## 3 DIKWP Semantic Interaction for Unidirectional Communication Impairments
### Purpose-Driven Decision-Making for Object Differentiation
**C. Purpose Formation**  
**Red Ball:**  
\(\forall t_{1}(S_{RelBall}(t_{1})\to PUP_{play}(t_{1}+\Delta t))\)  
\(\forall t_{2}(PUP_{play}(t_{2})\to SubPUP_{patRedBall}(t_{2}+\Delta t)\lor SubPUP _{chaseRelBall}(t_{2}+\Delta t)\)  
\(\lor SubPUP_{pushRedBall}(t_{2}+\Delta t))\)  
The infant gradually forms the primary intent to play with the red ball, along with sub-purposes such as patting, chasing, and pushing the ball. \(Output=playRedBall_{PUP}\wedge patRedBall_{Sub_PUP}\wedge chaseRedBall_{Sub_PUP}\)  
\(\wedge pushRedBall_{Sub_PUP}\)  
**Balloon:**  
The infant gradually forms the primary intent to play with the balloon, along with sub-purposes such as patting, chasing, and throwing the ball. \(Output=playBalloon_{PUP}\wedge patBalloon_{Sub_PUP}\wedge chaseBalloon_{Sub_PUP}\)  
\(\wedge throwBalloon_{Sub_PUP}\)  
**D. Purpose Decision**  
\(Input=patRedBall_{Sub_PUP}\wedge patBalloon_{Sub_PUP}\)  
\(\forall t_{3}\), \((SubPUP_{patRedBall}(t_{3})\wedge f_{WIS}(RedBall,t_{3})\wedge SubPUP_{patBalloon}(t_{3})\)  
\(\wedge f_{WIS}(Balloon,t_{3}))\to E_{patRedBall}(t_{3}+\Delta t)\)  
After filtering through the semantic space, the result is  
\(Output=E_{patRedBall}\)  
Finally, the action of patting the red ball is executed. The algorithm design is presented in Algorithm 2. ```
0:\(obj\), \(pup\)
0:act if\(obj=\"RedBall\"\)then if\(pup=\"play\"\)then \(SubPup\to ChooseSubPup(\"pat\",\"chase\",\"push\")\) \(act\to ExecateAction(SubPup)\) elseif\(pup=\"bounce\"\)then \(SubPup\to\"bounce\"\) \(act\to ExecateAction(SubPup)\) endif elseif\(obj=\"Balloon\"\)then if\(pup=\"play\"\)then \(SubPup\to ChooseSubPup(\"pat\",\"chase\",\"throw\")\) \(act\to ExecateAction(SubPup)\) elseif\(pup=\"bounce\"\)then \(SubPup\to\"bounce\"\) \(act\to ExecateAction(SubPup)\) else \(act\to\"Error:Balloonisnotsafetobounce\"\) endif endif
```  
**Algorithm 2** Infants' Purpose-Driven Discrimimatory Decisions. An interaction diagram of the DIKWP semantic space for an infant differentiating between the \"red ball\" and the \"balloon\" is shown in Figure 7.  
To better demonstrate the effectiveness of the DIKWP-oriented human-machine interaction model we constructed and the importance of purpose-driven decision-making, we conducted tests on the decisions made by infants under different purpose-driven scenarios. When the infant intends to \"play with a ball\", the infant will choose the object within their sensory range that belongs to the \"ball\" category and is closest to them. Assuming we exclude external interference, how would the infant choose between the \"red ball\" and the \"balloon\"? We use a cost function to evaluate the required cost under different purposes, assessing the number of expanded nodes during the search process. First, we define the symbols used:  
\(Start\) represents the starting node. \(Goal\) represents the goal node. \(S_{o}^{*}\) represents the semantic graph of object o, where the set of neighboring nodes for each node \(v\) is \(N(v)\). \(Input=\{playBall\}_{PUP}\). \(Processing\)  
\(f(Start,goal,S_{o}^{*})=1+\sum_{v\in N(start)}(v,goal,S_{o}^{*}),v\in DIKWP\)  
\(Output_{RedBall}=patRedBall_{act}\)  
\(f(playBall_{PUP},patRedBall_{act},S_{RedBall}^{*})=39\)  
\(Output_{Balloon}=chaseBallon\lor throwBallon_{act}\)  
\(f(playBall_{PUP},chaseBalloon\lor throwBalloon_{act},S_{Balloon}^{*})=69\)  
\(Input=patBall_{PUP}\)  
\(Output_{RedBall}=patRedBall_{act}\)  
Under the primary purpose of \"playing with a ball\", the infant's choice could be either the red ball or the balloon. However, if the infant's sub-purpose is further defined, such as \"patting the ball\", the infant can only choose the red ball because patting the balloon might cause it to explode. If the purpose is to \"chase the ball\" or \"throw the ball\", the infant can only choose the balloon because the rolling red ball might pose a danger to the infant. The decision-making process under the infant's purpose is illustrated in Figure 8.  
Figure 7: DIKWP Semantic space interaction for infant differentiation between “red ball” and “balloon”.