#
Problem-Oriented Foundations of Intelligence in the Context of Superintelligence^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Classification of Intelligence Models

**Proposition**

**1.**

**Proposition**

**2.**

**Corollary**

**1.**

## 3. Problem-Oriented Model of Intelligence

**P**of problems and two classes of systems

**H**and

**K**.

**Condition (A):**For any system T in

**K**, there is a system A in

**H**, which can produce all results (solve all problems) that T can produce (solve).

**Condition (B):**Any system A from

**H**can solve all problems from the set

**P**.

**Condition (C):**For any problem P from the set

**P**, there is a system A in

**H**, which can solve it.

**Lemma**

**1.**

**Definition**

**1.**

**H**is called complete for a class

**K**if it satisfies Condition (A).

**K**if the class {A} satisfies Condition (A).

**H**is called complete in a class

**K**if it satisfies Condition (A) and

**H ⊆ K**.

**K**is called universal in

**K**if the class {A} satisfies Condition (A).

**Example**

**1.**

**H**of Turing machines is complete in the class

**T**of all Turing machines if it contains at least one universal Turing machine.

**Example**

**2.**

**T**of all Turing machines.

**Example**

**3.**

**H**of inductive Turing machines is complete in the class

**T**of all inductive Turing machines if it contains at least one universal inductive Turing machine.

**Lemma**

**2.**

**K**is complete in itself.

**Lemma**

**3.**

**K**system is total for

**K**.

**Proposition**

**3.**

**H**is complete for (in) a class

**K**and

**H ⊆ G**, then the class

**G**is complete for the class

**K**.

**Corollary**

**2.**

**H**contains a total for

**K**system, then the class

**H**is complete for the class

**K**.

**Proposition**

**4.**

**H**is complete for (in) a class

**K**and

**F⊆ K**, then the class

**H**is complete for the class

**F**.

**Corollary**

**3.**

**K**and

**F ⊆ K**, then the system A is total for

**F**.

**Corollary**

**4.**

**H**contains a total for a class

**K**system and

**F ⊆ K**, then the class

**H**is complete for the class

**F**.

**P**, which is called an intelligence parameter, we define intelligent subclasses and systems in a class

**K**of systems.

**Definition**

**2.**

**H**of systems is called weakly intelligent with respect to

**P**if it satisfies Condition (B).

**H**= Int

_{w}

**, and take the class**

^{P}**KP**, that consists of all problems each of which can be solved by some system from a class

**K**of systems, and systems from a class

**H**can do necessary reductions of problems.

**Proposition**

**5.**

**H**is complete for a class

**K**if and only if

**H**= Int

_{w}

**.**

^{KP}**Corollary**

**5.**

**H**is complete in a class

**K**if and only if

**H ⊆ K**and

**H**= Int

_{w}

**.**

^{KP}**Proposition**

**6.**

**H**= Int

_{w}

**and**

^{P}**Q**

**⊆ P**, then

**H**= Int

_{w}

**.**

^{Q}**P**is determined by the class

**K**, we denote this by

**H**= Int

_{w}

**.**

^{P}K**Definition**

**3.**

**H**of systems is called robustly intelligent for a class

**K**with respect to

**P**if it satisfies Conditions (A) and (B). We denote this by

**H**= Int

_{r}

**.**

^{P}K**H**of systems is called robustly intelligent in a class

**K**with respect to

**P**if

**H**

**⊆ K**and it satisfies Conditions (A) and (B). We denote this by

**H**= Int

_{rin}

**.**

^{P}K**P**class of problems is complete and weakly intelligent.

**Proposition**

**7.**

**H**is robustly intelligent for (in) a class

**K**, i.e.,

**H**= Int

_{r}

**(**

^{P}K**H**= Int

_{rin}

**), and**

^{P}K**F ⊆ K**, then the class

**H**is robustly intelligent for the class

**F**., i.e.,

**H**= Int

_{r}

**.**

^{P}F**Proposition**

**8.**

**H**= Int

_{r}

**and**

^{P}K**Q⊆ P**, then

**H**= Int

_{r}

**.**

^{Q}K**H**= Int

_{rin}

**and**

^{P}K**Q ⊆ P**, then

**H**= Int

_{rin}

**.**

^{Q}K## 4. Conclusions

## Funding

## Conflicts of Interest

## References

- Bostrom, N. Superintelligence: Paths, Dangers, Strategies; Oxford University Press: Oxford, UK, 2014. [Google Scholar]
- Burgin, M. Swarm Superintelligence and Actor Systems. Int. J. Swarm Intell. Evol. Comput.
**2017**, 6, 3. [Google Scholar] [CrossRef] - Spearman, C. The Abilities of Man: Their Nature and Measurement; Macmillan: New York, NY, USA, 1927. [Google Scholar]
- Duncan, J.; Rüdiger, J.S.; Kolodny, J.; Bor, D.; Herzog, H.; Ahmed, A.; Newell, F.N.; Emslie, H. A neural basis for general intelligence. Science
**2000**, 289, 457–460. [Google Scholar] [CrossRef] [PubMed] - Sternberg, R.J. Beyond IQ: A Triarchic Theory of Intelligence; Cambridge University Press: Cambridge, UK, 1985. [Google Scholar]
- Burgin, M. Intellectual Components of Creativity; International Academy “Man in Aerospace Systems”: Kiev, Ukraine, 1998. (In Ukrainian) [Google Scholar]
- Thorndike, R.K. Intelligence and Its Uses. Harpers Mag.
**1920**, 140, 227–335. [Google Scholar] - Mayer, J.D.; Salovey, P. The intelligence of emotional intelligence. Intelligence
**1993**, 17, 433–442. [Google Scholar] [CrossRef] - Koonce, R. Emotional IQ, a new secret of success? Train. Dev.
**1996**, 50, 19–21. [Google Scholar]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Burgin, M.
Problem-Oriented Foundations of Intelligence in the Context of Superintelligence. *Proceedings* **2020**, *47*, 21.
https://doi.org/10.3390/proceedings2020047021

**AMA Style**

Burgin M.
Problem-Oriented Foundations of Intelligence in the Context of Superintelligence. *Proceedings*. 2020; 47(1):21.
https://doi.org/10.3390/proceedings2020047021

**Chicago/Turabian Style**

Burgin, Mark.
2020. "Problem-Oriented Foundations of Intelligence in the Context of Superintelligence" *Proceedings* 47, no. 1: 21.
https://doi.org/10.3390/proceedings2020047021