## 3 The Proposed Conversational System: CORES
### Problem Formulation and Overview  
We formulate the problem of this study as follows:  
1. The VR shop consists of several digital stores \(DS=\{DS_{1},DS_{2},\ldots,DS_{M}\}\). Each digital store \(DS_{i}\) is specialized in selling specific genres of items (kitchen, sports, choices, etc.). We define each store \(DS_{i}\) by the spatial 3D coordinates \(x_{i}\), \(y_{i}\), and \(z_{i}\) (latitude, longitude, and height) (e.g., latitude: 40.7128\({}^{\circ}\) N, longitude: 74.0060\({}^{\circ}\) W, height: 10 m). 2. The item dataset \(D=\{I_{1},I_{2},\ldots,I_{N}\}\) is classified by digital store and genre, where \(N\) represents the total number of items. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Related Works**} & **LLM** & **Context** & **Social** & **Emotions** & **3D Vis.** \\ \hline \multirow{8}{*}{**VR-Based Recommendation**} & [PERSON] et al. [17] & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [18] & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [19] & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [20] & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [21] & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [22] & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [23] & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & IKEA Kreative [24] & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [25] & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\
**Emotion-Based VR Shopping** & SNSs [26] & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\times\) \\  & [PERSON] et al. [27] & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\times\) \\  & [PERSON] et al. [28] & \(\surd\) & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [29] & \(\surd\) & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [30] & \(\surd\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\
**LLM-Driven VR Shopping** & [PERSON] et al. [31] & \(\surd\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [32] & \(\times\) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) \\  & [PERSON] et al. [33] & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) \\  & [PERSON] et al. [34] & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) & \(\times\) \\ \hline
**Our Proposed Approach** & & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Related works comparisons. Each item \(I_{i}\) is identified by \(id\), where it has a description \(d\) and a set of features \(F_{ij}=\{f_{i1},f_{i1},\ldots,f_{iM}\}\). \(M\) represents the total features by item. These features could include attributes such as size, price, color, brand, style, material, performance, popularity, durability, and other additional attributes for specific product genres such as laptops defined by battery life and capacity. 4. The conversational recommendation handler must recommend \(n\) items in the form of answers \(A_{i}=\{(\,I_{1},E_{1},V_{1},S_{1}),\ldots,(\,I_{n},E_{n},V_{n},S_{n})\}\) for the user based on its \(i\)th query \(Q_{i}\), where \(I_{j}\) represents the \(j^{th}\) recommended items, \(E_{j}\) represents the corresponding \(j^{th}\) explanation, \(V_{j}\) represents the corresponding \(j^{th}\) VR visualization, and \(S_{j}\) represents the corresponding \(j^{th}\) insight. 5. The user query \(Q_{i}\) is defined in terms of genre and intentions (i.e., characteristics). For example, if a user asks for kitchen appliance recommendations or mentions specific genres, this indicates their intentions, including modern styles and durability to discover new kitchen appliances.