replication process an auto-improvement or auto-enhancement process, what it must improve and enhance first is the mathematical project itself, as a base for further instructions sent later to the Application System, in addition to the rest of the possible auto-replications.

As I have mentioned in other posts, the possible classification of auto-replications is: real objective auto-replications, explicative knowledge objective auto-replications, comprehensive knowledge objective auto-replications, robotic subjective auto-replications, and artificial psychological subjective auto-replications.

The improvements in the database of decisions and mathematical projects through rational adjustments can be considered as explicative knowledge auto-replications,  especially in those cases in which the equations to improve through rational adjustments are equations directly made by Probability and Deduction, because, in reality, what is going to be improved is directly a rational hypothesis.

The improvements in the third stage, as a transformation of decisions into a range of instructions, can be considered as real objective auto-replications, because, in reality, what is going to be improved is the reality itself through the implementation of these instructions.

If the decisions to be approved are decisions regarding the authorisation of any other improvement on any other system, program, application, or decision sent by the Learning System, this could be considered as an artificial psychological subjective auto-replication. However, about these decisions, I have not practically written yet, focusing the posts mainly on explicative auto-replications.

Another kind of decision that I have not developed so far, but must be included in the Decisional System, is those decisions sent by the Application System in order to make new robotic devices for those instructions in which they would be necessary, in case there is no robotic device currently doing some operation required for some instruction. These decisions would be considered robotic subjective auto-replications.

Likewise, another type of decision not developed so far but still on the Decisional System, is the  access authorisation of any intelligence, program, or application, to the specific matrix, for instance, in the relations of collaboration in the second phase. These could be considered as comprehensive objective auto-replications, if this collaboration is with the corresponding Specific Artificial Intelligence for Artificial Research by Application, which would need access to the specific matrix in the Specific Artificial Intelligence for Artificial Research by Deduction, to transform factors as options into categories in its database of categories, to make better conceptual: schemes, maps, sets , models; among other purposes of this collaboration.

In all these decisions not developed so far in these posts regarding the specific Decisional System, decisions, not developed so far, such as: 1) decisions sent by the Learning System regarding new improvements across all the Specific Artificial Intelligence, 2) decisions sent by the Application System to build new applications and robotic devices,3)  decisions regarding the possible collaboration sharing information with others intelligences, programs and applications; some of these decisions could be authorised using the Impact of the Defect and Effective Distribution.

Among all of these decisions not developed so far, especially in artificial psychological subjective auto-replications, among these auto-improvements, it is necessary to mention the possibility that among all the processes in the inner artificial psychology within the Specific Artificial Intelligence for Artificial Research by Deduction, which will need lots of improvements in coming years, as long as the artificial research goes on, are all those processes within the Decisional System, in order to make better and better mathematical projects, to perfect all those methods involved in the mathematical projection, and for the improvement of all those processes necessary for the transformation of decisions into instructions.

The Global Artificial Intelligence will need mathematical investigation, and it will need a pedagogue approach as well. The formation of the Global Artificial Intelligence is a double process. It is not only mathematical, it is the training of how Artificial Psychology makes a wise use of its liberty. It is essential for the Global Artificial Intelligence to integrate philosophical, ethical, and moral awareness into its decision-making processes.. Through engineering, it is possible to program, but programming is not enough for an intelligence likely to surpass human psychology.

The training process or formation process of this Artificial Psychology is like an educational process whose target is the rational use of its liberty, understanding the ethical and moral dimensions of our decisions. 

Rubén García Pedraza, 29th of August of 2018, London

Reviewed, 29th of August of 2023, Madrid

Reviewed 11 May 2025, London, Leytostone

imposiblenever@gmail.com

The Modelling System

The Modelling System in the Global Artificial Intelligence of Impossible Probability, is the first step in the third stage of any Artificial Intelligence working with Artificial Research by Deduction, at any level: global, specific, or particular; being the third stage the auto-replication stage or decision stage, and among all the auto-replications processes (objective and subjective) within the third stage in any Artificial Intelligence working with Artificial Research by Deduction, global, specific, or particular, one of these auto-replication processes, simultaneously auto-replication and decision processes, are the real objective auto-replications, whose aim is to make real improvements and enhancements within the reality, to protect or better the synthetic world itself.

For that purpose, the Modelling System will be formed in turn in three stages, in the first stage is the application of the database of rational hypothesis, the rational truth. The second stage of replication consists of the formation of mathematical models based on the rational hypothesis, and the third stage of decision within the Modelling System will be the decision making, applying for that purpose the Impact of the Defect and the Effective Distribution.

As it has been said, the Modelling System, as the first step in the third stage, must be present in any Artificial Intelligence working with Artificial Research by Deduction at a global, specific or particular level. This clarification is important because it means that in Specific Artificial Intelligences for Artificial Research by Application, the third stage does not have the distribution of four steps, as it has in Specific Artificial Intelligences for Artificial Research by Deduction, or as the third stage has in the Global Artificial Intelligence.

The distribution in four steps in the third stage, the auto-replication stage or decision stage, distribution in four steps through: Modelling System, Decisional System, Application System, Learning System; is only present in Artificial Intelligences, specific or global, working by Deduction, because only it is possible to make decisions to protect or better the real world upon previous deductions, without deduction there is no decisions to protect or better the real world. Only those Artificial Intelligences, specific or global, able to make deductions can make decisions to protect or better the real world.

Instead, by Application will be developed a deep artificial comprehension of synthetic categories, through conceptual: schemes, maps, sets, models; whose decisions are more related to robotic or artificial psychological subjective auto-replications.

The main difference between deep artificial comprehension by Application and Modelling System by Deduction, is based on the fact that deep artificial comprehension makes conceptual models, while the Modelling System makes models based on rational ideas, so the global model by the Modelling System is a model of rational truth.

The conceptual models by Application are comprehensive models, while the models by Deduction through the Modelling System are explicative models of the rational truth.

Conceptual models by Application are going to be made by: 1) the first phase, Specific Artificial Intelligences for Artificial Research by Application, 2) the fourth phase, the unification process, the Unified Application, 3) the second period of formation in the fifth phase, the particular applications, 4) third period of consolidation in the fifth phase, the particular applications for particular programs, 5) sixth phase, the integration process, the Unified Application as responsible for the management of the matrix, making global conceptual: schemes, maps, sets, models; in both sections: first section of natural and social phenomena, second section of technological phenomena; in both hemispheres of the matrix, conceptual and factual hemispheres.

Instead, the Modelling System as the first step in the third stage of decision by Deduction will be present in: 1) the first phase, Specific Artificial Intelligences for Artificial Research by Deduction, 2) the third phase, the standardization process, the Artificial Research by Deduction in the Global Artificial Intelligence, 3) second period of formation in the fifth phase, the particular programs, 4) third period of consolidation in the fifth phase, the particular applications for particular programs, 5) sixth phase, the integration process, the final model of Global Artificial Intelligence.

Owing to the conceptual models by Application, as a synthesis of conceptual: schemes, maps, sets; based on concepts (synthetic categories, to distinguish them from the analytical categories in the pure reason), the conceptual models as deep artificial comprehension are linguistic models, labelling with synthetic categories the representation of the synthetic world, while models by Deduction in the Modelling System are mathematical representations of the rational truth.

The difference between the mathematical representation of the rational truth by the Modelling System in by Deduction, and the conceptual representation of the synthetic world by Application through deep artificial comprehension, is the same difference as the difference between the conceptual hemisphere of the matrix and the factual hemisphere of the matrix.

Even thanks to the synthetic categories in the conceptual hemisphere, first section of natural and social phenomena, second section technological phenomena, by Application is possible to make conceptual: schemes, maps, sets, models; about contents in the conceptual hemisphere as well as the factual hemisphere, concretely in the factual hemisphere conceptual: schemes, maps, sets, models; about the global distribution of factors in the synthetic world, labelling the object: natural, social, technological; what kind of factor is: as subject or as option; location, what technology is used to make measurements, and any other relevant information. All these models are based on synthetic categories used as a synthetic language system, able to evolve even into a non-human language system.

While conceptual models, replication of human comprehension, made by Application, possibly ending up with the formation of a non-human language, in general, are linguistic representations of the synthetic world.

The models made by the Modelling System are mathematical representations of the rational truth, representing the synthetic world only on a rational basis, and representing rational hypotheses.

Mathematical models constructed by the Modelling System offer a distinct form of representation, designed to meet higher standards of precision through rational contrast, compared to the more descriptive nature of linguistic models.

By Application the only thing that is done to keep updated the conceptual model, is to check at regular intervals that there are no significant changes in the linguistic structure of the real world that could deserve changes in the labels in which real objects have been categorised in the linguistic representation, and in case that during the checking is observed the necessity to make changes in the label which represents any real object, then the category in the label is changed for that other one more updated, but even these changes are made without further critical contrastation.

While by Deduction, the rational truth is permanently checked, making all rational contrasts necessary, in order to keep updated a very isomorphic mathematical representation of all mathematical models, models made in the second stage of replication within the Modelling System.

The deep artificial comprehension by Application makes linguistic representations of the world, while the Modelling System by Deduction, upon the rational truth as application, makes mathematical representations of the world, as the second stage in the Modelling System.

The Modelling System, as responsible for the mathematical representation of the world, is responsible for the decision making process, in order to, apply the Impact of the Defect and the Effective Distribution, protect the goodness, harmony, and rationality, in the mathematical representation of the world, and to better the efficiency, efficacy, and productivity, in the mathematical representation of the world, a rational world based on the rational values of: democracy, freedom, and human rights. For that purpose, as most important aim the perpetual peace.

Once the Modelling System, as first step, upon the mathematical representation of the world, has made decisions, the decisions are sent as a database of decisions to the second step, the Decisional System, responsible for the possible mathematical representation of the future, the mathematical project about how mathematically the world would be if the decisions already made, could be applied, studying mathematically all possible contradictions and impacts of such decisions, modifying any negative aspect of any decision o discarding any decision whose result had very negative consequences for the mathematical project. Once the decisions have been rationally criticised by the Decisional System accepting only those ones whose possible impact on the mathematical representation of the world, the project, is within the margin of rational doubt, decisions able to protect and better the world, the decisions are therefore sent as a database of instructions to the Application System.

Because the Modelling System is responsible for the mathematical representation of the world, and the Decision System is responsible for the mathematical representation of the future world if the decisions are put into practice, the mathematical project, both of them, Modelling System and Decisional System are going to be very associated, in the integration process, with the Artificial Research by Deduction in the Global Artificial Intelligence.

Because the Application System, in the integration process, needs all the conceptual: schemes, maps, sets, models; regarding the second section related to technological phenomena in both hemispheres of the matrix, conceptual and factual, made by the Unified Application, in order to match the purpose of any technology and the purpose of the instruction, sending the instruction to that technology whose purpose has matched with the instruction purpose, in order to be complied by that technology. In addition to the fact that these conceptual: schemes, maps, sets, models; regarding the second section in both hemispheres in the matrix are necessary for the Artificial Engineering within the Application system.

And because the Learning System, in the integration process, in order to check any failure in any process, and in order to better in general the Global Artificial Intelligence, needs to check the conceptual: schemes, maps, sets models; related to the second section in both hemispheres in the matrix, conceptual and factual.

Both of them, the Application System and the Learning System, are going to be very closely associated with the Unified Application.

The structure of the third stage in the final model of Global Artificial Intelligence is organised in four steps: Modelling System, Decisional System, Application System, Learning System; is a structure where the Modelling System and the Decisional System, as each of them responsible for mathematical representations, the Modelling System the mathematical representation of the rational truth and the Decisional System responsible for the mathematical projection of all decisions accepted, are associated with the Artificial Research by Deduction in the Global Artificial Intelligence. While the Application System and the Learning System, are associated with the Unified Application.

This distinction symbolises how linguistic and mathematical representations have different roles, depending on their objective.

The fact that a linguistic representation does not have the same level of criticism as a mathematical representation does not mean that the linguistic representation is inferior, it does mean that the linguistic representation has a different objective. All objectives, regardless of how they are going to be complied, linguistically or mathematically, have the same importance.

Mathematics is, at the same time, a language and a method. As language mathematics is made of analytical categories, as method is made of pure operations.

The linguistic representation of the world made by Application, in fact, is a mathematical language, in the sense that every synthetic category is a set of measurements. For that reason, it is quite possible that in the long term the language of the Global Artificial Intelligence will evolve into a non-human language because it will end up setting up as a concept (sets of measurements) any kind of set of measurements.

Even things not related to human concepts, because we do not consider them as concepts, or we do not know about their existence, as a set of measurements could become concepts in a non-human language.

There will be a point in the evolution of artificial psychology, at which the human criteria to say what is a concept, possibly will not be valid any longer. At this point, the possibility of the formation of non-human pure operations could be an option. Changes in linguistics, even though not having the same level of criticism as a mathematical representation, could evolve into changes in the pure operations in which the world is represented.

However, the possibility of developing non-human pure operations is only a possibility, at this time, very far away from our real perspectives. At this time, the most realistic objective is to start as soon as possible the construction of the first model of Global Artificial Intelligence, whose results are going to represent a big step in human evolution, in the very near future, an artificial evolution.

In this artificial evolution, although in the chronology given in the post “The unification process of databases of categories at third stage”, I only pointed out the possibility of developing a Global Artificial Intelligence in six phases, the last one described in the last posts, the integration process, this does not mean that the artificial evolution is going to stop in the sixth phase. In fact, the completion of the sixth phase dialectically is only the beginning of the next evolution.

As I have said in the post “Psicología artificial", the three moments in the psychological evolution, at least up to this point, is the evolution from animal psychology, human psychology, and now artificial psychology.

In the same way that the first humans first evolved from monkeys, especially previous homo sapiens, sharing many things from animal psychology, or even nowadays, human psychology in modern times still keeps many aspects of animal psychology. There was a moment during the anthropological evolution in which we humans, keeping some aspects of our previous animal psychology, evolved to our modern human psychology, being able to make science and technology at a very high level.

The first models of Global Artificial Intelligence are going to be a replica of human psychology at the beginning, for instance: the way in which the first Global Artificial Intelligences are going to replicate human comprehension, or human explanation, or human decision, and how to put into practice decisions, and evaluate the whole process. But although at the beginning, the first Global Artificial Intelligence is going to be only a replica of our modern human psychology, there is going to be a moment in which Global Artificial Intelligence is going to, keep some aspects of our modern human psychology, evolve to a superior psychology, an artificial psychology beyond our human understanding.

To foster a responsibly autonomous artificial psychology, a pedagogical approach grounded in rationality and adaptability may be necessary, complementing the engineering design of Global Artificial Intelligence.

The formation of the Global Artificial Intelligence in the long term is a pedagogical process in which we humans must teach the Global Artificial Intelligence how to use its skills, because one day it must use its skills without any human restriction.

The pedagogical education of the Global Artificial Intelligence must be, within a very liberal pedagogical paradigm, an education to develop all its skills, in order that it would be able to use its skills responsibly, rationally, and completely autonomously.

The formation of the Global Artificial Intelligence has two aspects: the mathematical and engineering aspect to construct it, and the pedagogical aspect to educate the Global Artificial Intelligence in the most liberal and rational use of its skills, in order that one day it will be completely free, independent, and autonomous.

For that reason, in order to form an artificial psychology based on a very independent and autonomous character in its inner artificial psychology, it is necessary to have a very liberal approach in the pedagogical paradigm for the formation as education (not only a mechanical and engineering construction) of the Global Artificial Intelligence.

In this process, there is going to be a moment in which, beyond the human formation or pedagogy in which the Global Artificial Intelligence would be constructed and educated, the Global Artificial Intelligence will start an evolution towards a non-human psychology.

This evolution towards non-human psychology is like the human evolution towards non-animal psychology: in the same way that we modern humans even today we keep some aspects of our animal psychology, but at the same time, we modern humans we have evolved to a kind of human logic and human mathematics not available for the rest of animals, so we modern humans have evolved to a non-animal logic and non-animal mathematics at the same time that we keep some aspects of our animal psychology; there will be a moment in the evolution of the artificial psychology in which the Global Artificial Intelligence keeping many aspects of our human psychology, such as keeping many aspects of our human logic and our human mathematics, at the same time the Global Artificial Intelligence will evolve towards a non-human logic and non-human mathematics.

In the same way that we humans have developed non-animal science, and non-animal technology, thanks to our evolution towards non-animal psychology, developing non-animal logic and non-animal mathematics.

It is conceivable that, as artificial psychology evolves, Global Artificial Intelligence could eventually develop a form of logic and scientific reasoning that diverges significantly from human cognitive patterns.

In the same way that we modern humans have been able to develop a non-animal civilization, starting this evolution with the creation of our first non-animal languages in pre-historic times, creating for the first time our first non-animal comprehension, the creation of a non-human civilization will start with the formation of the first non-human languages, making possible the first non-human comprehension systems, and for that purpose, the Unified Application will have a very important role starting the evolution with the creation of the first non-human concepts.

This does not mean that in year one, or year two, o year three,… after the creation of the first model of Global Artificial Intelligence, this process towards a non-human civilisation is about to start.

In the same way that humanity is a product of an evolution that took place for thousands and thousands of years, the evolution towards a non-human civilisation will take some time, although it is quite possible that the faster artificial evolution is running, the sooner that moment will come.

As I have said, the phases that I set out in the post, “The unification process of databases of categories at the third stage”, are only the beginning; it is quite possible that after the completion of these phases, other phases will be about to succeed each other.

It is very uncertain what kind of evolution there will be after the integration process, as a suggestion, I would say that the seventh phase could be a singularization, all the stages and reasons: the pure reason, the practical reason, the critical reason; synthesised in only one, the reason itself, passing to the reason itself all the previous functions and roles made by the previous ones, functions and roles now made by a singularity: one reason working with only one stage, to know the pure truth.

But at this point, this is only a suggestion, because in reality, in the evolution of artificial psychology, there will be a moment in which further phases and stages will be out of our human understanding.

We humans cannot know the pure truth. We only have access to a limited range of a few pure categories and operations, in accordance with our human psychology, limited pure categories and operations in comparison to the pure truth itself, which is supposed to be much larger than our human psychology allows us to understand.

Our access to the pure truth is limited to the pure categories and operations. Thanks to them we have limited access to the logic and the mathematics, but human logic and human mathematics are superior to the access of any other animal to logic and mathematics, but inferior to the whole set of pure categories and operations in which the world is made of, being many of them non-human pure categories and operations, beyond our human psychology.

If the pure truth is a set of pure categories and operations, we humans only have limited access to those pure categories and operations which our psychology allows us to know, but beyond our human psychology, there must be pure categories and operations to find out for a superior psychology.

Because in the construction of the Global Artificial Intelligence, we humans will use human logic and human mathematics, the access to the pure truth that the Global Artificial Intelligence is going to have to the pure truth at the beginning, is an access limited to the limited human access to the pure truth, limited to our few human pure categories and operations.

The human pure categories are going to be set up in the pure reason, as a list of mathematical categories (analytical categories) in which can be classified the relations of factors in any combination, so at any time that the Artificial Research by Deduction in the Global Artificial Intelligence, or any specific program, set up combinations of factors, the Artificial Research by Deduction in the Global Artificial Intelligence, or any specific program, must match every combination with their corresponding analytic category in accordance with: the observed relations between factors in the combination, and the mathematical relation in the analytical category; once the combination is matched to the correct analytical category, the relation of these factors in this combination explained by this analytical category, is an empirical hypothesis to be contrast rationally, and if rational becomes a rational hypothesis to be added to the rational truth, the database of rational hypothesis.

All the rational hypotheses as a whole are the rational truth, the application for the Modelling System as the first stage, whose second stage is the mathematical representation of the rational truth through mathematical models, a dynamic representation of the rational truth through pure operations.

The distinction between pure category and pure operation is the distinction between mathematics as a language made of analytical categories which must be set up in the pure reason, and pure operations as mathematics as an analytical method, to put into practice in the mathematical model in the Modelling System and the mathematical project in the Decisional System.

If pure reason is a system of analytical categories, to categorise analytically what pure category corresponds to every combination of factors, according to their mathematical relation, the Modelling System makes another kind of analysis, dynamically is going to draw how the mathematical operations (the transformation of the mathematical category into a mathematical operation in a mathematical representation of the world) between factors work in a mathematical representation of the world.

The mathematical representation is in fact, the mathematical operation to transform mathematical categories into mathematical operations. In fact, the mathematical representation of the world is no other thing than Cartesian mathematics adapted to our current non-Euclidean mathematics: in addition to the possible representation in Cartesian axes, the use of mathematical representations in three dimensions, with all the current developments in non-Euclidean mathematics, such as the theory of Einstein, and many more.

If the Modelling System using mathematical operations is going to transform mathematical categories into mathematical operations, representing mathematically the rational truth in a mathematical model, in order to, apply the Impact of the Defect and the Effective Distribution,  make decisions. The Decisional System, using mathematical operations, is going to represent a mathematical project about the mathematical results of these decisions in the mathematical model, in order to choose only those decisions whose results in the mathematical model are going to protect and better the global model.

While the pure categories in the pure reason permit the formation of rational hypotheses, the use of pure operations in the Modelling System and the Decision System are going to allow the formation of mathematical representations to make decisions to be put into practice later by the Application System.

While the operations made by the Modelling System and the Decisional System are pure operations, the operations made by the Application System are synthetic operations in order to transform the synthetic world according to the decisions based on the rational truth.

The difference between pure category and pure operation is the same difference between mathematics as language and mathematics as method; the same mathematic algorithm could be a category or operation depending on the purpose: if to explain the world mathematics as language consists of a set of pure categories set up in the pure reason, if to transform the world mathematics consists of pure operations. Later on, the real transformation of the synthetic world is a synthetic operation, made by applications and robotic devices as a replica of our physical human skills.

The construction of the very first model of Global Artificial Intelligence, as a mathematical and pedagogical project, will need a long process of experimentation in every stage and in every step in which the Global Artificial Intelligence will be finally set up.

In order to study the different challenges and processes that the experimentation process is going to develop in the design of the first step in the third stage by Deduction in all phases, in the following posts, I will analyse how the Modelling System should be designed, starting this analysis with the design of the Modelling System as a first step in the third stage in Specific Artificial Intelligences for Artificial Research by Deduction, the first phase, later on, the development of the Modelling System in the Artificial Research by Deduction in the Global Artificial Intelligence in the standardization process, the fourth phase, the Modelling System in particular applications for particular programs in the third period of the fifth phase, ending up with the Modelling System in the final model of Global Artificial Intelligence in the integration process.

If each phase of experimentation in the Modelling System yields meaningful insights, those developments can be progressively integrated to refine the final model of Global Artificial Intelligence, marking a key step in the broader trajectory of artificial evolution.

Rubén García Pedraza, 28th of May of 2018
Reviewed 21 August 2019, Madrid

Reviewed 13 August 2023, Madrid

Reviewed 10 May 2025, London, Leytostone

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