## 3 Results: AGA Logic Variables for Scene Description and Dialog Communications
### Representation of the Scene of Action by Natural Language, Numerical Codes, and Truth Levels
Check coefficients, \(C^{N}_{i,j}\), \(C^{K}_{i,j}\), \(C^{NXR}_{i,j}\), \(C^{KXR}_{i,j}\), are to be calculated within the mapping of AGA to the natural-number scale (see Section 3.3). Verification procedures, shown in Figure 8a, can involve two data input channels, using truth-level codes and natural-number ones. One can process and compare data coded in both variants. That gives the possibility to separately compare the final and intermediate results and to detect errors or illegal modifications of data. For example, the final results in both representations should be the same or close if approximate estimations were used. Also, three equivalent representations are considered as the binding tool for the heterogeneous logic architecture of agent [75], which supposes parallel calculations in various logic models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**N**} & **Natural Language** & **Natural-Number Code** & **Truth-Level Code of** & \\  & **Vocabulary** & **of Vocabulary** & **Vocabulary** & **Content** \\ \hline
1 & \(V^{L}_{1,1}\) & \(V^{N}_{1,1}\) & \(V^{K}_{1,1}\) & Format of message \\  & \(w^{L}_{1,1,1}\) & \(w^{N}_{1,1,1}\) & \(w^{K}_{1,1,1}\) & “SOS” \\  & \(w^{L}_{1,1,2}\) & \(w^{N}_{1,1,2}\) & \(w^{K}_{1,1,2}\) & “Hi, read 2 parts message”; Initiation of the new phrase \\  & \(w^{L}_{1,1,3}\) & \(w^{N}_{1,1,3}\) & \(w^{K}_{1,1,3}\) & “Hi, read 3 parts message”; \\  &... &... &... &... \\  & \(w^{L}_{1,1,7}\) & \(w^{N}_{1,1,7}\) & \(w^{K}_{1,1,7}\) & “Ready to continue” \\  &... &... &... &... \\ \hline
2 & \(V^{L}_{1,2}\) & \(V^{N}_{1,2}\) & \(V^{K}_{1,2}\) & Fixed parole \\  &... &... &... &... \\ \(\text{K}\times\text{M}\) & \(V^{L}_{K,M}\) & \(V^{N}_{K,M}\) & \(V^{K}_{K,M}\) & Content given by expert \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The equivalence of words in vocabularies \(V^{L}_{v,m}\), \(V^{N}_{v,m}\), and \(V^{K}_{v,m}\). At the same time, natural-number code and mapped AGA truth levels have different number profiles for comparison. Figure 8b shows the principle of brief verification procedure for used vocabularies in the agent. Data representation by the histogram shown in Figure 8b is convenient for human checks. Within the proposed scheme of vocabularies, known types of activity and coded tasks' execution should lead to a preliminary known set of vocabularies, describing the task of the agent. Independent checks may be held in both vocabularies \(V^{N}_{v,m}\) and \(V^{L}_{v,m}\). As AGA truth-level representation \(w^{K}_{v,m}\) is compatible with the secret data coding scheme [18] and the scheme for distant comparison of data without their disclosing [68,69], it is preferable to use it for the control of data access in agents. Natural-number codes, \(w^{N}_{v,m}\), are better to describe common access content and less confidential data. A full check of the agent will need a comparison of all words, \(w^{K}_{v,m}\) and \(w^{N}_{v,m}\), in used matrixes, \(V^{K}_{v,m}\) and \(V^{N}_{v,m}\). However, all such procedures need one more critical component. Figure 8: **(a)** Two channels to provide separate access to internal data by more protected AGA truth-level codes and by simpler natural-number codes. **(b)** The principle of brief verification of vector components’ histogram in possessed and needed profiles for root vocabularies, \(V^{N}_{v},V^{K}_{v}\), and further chain ones. Figure 7: The scheme of transitions from natural-number code to logic truth-level code is necessary for the heterogeneous logic architecture of the agent. Equal scales for natural numbers and truth levels make this transition just a formal step.