## 3 Method
### Proposed Semi-Supervised Explainable BRBES Framework  
**Initial Facts:** The architectural design of the proposed semi-supervised explainable BRBES framework for predicting energy consumption in buildings is shown in Figure 1. Figure 1a represents the BRBES as symbolic AI which has five input values: interior space, month, day, hour, and heating method. The unit of interior space is the square meter, the month range is from January to December, the day range is from Monday to Sunday, the hour range is from 00:00 to 23:00, and heating method is either district or electric. These five values constitute five initial facts for the BRBES to provide energy consumption prediction. Among these facts, month, day, and hour are used to calculate solar illumination and interior inhabitance level of a building at a specific time instance. Against these initial facts, the BRBES predicts the energy consumption level in kWh by reasoning over its rule base. We now proceed to illustrate how this rule base of the BRBES models energy consumption knowledge to deliver transparent and explainable prediction. **Formalization of Domain Knowledge:** The body of knowledge that individuals have acquired in a particular area of expertise is called domain knowledge [62]. It can be viewed as a specialized manifestation of prior knowledge held by a domain expert or individual [63]. Knowledge of the energy consumption domain is represented by the rule base of the BRBES. Here, energy consumption serves as the domain of interest, and the rule base embodies the corresponding domain knowledge. A belief rule consists of two components: an antecedent part and a consequent part. In the rule base of the BRBES within our proposed semi-supervised framework, the antecedent part comprises three attributes: interior space, solar illumination, and interior inhabitance. The solar illumination value, ranging from 0 to 1, is derived based on the month and hour, as illustrated in Table 2. Sunrise and sunset times are utilized to determine the corresponding solar illumination level. Tables 3 and 4 present the calculation of interior inhabitance (ranging from 0 to 1) in an apartment, in line with the hour of the day, month of the year, and category of the day (weekday/weekend). Each antecedent attribute is assigned three referential values: high (H), medium (M), and low (L). The consequent attribute, Energy Consumption, shares the same referential value structure. We show the hierarchical relationship between three antecedent attributes and their consequent attributes in Figure 2. Against three referential values of each of the three antecedent attributes, the rule base of the BRBES contains twenty-seven rules. There are four ways to create this rule base [47]: transforming expert knowledge into belief rules, formulating belief rules from historical data, leveraging the existing rule base, and generating rules at random without any prior information. Drawing upon the knowledge provided by energy experts, the initial rule base of the BRBES is constructed in this article. These rules, outlined in Table 5, serve as the formal representation of the domain knowledge employed in this work. Initially, for all the rules of the rule base, we assign an equal value (\"1\") to both the rule weight and antecedent attribute weight. The consequent component of the rule base contains numerical values that quantify the belief degrees for the associated referential values. The initial belief degrees allocated to these referential values of the consequent attribute of a belief rule are assigned by taking opinions of two energy experts. These belief degrees enable the BRBES to effectively handle uncertainties [47]. This table's 'Activation weight' column is interpreted subsequently in this subsection. Figure 2: Three antecedent attributes and one consequent attribute of BRBES.