## 3 Results: AGA Logic Variables for Scene Description and Dialog Communications
### Communication Phrase
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & (KxM-4)/2 th 8-byte part-content & & & & \\ \hline Variable & \(x_{K-8}\) & \(x_{K-7}\) & \(\ldots\) & \(\ldots\) & \(x_{K-2}\) & \(x_{K-1}\) & \(x_{K}\) \\ \hline Name & Assigned & Arbitrary & Arbitrary & \(\ldots\) & Arbitrary & Arbitrary & Total check \\  & hash, & word, & word, & & word, & word, & coefficient of all \\  & \(w_{v,m}\) & \(w_{v,m}\) & & & \(w_{v,m}\) & \(w_{v,m}\) & previous parts and \\  & & & & & & & & the current \\  & & & & & & & & one, \(C^{K}\) or \(C^{N/K}\) \\ \hline Vocabulary & \(V_{1,3}^{K}\) & \(V_{v,m}^{K}\) & \(V_{v,m}^{K}\) & \(\ldots\) & \(\ldots\) & \(V_{v,m}^{K}\) & \(V_{v,m}^{K}\) & \(V_{v,m}^{K}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._  
**Definition 1**. : _Total check coefficient, \(C_{i}^{K}\), of mapped truth levels is given for a phrase, \(\mathbf{W}_{i}\), written in AGA logic codes and is the arithmetic summation, \(C_{i}^{K}=\sum_{v}^{K^{\prime}}w_{v}^{K}\), carried out within Boolean logic for truth values of all words, \(w_{v}^{K}\), used in the phrase, \(\mathbf{W}_{i}\), and given by arbitrary sampling of vocabularies \(V^{K^{\prime}},K^{\prime}\leq\ K\). AGA truth levels before summation are mapped onto the linear scale of natural numbers, \(N\)._  
Application of the def. (3.1) is supposed to be convenient both for independent human checks and for automatic comparison with template data. Another convenient coefficient for checks is given by Definition 2. **Definition 2**. : _Total check coefficient, \(C_{i}^{N/K}\), of arithmetic summation of natural-numbers codes is given for a phrase, \(\mathbf{W}_{i}\), written in mixed natural-number and truth-levels code and is the arithmetic summation \(C_{i}^{N/K}=\sum_{v}^{N^{\prime}}w_{v}^{N/K}\), carried out for natural-number codes and mappings of truth-level codes of words \(w_{v}^{N}\) or \(w_{v}^{K}\), used in the phrase \(\mathbf{W}_{i}\) and taken from the sampling set of vocabularies \(V^{N^{\prime}}\) and \(V^{K^{\prime}}\), \(N^{\prime},K^{\prime}\subset N\)._  
The coefficient \(C_{i}^{N/K}\) is necessary for human or automatic checks within the heterogeneous logic architecture of agent, where one can independently visualize natural-number codes and evaluate the integrity of the dialog data exchange by the summation of all values, \(w_{v}^{N}\), in the phrase. One more useful tool for the logic verification in agent is the well-known Boolean logic operation XOR, used for the set of words in the phrase \(\mathbf{W}_{i}\), represented by truth levels or natural numbers. Its destination is to make digital \"fingerprints\" for phrases and their parts. XOR operation can help to compare identity and to hide real codes used in data channels without secret coding. **Definition 3**. : _Total coefficient \(C_{i}^{XRK}\) of check XOR binary logic operation taken for mapped truth levels is the set of Boolean XOR operations, \(C_{i}^{XRK}=\widetilde{w_{1}^{K}}\bigoplus\ldots\bigoplus\widetilde{w_{K^{ \prime}}^{K}}\) carried out in the phrase \(\mathbf{W}_{i}\) for binary representation of AGA truth levels of words, \(w_{v}^{K^{\prime}}\), mapped onto the linear scale of natural numbers \(N\)._  
**Definition 4**. : _Total coefficient \(C_{i}^{XRN}\) of check XOR binary logic operation is the set of Boolean XOR operations, \(C_{i}^{XRN}=w_{1}^{N}\bigoplus\ldots\bigoplus w_{K^{\prime}}^{N}\) carried out in the phrase \(\mathbf{W}_{i}\) for binary representation of natural-number codes of words, \(w_{v}^{K^{\prime}}\)._  
One should note that coefficients Def. \(1\div 4\) also can be easily used in phrases \(\mathbf{W}_{i}\), transmitted by parts, as shown in Table 4. \"Sewing\" or ordering of parts of the phrase \(\mathbf{W}_{i}\) in the addresser agent supposes the check of coefficients Def. \(1\div 4\) as for whole phrases, as for their separate parts.