The search for a chain of situations from the current situation to the target one is the result of planning purposeful behavior. Planning purposeful behavior is a procedure for choosing a path (chain of events) on the hierarchy of representations of motor actions, which is realized in the anterior (motor) cortex of the human brain, where a hierarchy of levels of dictionaries is represented that reflect varying degrees of generality of fragments of motor behavior. This chain is constructed by fitting (for example, by means of fuzzy logic ( Borisov & Kharlamov, 2023 )) a chain of situations, from the current situation to the target one ${\hat{I}}_1$ and ${\hat{I}}_{fin}$ (which is selected in the hierarchy of representations of the motor—i.e. anterior-cortex), by projecting into the representation of situations on the world model presented in the lamellae of the hippocampus ( Kharlamov, 2023a ) from the template of the current situation to the template of the target situation $S_1$ and $S_{fin}$; and then projecting the representation of the combinatorics of objects and events (represented within the templates of situations in the hippocampal world model) into the world model of the sensory cortex, represented in the columns of the sensory cortex containing representations of the objects and events themselves ( Kharlamov, 2023a ) ${\hat{S}}_1$ and ${\hat{S}}_{fin}$, see Figure 1(A) . The cap above the symbol indicates the so called trajectory in the multidimensional space modeled by the cortex column (see formula (1) in Section 2.1) in which the dictionary is formed.

This purposeful behavior (see Figure 1(B) ) is implemented in the reverse order: searching for a counter text, followed by identifying, within the semantic network of this text, a chain of situations from the current situation to the target one ${\hat{S}}_1$ and ${\hat{S}}_{fin}$, respectively, identifying a chain of suitable templates of situations $S_1$ and $S_{fin}$ from the current situation to the target one in the lamellae of the hippocampus, and finally—identifying appropriate actions in the hierarchy of the anterior (motor) cortex bridge the original pair of events ${\hat{I}}_1$ and ${\hat{I}}_{fin}$, which originated all these processes.

A set of pairs of word root stems (since we are considering the example of the language part of the world model), presented in the dictionaries (see Figure 2 ) of the upper (semantic) level of the hierarchy of representations in the columns of the sensory cortex, which is obtained during the processing of a particular text, that is, a semantic network (homogeneous, directed, with weighted vertices and connections ( Kharlamov, 2023a )) is virtually united into a semantic network of the t-th text, ${\hat{M}}_t$. On this semantic network, the desired pair of situations is sought: ${\hat{S}}_1$ and ${\hat{S}}_{fin}$. This pair in the lamellae of the hippocampus corresponds to a pair of situations $S_1$and $S_{fin}$, which are the beginning and end of the desired chain of situations. Next, in the anterior cortex, the names of ${\hat{I}}_1$ and ${\hat{I}}_{fin}$ are sought, corresponding to the beginning and target of this chain of situations.

The code sequence corresponding to the analyzed text forms a dictionary ${\left\{B_i\right\}}_1$ of the most frequently repeated fragments of the sounding text at the first level in the cortex, that is, phonemes.

At the next level of processing (let us call it morphological), a dictionary of the morphological level ${\left\{B_j\right\}}_2$ is formed that characterizes the most frequently encountered units of the text, that is, inflectional morphemes. At the next (lexical) level, dictionaries of word root stems ${\left\{B_k\right\}}_3$ are presented. The syntactic level presents a dictionary of syntaxemes, which are an inflectional structure of successive pairs of words of the text with cuts instead of word stems ${\left\{B_l\right\}}_4$. Here, when forming syntactic sequences, at the input of the word stem level, elements of the morphological level are filtered from the input texts that connect word stems into more complex images—pairs of root stems for successive pairs of words in the text. At the output of this level, only a sequence of pairwise combined root stems of words ${\left\{B_m\right\}}_5$ remains in the so called “syntactic” sequence—a sequence of connections of filtered elements of the bottom level (see formulae (3) of section 3.1).

Weighing of nodes is a separate procedure, see formula (6), which takes into account the depth of connections of individual nodes on this semantic network – see section 4.2.

Thus, one can talk about multi-level structural processing of information in the columns of the cortex.

Similar to the hierarchy of dictionaries of level-forming elements of language, one can consider hierarchies of level-forming elements of quasi-language, for example, in the visual modality. The top level of this hierarchy corresponds to the semantic network of the extralinguistic world model, and these two semantic networks (linguistic and extralinguistic) represent the world in the same way (at least in their core part), that is, their core parts are isomorphic (“mapped one-to-one and onto”).

From these chains, a chain is selected that optimally matches the individual’s world model.

We have considered purposeful behavior in the context of searching for “counter text”. However, such a counter text may not necessarily be a language text: the counter text sought may also be a quasi-text in an extralinguistic representation. In this case, the order of planning and implementing purposeful behavior is completely preserved, however, quasi-texts of the corresponding modalities are used instead of texts; in the hippocampus, the processes occur in both hippocampal dominant and subdominant parts; and in both the sensory and anterior cortex, the model is presented in both the dominant and subdominant hemispheres, since in fact, with the exception of special cases, purposeful behavior is always mixed (with the participation of linguistic and extralinguistic representations in both the cortex and the hippocampus).

The text search procedure is reduced to searching for a text that contains the desired chain. The search for such a text can be shown on the example of forming a semantic network of text in the TextAnalyst program ( Kharlamov, 2023b ; Kharlamov, 2025 ). The TextAnalyst program solves the problem of constructing a homogeneous directed weighted semantic network where the desired chain can be found. Constructing a semantic network of text involves implementing several steps:

1) Removal of non-textual information form the text.

2) Removal of redundant information from the text.

3) Splitting the text into tokens and sentences.

4) Counting the frequency of occurrence for tokens and token pairs.

5) Developing a primary network.

6) Calculating the semantic ranks of network nodes.

Removal of non-textual information form the text. It is necessary to remove information that is not involved in the formation of the semantic network: this means removal of non-textual information, that is, pictures, diagrams; replacing numbers with words; decoding abbreviations and acronyms.

Removal of redundant information from the text. Pronouns, prepositions and articles are removed from the text. Since a homogeneous semantic network is constructed based on the text, verbs are no longer in demand as all relations in the representations of text sentences are replaced by an associative type of connection (to be close to each other in the text).

Splitting the text into tokens and sentences. Since it is necessary to identify individual units of text when constructing a network, it is split into tokens. To identify the degree of coherence of words included in the text, it is split into pairs of words within individual sentences.

Counting the frequency of occurrence for tokens and token pairs. To further calculate the ranks of network nodes and the values of the weights of word connections in the network, the frequency of occurrence for tokens and token pairs is counted in the primary network.

Forming a primary network. From the remaining (not removed during preprocessing) words of the text, a primary directed homogeneous semantic network is constructed, the nodes of which and the connections between the nodes are weighted by the calculated frequencies of occurrence.

Calculating the semantic ranks of network nodes. Finally, the weight characteristics of words are replaced by semantic ranks: the weight characteristics of network nodes are recalculated. Those nodes that are connected in the network with a large number of nodes with a large weight increase their weight to the detriment of the weights of other nodes, see formula (6).

This procedure is implemented for all candidate texts. As a result, in the obtained semantic networks of texts, chains of nodes are identified from the node describing the current situation ${\hat{S}}_1$ to the node describing the target situation ${\hat{S}}_{fin}$. Of these texts, one is selected where the obtained chain is more effective than the others: shorter, having a greater weight, or selected according to some other criteria.

Since both the counter text and the counter quasi-text are structures that allow solving the problem (as in this case both the text and the quasi-text are transformed into semantic networks ( Kharlamov, 2017 ), in one case linguistic, in the other case extralinguistic, which both describe the world in which a person lives), it turns out to be insignificant in which modality the problem is solved. In the human world model, both linguistic and non-linguistic descriptions of the world are presented in the form of semantic networks. These descriptions are isomorphic: what is in one description is also in the other. Therefore, the problem posed can be solved in any of the modalities by obtaining a text (quasi-text) that forms a chain of situations from the current situation to the target one. Therefore, we can further consider the solution to the problem on the example of using the language text.

A counter text of a natural language (quasi-text) can be searched for in three ways. 1) Search in the internal database of texts (quasi-texts), which are available as a result of accumulated life experience. 2) Search in the external database of texts (quasi-texts). 3) Formation of such a text (quasi-text), if there is no suitable text in either the internal or external databases.

The search procedure includes ( Kharlamov, 2023b ) comparison of texts, classification of texts and selection of relevant texts. Formation of a counter text not available in the internal and external databases turns out to be a significantly more complex procedure, since it is associated with the generation of texts describing the solution of problems in specific subject domains. Formation of such behavior is an example of creative behavior and is beyond the scope of this work. Moreover, at the present, neither an implementation, nor even a description of this procedure exists (at least for artificial systems).

As a historical anecdote, the generation of a counter-text for solving a specific problem can be illustrated by Isaac Newton’s formulation of the law of universal gravitation. The story of Newton sitting under an apple tree heavy with ripe fruits and being struck by a falling apple represents a counter-quasi-text that allowed him to bridge the gap and complete the solution to the problem of formulating his famous law.

The sensory level of purposeful behavior is based on the world model presented in the sensory cortex. The world model in the sensory cortex is formed as a set of hierarchies of dictionaries of various modalities (see Figure 2 ), which at the top level of the hierarchies are combined into two semantic networks – linguistic and extralinguistic ( Kharlamov, 2023b ).

Let us demonstrate this, as usually, on the example of linguistic behavior, which is currently formalized within the subject domain of “Linguistics” quite well ( Kharlamov, 2023b ). The language world model is a hierarchy of dictionaries of level-forming elements of language (see Figure 2 ) from phonemes (for sounding text) to the level of permissible pairwise compatibility of dictionary words (semantic level), which can be represented by a directed weighted semantic network.

The hierarchy of level representations is formed as a result of the structural analysis of input sensory sequences $\left\{A\right\}$ ( Kharlamov, 2023b ). In this case, the input code sensory sequences are displayed (see formula (1)) in the columns of the cortex by pyramidal neurons of the 3^rd layer of the cortex as neurons with temporal summation of signals in trajectories in a multidimensional space, which (trajectories) are repeatedly traversed in the presence of repeating fragments in the input text, thereby forming dictionaries (see formula (2)) of these level-forming elements in the learning process.

Let $\left\{A\right\}$ denote the set of code sequences formed by the signal periphery of analyzers, the elements of which are the symbols that make up the codes of the input sequences $A=\left(\cdots ,a_{-1},a_0,a_1,\cdots ,a_i,\cdots \right)$. Hereinafter, for simplicity, we will consider everything on the example of processing binary sequences. In the binary case, $a_i\in \left\{0,1\right\}$. As such a sequence, we can, for example, take the read over text of L. N. Tolstoy’s novel “War and Peace”, encoded with a binary code.

Let $\left\{\hat{A}\right\}$ denote the set of trajectories of sequences corresponding to the set of input sequences $\left\{A\right\}$, the elements of which ${\hat{a}}_i$ are points of the space $R^n$, i.e. nodes of the unit hypercube ${\hat{a}}_i\in G_e^n$, where ${\hat{a}}_i=\left(a_{i-n+1},a_{i-n+2},\cdots ,a_i\right)$ are successive fragments of length n of sequence A symbols, shifted relative to each other by one symbol (by one time unit) – coordinates of points in the multidimensional space $R^n$ (due to the binarity of the representation – nodes of the unit hypercube $G_e^n$). Then:

$F_n:A\to \hat{A},F_n\left(A\right)=\hat{A},$ (1)

where $A=\left(\cdots ,a_i,\cdots :a_i\in \left\{0,1\right\}\right)$, а

$\begin{array}{c}\hat{A}=\left(\cdots ,{\hat{a}}_{-2},{\hat{a}}_{-1},\cdots ,{\hat{a}}_i,\cdots \right)\\ =\left(\cdots ,\left(a_{-n-1},a_{-n},\cdots ,a_{-2}\right),\left(a_{-n},a_{-n+1},\cdots ,a_{-1}\right),\cdots ,\left(a_{i-n+1},a_{i-n+2},\cdots ,a_i\right),\cdots \right).\end{array}$

The dictionary as a set of repetitions of fragments of input sensory sequences is formed from a set of sequences ${\left\{A\right\}}_k$, in each of which, using the transformation $H_{h}RM{F}_n$ (mapping sequences of class ${\left\{A\right\}}_k$ into an n -dimensional space and applying a threshold transformation to them), subsequences $B_j$ ∁ $A_k$ included in it at least h times are selected. Thus, the transformation $H_{h}RM{F}_n$ when interacting with the input set ${\left\{A\right\}}_{k_1}$ in the space of a given dimension restores the dictionary ${\left\{\hat{B}\right\}}_{k_1}$ of subsequences $B_i$ included in the trajectories of the input set:

${\left\{{\hat{B}}_i\right\}}_{k_1}=H_{h}RM{F}_n\left({\left\{A\right\}}_{k_1}\right).$ (2)

The resultant dictionary functions as a filter, identifying the connections of words of the lower level dictionary within the input code sequences (3).

$F_{n,C}^{-1}\left(\tilde{A},\left\{{\hat{B}}_j\right\}\right)=C,$ (3)

where $C={\left(\begin{array}{cc}{\tilde{a}}_i|{\widehat{\stackrel{˜}{a}}}_i\ne {\hat{b}}_j& 0|{\widehat{\stackrel{˜}{a}}}_i={\hat{b}}_j\end{array}\right)}^{\text{T}}$, here, ${\tilde{a}}_i\in \hat{A}$ и ${\widehat{\stackrel{˜}{a}}}_i\in \widehat{\stackrel{˜}{A}}$, а ${\tilde{b}}_j\in \hat{B}$ и ${\widehat{\stackrel{˜}{b}}}_j\in \widehat{\stackrel{˜}{B}}$.

The so-called “syntactic” sequences obtained as a result of filtering form the dictionary of the next level (see Figure 3 ).

All of this taken together can be represented as a hierarchy of dictionaries of level-forming elements of language of various levels of complexity (see Figure 2 ).

The world model in terms of level-forming elements represented in the columns of the sensory cortex represents the modeled world virtually (see Figure 2 ): pairs of root stems of the top-level words of the language model and pairs of images of objects and events of the top-level extralinguistic model are combined into language and extralinguistic networks, which are essentially semantic: pairs of events of the extralinguistic network characterize the permissible compatibility of objects and events of the modeled world, as do pairs of root stems of the language network that describe them. These objects and events (and the root stems that describe them) are used to form models of the next stratum of representations formed and stored in the lamellae of the hippocampus as combinations of images of these objects and events (and, in the dominant hippocampus, of words that describe them). These hippocampal models are models of scene templates (sequences of scenes—beginning-continuation-end—describe complete situations).

$\hat{F}=\ast {\widehat{Sf}}_p={\hat{f}}_1\ast \left(\ast {\widehat{Sf}}_p\right)=\hat{I}\ast \left(\ast {\widehat{Sf}}_p\right),$ (4)

where ${\widehat{Sf}}_p$ can be conventionally referred to as a subframe, where $\hat{I}$ is the name of the frame (e.g., a word in one of the modalities). The subframe $\widehat{Sf}$ can be represented as a union of the frame components, where ${[\ast ]}_i$ is the concatenation by sequential index i:

$\begin{array}{c}\widehat{Sf}={\displaystyle {\cup }_m\left({\hat{f}}_m\right)}={\displaystyle {\cup }_m\left(\ast {\hat{A}}_{ijKm}{{\displaystyle V}}_{ijk<K}{\hat{A}}_{ijkm}\right)}\\ ={\displaystyle {\cup }_m\left(\ast {\hat{A}}_{ijKm}{{\displaystyle V}}_{ijk<K}{\hat{A}}_{ijkm}\right)}={\hat{f}}_1\cup \left({\displaystyle {\cup }_{m\ne 1}{\hat{f}}_m}\right),\end{array}$ (5)

${\hat{f}}_m$ is a frame component: ${\hat{f}}_m={\hat{A}}_{ijKm}V{\hat{A}}_{ijkm}$, where ${\hat{A}}_{ijkm}$ are chains on the graph, and $V$ represents inclusion in its place into the words of a higher level dictionary.

According to biologists ( Rolls, 1990 ), these models represent the contents of the memory of the CA₃ fields of the hippocampal lamellae, which are modeled by Hopfield artificial neural networks ( Figure 4 ): with each lamella representing a separate situation.

The scene model stored in the associative memory of the Hopfield network of the hippocampal lamella represents a combinatorics of images of events and objects that are part of the situation (more precisely, indices of their representations in the columns of the sensory cortex ( Bekhtereva, 1978 )), as well as phrases of the language that describe them (where words are also represented as indices of their storage in the columns of the sensory cortex, where their images are presented in detail) ( Kharlamov, 2023b ).

Individual fragments of the associative memory of the hippocampus, represented in individual lamellae, are a unified world model in the form of a total associative network, where individual events are dependent on other events they are connected with in this associative network, and therefore their ranks in the model are calculated iteratively—see formula (6)—taking into account these connections in the process of iterative access to storage (up to 20 cycles) ( Vinogradova, 1975 ).

The initially formed statistical representation of the text (a network of event images with their connections as the frequency of occurrence of events and connections between them) undergoes re-ranking, thus allowing move from a frequency portrait of the text to an associative network of key images of text events (networks with ranks of these events, that is, their semantic weights):

$w_i\left(t+1\right)=\left({\displaystyle {\sum }_j{w}_j\left(t\right)w_{ij}}\right)\sigma \left(\bar{E}\right),$ (6)

where $w_i\left(0\right)=z_i$; $w_{ij}=z_{ij}/z_j$ and $\sigma \left(\bar{E}\right)=1/\left(1+{\text{e}}^{-k\bar{E}}\right)$ is a function normalizing to the average energy value of all network nodes $\bar{E}$; $z_i$ is the frequency of occurrence of the i-th word in the text, $z_{ij}$ is the frequency of co-occurrence of the i-th and j-th words in text fragments; t is the iteration number. The resulting numerical characteristic of words (their semantic weight) characterizes the degree of their significance in the text.

There is also a third stratum of representation of the world model in the human brain (see Figure 1(B) ). It is represented in the anterior cortex, where this model is represented (at the lowest level in the hierarchy of representations) in the form of motor activity control, and at higher levels—in the form of fragments of generalized behavior plans of varying degrees of generalization. At the highest level of representation in this hierarchy, this stratum is represented in the form of images of ideas of behavioral activity in generalized situations. These generalized representations at lower levels unfold into increasingly detailed behavioral acts, and at the lowest level—into acts of motor control. For example, articulatory—in the case of using motor function when producing voiced speech.