## 3 Results: AGA Logic Variables for Scene Description and Dialog Communications
### Communication Module and the Dialog Protocol
## 5 Results: Fragmentation of AGA Function into Diagrams of Logic States for Verification

The most obvious way to hold selective verification procedure is to map the set of critical data from the holistic logic model onto low-dimensional 1D, 2D, or 3D charts or diagrams of logic parameters, which are convenient for quick visual checks by human experts, who are the final authority. For verification, e.g., in the position-based cryptography and route passing tasks [22], one can use time diagrams of visits to check points, 2D space maps of alternatively visited checkpoints or cargo terminals, time diagrams of the execution of the quantum protocol and verification procedures [68; 69]. But the design of such procedures for AGA needs to give several definitions. **Definition 5**. : _Fragmented mapping function (FMF) \(F(x_{l},\ldots,x_{m})\) taken within AGA is the result of the injective mapping \(F(x_{1},\ldots,x_{n})\to\ F(x_{l},\ldots,x_{m})\), where we have the following:_

1. \(n,l,m\in N=\{0,1,\ldots,\,k-1\},\ m\geq l\)_, and_ \(n-1\geq m-l\)_, (i.e., the mapping shortens the number of initially taken input variables);_
2. _Truth tables of the mapping function_ \(F(x_{1},\ldots,x_{n})\) _and the mapped one_ \(F(x_{l},\ldots,x_{m})\) _have the following:_ 1. _Identical data in columns for coinciding input variables_ \(x_{l},\ldots,x_{m}\)_;_ 2. _Identical logic constants_ \(C_{k}\) _in columns for output variables_ \(F(x_{l},\ldots,x_{m})\) _and_ \(F(x_{1},\ldots,x_{n})\)_._

Consequence. FMF can be defined for any sample of initially given input variables. For its practical formation, one should simply strike out further in Table 8 all columns for unused input variables, not included into the necessary set \(x_{1},\ldots,x_{m}\). **Definition 6**. : _The fragmented map \(M\) of the fragmented mapping function \(F(x_{l},\ldots,x_{m})\) is the group of points, mapping all given samples of input variables \(x_{l},\ldots,x_{m}\) from the truth table onto the arbitrarily chosen set of: (1) logic constants \([\,C_{k1},\ldots,C_{k2}\,]\), where \(C_{k1,\ k2}\in\ \{1,..,k-1\}\), or (2) output variables \(x_{j},j\in\ \{l,..,m\}\)._Note. The fragmented map, \(M\), shows the location of all objects or events with the chosen class given by the constant, \(C_{k}\); the limiting band for logic constants or input variables corresponds to critical parameters given by the task. **Definition 7**. : _Fragmented mapping function (FMF) is named the verification function (VF), if it belongs to the list of formal criteria \(L_{e}\), formed and checked by the knowledge expert._

Given above definitions are illustrated further by Table 10, demonstrating the example of formation of FMF \(F(x_{3},x_{4})\) by striking out unnecessary variables \(x_{1},x_{2},x_{5}\) from the initially given truth table. We suppose that coordinates \(x_{3},x_{4}\) correspond to space parameters \(x,y\), which can be the correlated ones if, e.g., the FMF \(F(x_{3},x_{4})\) shows the location of visited by robot objects or checkpoints. As correlated space and time variables (see Section 2.3) are considered in the AGA model to be different logic variables, they also can be selected for checks. Principally, any 2D or 3D mapping diagrams, like \(F(x,t)\), \(F(x,y)\), or \(F(x,y,t)\), given in the band \([0,\ k-1]\) can be considered as verification functions if adopted by the knowledge expert. The 2D logic diagram, in fact, resembles group point images, known in star navigation systems [88], which can be checked directly on the display or may be additionally processed. It is necessary to accent the fact that FMF can be formed arbitrarily for visual checks, but the reverse aggregation into new AGA functions needs to monitor the values of all the variables, for which FMF was initially defined.