1. Introduction

2. Background and Related Work

2.2. Intelligence: Classification of environment

The development of intelligence ($I_n$) and collaborative intelligence ($C{I}_n$) requires a thorough understanding of the attributes of the environment. The customization of the $C{I}_n$ framework should be tailored to accommodate the distinctive characteristics of the context in which the intelligences are intended to be implemented. Categorizing environments based on observable characteristics is a prevalent approach within artificial intelligence (AI). The classification of environments is determined by the functional capabilities of artificial intelligence agents operating within these particular environments. Agents have the ability to observe and engage in collaboration with their counterparts within these given environments.

The classification of information environments mainly relies on the constituent elements they encompass rather than the agents’ skills. Theoretically, this classification framework offers a more comprehensive view since it enables systematic categorization of diverse contexts within artificial intelligence. The essentially lies in the consideration that the universe can be understood as an environment characterized by a set of guiding principles that regulate its constituent elements. The classification of environments in computers and information is determined by three key aspects. There are three key factors that need to be considered: 1) the extent of authority and decision-making power, 2) the level of distribution of decision-making and intelligence, and 3) the state of the environment, specifically any changes in its structure in terms of entities and relationships between them.

• Centralized and Decentralized Environment
  The first factor evaluates whether the environment exhibits characteristics of centralization or decentralization, whereas the next factor determines the presence of a distributed environment. Centralization and decentralization in an information environment refer to an organization’s strategies to govern and disseminate its information resources, systems, and authority to make decisions. The notions above affect how knowledge and data are spread throughout an organization. In contrast, "distributed" commonly denotes the spread or allocation of information, data, or computing resources among different locations, systems, or entities. [9].
  Centralized environments are characterized by the concentration of power, decision-making, and authority in a singular human or geographical location. Every individual entity (i.e., a system component) possesses a finite level of autonomy. As [9] stated, the entity cannot make independent decisions unless it is governed by the authority and influence of the most dominant entity.
  The decentralized information environment refers to a type of environment that lacks a central coordinating or governing organization. The collection consists of many independent entities, which may be situated in the same or disparate geographic locations. An autonomous entity is characterized by its capacity to operate autonomously to accomplish its objectives [10]. In other words, each autonomous entity represents an information system in which no single entity is the exclusive authority. Each entity in such environments can perceive and capture the environment’s state and develop intelligence about it (typically equipped with its intelligence). It can make decisions locally, and each entity can choose how to use these local intelligence resources to fulfill that entity’s objectives. However, there is a freedom of action within each entity, which guarantees that no single node has complete intelligence.
• Distributed Environment
  In this case, the categorization of the environment is predicated on the second factor. A distributed information environment can encompass systems that are either geographically dispersed or locally located. One distinguishing characteristic of a distributed environment is its collaborative utilization of various entities, nodes, or components responsible for overseeing and executing the processing and administration of resources and data. These entities can exist in a shared physical space, such as a data center, or they can be distributed across several geographic locations, including distinct data centers in different cities or countries. [11].
  The apparent paradox of a system being distributed and centralized can be resolved by analyzing the definitions of location and control. A distributed system consists of multiple software components that are physically spread across various entities (computers), but operate together as a cohesive system. In a distributed system, entities can be geographically far and connected by a wide area network or physically close and linked through a local network[12].
  Let us contemplate a cloud service enterprise that offers data storage solutions. In terms of physical implementation, the data have the potential to replicate and distribute on various devices, taking into account the availability and resilience of the resources (distributed)[13]. Nevertheless, irrespective of the geographical location of the equipment and data storage facilities, the cloud service provider assumes centralized management over them. On the contrary, the notion of a decentralized and distributed system may appear rational. Bitcoin will be used as our illustrative case. Bitcoin is a decentralized system characterized by immutability, meaning that any entity cannot alter it. Furthermore, it functions as a distributed global peer-to-peer network of autonomous computers.
• Open and Closed Environments
  Prior studies, such as those referenced in [14], indicate that the observable environment may present itself as either closed or open. The genesis of states within these environments is often a consequence of modifications in their fundamental components. As delineated in [14], the classification of environmental states falls into two primary groups: identical and varying. By scrutinizing the observable alterations in entities and their interrelations, one can anticipate the classification of an environment. This predictive capability is crucial for understanding the dynamics of open versus closed systems and their respective states.

In dynamic environments, entities and relationships exhibit varying degrees of flexibility, allowing for the entrance or departure of any entity within the specified environments. The designation employed to characterize these environments is that of open universes ($OE$). Conversely, in closed environments that exhibit a consistent number of entities, entry and exit of these entities are rigorously prohibited, and modifications are only limited to the relationships among the entities.

These specific categories are commonly known as closed universes ($CE$). Closed universes can be classified into two main categories: static and dynamic. Entities and relationships within the static closed environment ($SCE$) demonstrate stability and remain unchanged without any alterations. On the contrary, in a dynamic closed environment ($DCE$), the entities remain fixed while their relationships demonstrate flexibility. The main aim of this work is to investigate the dynamic closed environment ($DCE$), which includes the static closed environment ($SCE$) as an essential element.

In this context, [14] proposed a model for distinguishing between open and closed environments. The classification of the environment as closed or open can be ascertained through an analysis of the determinant of W. The environment’s categorization, whether open or closed, can be identified by examining the determinant of W. More precisely, the determinant of W can take on one of two specific values: either equal to one or greater than one. The determinant of $St$ is equal to one, signifying that all environment states are similar, suggesting a closed and unchanging environment. On the contrary, if the determinant of $S_t$ is more than one, it indicates that at least one state in the environment differs from the rest. Hence, the categorization of the environments can be classified as either closed dynamic or open, as depicted above:

3. Levels of Observation in the Information Environment

4. Intelligence: Definition

5. Intelligence: Ontological view-based model

• Firstly, it provides the interconnected information on two parts of semantics:

  -

  The connection between the state and the appropriate conceptualization structure.

  -

  The data is associated to the relevant specification through the use of a supporting language.

• Additionally, the association axioms of $OV$ facilitate the transformation of knowledge in a manner that enables direct reasoning, hence enhancing the actionable form of intelligence.

• Captured state: refers to the current snapshot of the environment’s structure, represented by entities and relationships.
• Data: is a form of raw intelligence that has been obtained by converting the captured state, but has not been organized or processed in any way.
• Information:is the second form of intelligence that can be generated through data transformation. Information is data that has been organized, structured, and presented meaningfully.
• Knowledge: Knowledge is the third form of intelligence that can be formed through the transformation of information. Knowledge is explicit information retrieved from implicit information by adding rules (axioms).
• The Observer Universe (also known as $U_{in}$-Intelligence space) is where forms of intelligence will develop.
• The Observed Universe, known as ($U_r$-Reality), is where the existences known as “entities” and the coexistences known as “relationships” between them exist. This universe can be broken down into two subcategories based on the possible alterations to its states (entities and relationships).
• Converting function: It is the process of expressing the conversion of the captured state formats into other formats, representing the first form of intelligence (data). However, the universe (intelligence space) may keep the same formats without any changes.
• Transformation function: it is a function that takes a form (information) and produces an output that has been transformed into another form (knowledge).
• Decentralized Environment: is often characterized by decentralized control, which means that there is no single controlling entity or authority. This can contrast with centralized environments, where a single central authority or entity makes decisions. Entities in a decentralized environment are often distinguished by their ability to perceive their environment. They are autonomous entities that can operate independently and make their own decisions without external direction or control.

6. Forms of Intelligence

• Captured state: To analyze the distinctions between "conceptualization" and "capturing the state of an environment" in the context of observation, it is necessary to comprehend how each concept relates to the act of observing and the outcomes of this observation. The correlation between conceptualization and the representation of the state of an environment is intricately related to the observation process, although its objectives may differ depending on the observation being carried out.
  $[\mathbf{Proposition}\mathbf{5}.\mathbf{1}]$: Assuming C =<D, W, $\mathcal{R}$ >as a conceptualization structure representing entities and relationships within a decentralized environment, with a conceptualization structure defined as an abstract view of the environment, we can infer that this structure provides a higher-level perception of the observed environment.
  In contrast, the fundamental aspect of the environment’s structure, denoted as St =<$\mathcal{G}$, $\mathcal{S}$,$\mathcal{T}$>, represents the environment’s actual manifestation. This structure corresponds to a lower-level perception, wherein entities and their relationships coexist within the same framework.
  

  Figure 3. shows different ways to observe U-Reality

  Figure 3. shows different ways to observe U-Reality

  
  The state structure comprises three elements: $\mathcal{G}$, representing the domain of the universe of reality, including entities and relationships; $\mathcal{S}$, representing the possible states; and $\mathcal{T}$, representing the intensional relations. The constituent elements of the conceptualization framework have been delineated in [6].
  The correlation between the conceptualization structure, representing a high level of understanding of the universe of reality [6], and the state structure resulting from our approach, indicating a low level of understanding of the universe of reality, is depicted in Figure 2.
  The captured states can be classified into two separate structures based on the basic alterations that will take place in the elements of the reality universe. Conversely, they are confined to the observer universe. These structures may exhibit variations or resemblances.
• First form of intelligence (Data): It can be reached by converting a function that converts the captured state of reality ($U_r$) into this form within the intelligence space universe ($U_{in}$). The converting function follows:

  $$\begin{array}{c}\hfill C_f\left(S{t}_r^{U_r}\right)=D_t^{U_{i}n}\end{array}$$

  (1)

  where $S{t}_r$ denotes the state of the ($U_r$), which is $S{t}_r$=<$\mathcal{G}$, $\mathcal{S}$, $\mathcal{T}$>where $D_t^{U_{i}n}$ represent data within the intelligence space and has the same structure of the captured state where:

  $$\begin{array}{c}{C}_f{(St<\mathcal{G},\mathcal{S},\mathcal{T}>)}_r^{U_r})=D<\mathcal{G},\mathcal{S},\mathcal{T}{>}_t^{U_{i}n}\\ D_t^{U_{i}n}=<\mathcal{G},\mathcal{S},\mathcal{T}>.\end{array}$$
• Second form of intelligence (information): Data alone is insufficient and unintelligible. So, it is necessary to add meaning to the data. Adding semantics derived from $OV$ transforms data within $U_{in}$ into information. $U_{in}$ may have a transformed function that allows it to do this:

  $$T_{f_1}^{U_{in}}<D^{U_{in}},OV>=I^{U_{in}}$$

  (2)

  where $D^{U_{in}}$ represents form1 within the observed universe, and $OV$ is an ontological view that enables the transformation from data to Information $I^{U_{in}}$ denotes Information.
• Third form (knowledge): $U_{in}$ may be equipped with a function to extract new implicit information from existing information (explicitly). The function will employ axioms derived from the ontological view (these axioms are a set of logical formulae). Due to this knowledge, the intelligence space can make wise decisions and solve problems. The function of transformation can be expressed as follows:

  $$T_{f_2}^{U_{in}}<I^{U_{in}},OV>={\mathcal{K}}^{U_{in}}$$

  (3)

  where $I^{U_{in}}$ is explicit information possessed by $U_{in}$, and $OV$ will be applied to extract axioms used in deducing. The if-then statement is a common example of deductive reasoning. Using logic, if $A=B$ and $B=C$, then A must $=C$. However, because the FOL was used as a logic language to specify data, its deduction rules will also be applied. The three equations (1, 2 and 3) represent the three forms of intelligence (Data, information and Knowledge, respectively).
  

  Figure 4. shows the nature of intelligence and its form.

  Figure 4. shows the nature of intelligence and its form.

  

7. Collaborative Intelligence (CIDE): Framework and Definition Aspects"

Figure 5. demonstrates the emergence of Collaborative Intelligence.

Figure 5. demonstrates the emergence of Collaborative Intelligence.

7.1. Categories of Overlap among Distributed Intelligences

In this context, "overlap" pertains to the intersection of intended intelligences. These intended intelligences emerge from the intersection of numerous distributed intelligences originating from various intelligence spaces. As previously mentioned, our perception and comprehension of intelligence play a pivotal role in developing collaborative intelligence.

In our endeavour to develop intelligence and collaborative intelligence, we have adopted an approach closely aligned with the one outlined in the reference [23]. This particular study [23] involves the construction of intended models within a conceptualization framework. The primary focus of our study is information, considered the second form of intelligence. By employing semantics by adding it to data, which represents the first form of intelligence, we can effectively transform it into significant and essential information. This transformation is rooted in the ontological view used in the conceptualization model.

We base our assumption on utilizing the conceptualization model and applying an ontological view to determine the intersection between intended intelligences. To streamline our concept, we can assume the existence of two observer universes called intelligence spaces, namely $U_{in1}$ and $U_{in2}$, which will each capture distinct states of the observed universe, referred to as reality $U_r$. The intelligence spaces will develop their intelligence model by utilizing different ontological views, namely ${\mu }_F$ and ${\pi }_s$.

The intended models within ontological views ${\mu }_F$ and ${\pi }_s$ align with a second form, denoted as the intended intelligences, in each intelligence space ($U_{in1}$ and $U_{in2}$). ${ı}_{\mathcal{HF}\left(L1\right)}$ denotes the first set of intended intelligences generated by the first intelligence space through ${\mu }_F$. Conversely, ${ı}_{\mathcal{HS}\left(L2\right)}$ signifies the intended intelligences of the second intelligence space, employing ${\pi }_s$.

Subsequently, the potential overlap of distributed intelligences, which are categorized into three distinct classes based on the intersection of their intended intelligences, will be delineated:

• [Definition 7.1.1 Partial Overlap] Given two sets of intended intelligences, the first intended intelligence, denoted as ${ı}_{\mathcal{HF}\left(L1\right)}$, pertaining to language $L_1$, is derived from the first ontological view, represented as ${\mu }_F$. Similarly, the second intended intelligence, denoted as ${ı}_{\mathcal{HS}\left(L2\right)}$, associated with language $L_2$, is derived from the second ontological view, represented as ${\pi }_s$. ${\mu }_F$ is Partially Overlapping (symbolized by $\Xi$) with ${\pi }_s$ if only if ${ı}_{\mathcal{HF}\left(L1\right)}$ partially intersect (⋈) with ${ı}_{\mathcal{HS}\left(L2\right)}$. In other words, the intersection between these two intended intelligences is true (not empty) and unequal.

  $$\begin{array}{c}({ı}_{\mathcal{H}F\left(L1\right)}\bowtie {ı}_{\mathcal{H}S\left(L2\right)})\leftrightarrow \left({\mu }_F\Xi {\pi }_s\right)\\ (({ı}_{\mathcal{H}F\left(L1\right)}\cap {ı}_{\mathcal{H}S\left(L2\right)}\ne \varnothing )\wedge (({ı}_{\mathcal{H}F\left(L1\right)}\cap {ı}_{\mathcal{H}S\left(L2\right)}\subset {ı}_{\mathcal{H}F\left(L1\right)})\\ \wedge ({ı}_{\mathcal{H}S\left(L2\right)}\cap {ı}_{\mathcal{H}F\left(L1\right)}\subset {ı}_{\mathcal{H}S\left(L2\right)}))\leftrightarrow \left({\mu }_F\Xi {\pi }_s\right)\\ (({ı}_{\mathcal{H}F\left(L1\right)}\cap {ı}_{\mathcal{H}S\left(L2\right)}=\varnothing )\wedge ({ı}_{\mathcal{H}F\left(L1\right)}\ne {ı}_{\mathcal{H}S\left(L2\right)}))\leftrightarrow \left({\mu }_F\Xi {\pi }_s\right)\end{array}$$
• [Definition 7.1.2 Completely Overlap] Given two sets of intended intelligences, the first intended intelligence, denoted as ${ı}_{\mathcal{HF}\left(L1\right)}$, pertaining to language $L_1$, is derived from the first ontological view, represented as ${\mu }_F$. Similarly, the second intended intelligence, denoted as ${ı}_{\mathcal{HS}\left(L2\right)}$, associated with language $L_2$, is derived from the second ontological view, represented as ${\pi }_s$. ${\mu }_F$ is Completely Overlapping (symbolized by ⊡) with ${\pi }_s$ if only if ${ı}_{\mathcal{HF}\left(L1\right)}$ completely intersect (⋉) with ${ı}_{\mathcal{HS}\left(L2\right)}$. In other words, the intersection between these two intended intelligences is equal to whole elements in these intended intelligences; the two ontological views either overlap completely or partially.

  $$\begin{array}{c}({ı}_{\mathcal{H}F\left(L1\right)}⋉{ı}_{\mathcal{H}S\left(L2\right)})\leftrightarrow ({\mu }_F⊡{\pi }_s)\cap \left({\mu }_F\Xi {\pi }_s\right).\\ \\ (({ı}_{\mathcal{H}F\left(L1\right)}\cap {ı}_{\mathcal{H}S\left(L2\right)}\ne \varnothing )\wedge (({ı}_{\mathcal{H}F\left(L1\right)}\subset {ı}_{\mathcal{H}S\left(L2\right)})\\ \wedge ({ı}_{\mathcal{H}S\left(L2\right)}\subset {ı}_{\mathcal{H}F\left(L1\right)}))\leftrightarrow ({\mu }_F⊡{\pi }_s)\cup \left({\mu }_F\Xi {\pi }_s\right).\\ \\ (({ı}_{\mathcal{H}F\left(L1\right)}\cup {ı}_{\mathcal{H}S\left(L2\right)}\ne \varnothing )\wedge ({ı}_{\mathcal{H}F\left(L1\right)}={ı}_{\mathcal{H}S\left(L2\right)}))\leftrightarrow \\ (({\mu }_F⊡{\pi }_s)\cap \left({\mu }_F\Xi {\pi }_s\right)).\end{array}$$
• [Definition 7.1.3 Non-Overlap] Given two sets of intended intelligences, the first intended intelligence, denoted as ${ı}_{\mathcal{HF}\left(L1\right)}$, pertaining to language $L_1$, is derived from the first ontological view, represented as ${\mu }_F$. Similarly, the second intended intelligence, denoted as ${ı}_{\mathcal{HS}\left(L2\right)}$, associated with language $L_2$, is derived from the second ontological view, represented as ${\pi }_s$. ${\mu }_F$ is non-Overlapping (symbolized by ⊠) with ${\pi }_s$ if only if ${ı}_{\mathcal{HF}\left(L1\right)}$ is not intersect (⋊) with ${ı}_{\mathcal{HS}\left(L2\right)}$. In other words, the intersection between these two intended intelligences is empty (∅); the two ontological views will not overlap.

  $$\begin{array}{c}({ı}_{\mathcal{H}F\left(L1\right)}⋊{ı}_{\mathcal{H}S\left(L2\right)})\leftrightarrow ({\mu }_F⊠{\pi }_s)\\ ({ı}_{\mathcal{H}F\left(L1\right)}\cap {ı}_{\mathcal{H}S\left(L2\right)}=\varnothing )\leftrightarrow ({\mu }_F⊠{\pi }_s)\end{array}$$

Figure 6 illustrates the categorization of the overlap of many distributed intelligences in a decentralized environment, which occurs when their intended intelligences intersect.

Figure 6. Displays the degree of overlap and models of languages, approaches, Intended models, and CI.

Figure 6. Displays the degree of overlap and models of languages, approaches, Intended models, and CI.