*2.2.2. For all the components mentioned above the following guiding rules to describe them will be used*


It is considered that the models generate a topological knowledge structure *K*(*i*) , that is based on a certain (dominating) theory (Th *K*(*i*) ). The topological structure that results as a knowledge model and the rules of emergence of the physical system itself are described by an isomorphic relationship.

*2.2.3. The three principles of the approach mentioned above are as follows [8–10]*

*Principle 1:* The topological structure *K*(*i*) is described by the notion of category that is consid‐ ered to:

	- **•** Objects Obj1, Obj2, Obj3
	- **•** Morphisms f1, f2, f1\* f2, si
	- **•** Three identity morphisms (not illustrated in the figure) 1X, 1Y, and 1Z

**Figure 1.** F Description of the category concept

	- **•** class Ob(C) with elements called objects
	- **•** class Hom (C) with elements called morphisms/maps.

*Principle 2:* The knowledge process (KP) takes place (we will underline that the words "progress" or "evolve" are actually hard to prove and not obvious at all) in iterations made for the categories defined for


*2.2.3. The three principles of the approach mentioned above are as follows [8–10]*

ered to:

46

objects/models.

in the Knowledge Society

**b.** The descriptions of Figure 1 are applicable:

**•** Objects Obj1, Obj2, Obj3 **•** Morphisms f1, f2, f1\* f2, si

**Figure 1.** F Description of the category concept

**c.** C (in the chosen cases) consists of:

process that lead to a certain *K*(*i*)

defined by the set of syzygies.

**•** class Ob(C) with elements called objects

**•** class Hom (C) with elements called morphisms/maps.

**d.** to be able to define set of minimal conditions describing each phase, that are called syzygies of that set of knowledge relationships that define an algebraic structure. **e.** consider that the process of model change consists of having phases of the knowledge

that may be also called paradigms. These paradigms carry with them a set of deviations from the real system/object that are intrinsic to the modeling process and their limits are

, i.e., a set described by the rules generated by syzygies,

*Principle 1:* The topological structure *K*(*i*) is described by the notion of category that is consid‐

Proceedings of the International Conference on Interdisciplinary Studies (ICIS 2016) - Interdisciplinarity and Creativity

**a.** Reflect a hierarchical structure of "matrioshka" type, that may be described as a more generalized type of cybernetic system, in which the the objects under study and their models are "black boxes" for every level of emergence and, respectively, modeling of the

**•** Three identity morphisms (not illustrated in the figure) 1X, 1Y, and 1Z

Up to the point of reaching a critical state due to the number and type of paradoxes embedded in the model [8,9]:

	- **•** Subquantic **SQ**
	- **•** Quantic **Q**
	- **•** Electromagnetic **EM**
	- **•** Molecular **MO**
	- **•** Molecular and life **MOL**
	- **•** Conscient planetary life **CPL**
	- **•** Stellar and universe without life **SUNA**
	- **•** Stellar and universe with life **SUA**
	- **•** Stellar and universe with conscience **CSU**

**Principle 3:** The KP is asymptotically stable and complete. Nevertheless, the final structure that results for the KP on a given object cannot be known in its phenomenological detailed characteristics, nor predicted. But the most probable status is that the existence of such a final state can be predicted [8,9].
