# Semantic Representation Using Sub-Symbolic Knowledge in Commonsense Reasoning +
## 4 Experiments
### Experimental Results  
#### 4.4.1 Diverse Expansion Methods  
In the experiments, we demonstrated the effect of our various expansion methods on pre-trained language models and compared in-depth the ability to answer commonsense questions. To this end, we demonstrated how the AMR graph enables pre-trained language models to understand the semantics of a question and expands the graph with ConceptNet for comprehensive knowledge acquisition. However, expanding the AMR graph with all concepts in the knowledge graph wastes computational resources. Additionally, external knowledge of a few concepts requires a proper reasoning process. We conducted a study to determine which expansion method is the most effective for commonsense reasoning.  
For ConceptNet, we expanded the graph based on all words in the question, called the CN full graph. The ConceptNet graph is denoted by \(\mathcal{G}_{CN}=\{\mathcal{V}_{cn},\mathcal{E}_{cn}\}\) and the subgraph of ConceptNet corresponding to the question token is denoted by \(\mathcal{G}_{CN}^{token}=\{\mathcal{V}_{cn}^{token},\mathcal{E}_{cn}^{token}\}\).  
The CN full graph (CF) is depicted in Figure 4a and defined as follows:  
\[\mathcal{G}_{CF}=(\{\mathcal{V}_{token}\cup\mathcal{V}_{cn}^{token}\}\cup\{ \texttt{root}\}),\{\mathcal{E}_{cn}^{token}\cup\{\texttt{token}\}\}) \tag{6}\]  
The AMR-CN-Full (ACF) graph is an integrated graph in which all nodes of the AMR graph connect to the ConceptNet graph. Additionally, we limited ConceptNet (CN) for the experiments to just two methods. One method was to use the ConceptNet graph corresponding to all question tokens separated by a space in the sentence, as shown in Figure 4b. The graph path learning module could not use the reasoning CN graph owing to the initial disconnection of the question token and disconnection between the concept nodes. Therefore, we combined all tokens from the question to the root node to ensure that our model performed effectively in commonsense reasoning. The ACF graph was identical to the graph before pruning when creating the ACP-ARG.  
Figure 4: ConceptNet-Full graph (**a**) expands ConceptNet based on all words in the question. AMR-CN-Full graph (**b**) expands all the concepts in the AMR graph with ConceptNet graph.  
The ACF graph can be expressed as follows: The AMR graph is denoted as \(\mathcal{G}_{AMR}=\{\mathcal{V}_{amr},\mathcal{E}_{amr}\}\). Additionally, the subgraph of ConceptNet matched with the ACF graph is denoted by \(\mathcal{G}^{AMR}_{CN}=\{\mathcal{V}^{amr}_{cn},\mathcal{E}^{amr}_{cn}\}\).  
\[\mathcal{G}_{ACF}=(\{\mathcal{V}_{amr}\cup\mathcal{V}^{amr}_{cn}\},\{\mathcal{E} _{amr}\cup\mathcal{E}^{amr}_{cn}\}) \tag{7}\]  
We also conducted ACP-ARG-mini, which is identical to ACP-ARG except for the types of arguments that are pruned. For ACP-ARG, we pruned the nodes that lack edges known as ARGO, ARG1, ARG2, ARG3, and ARG4 with ConceptNet from the ACF graph. Unlike ACP-ARG, ACP-ARG-mini prune nodes lack ARGO and ARG1 edges, which possess more than 50% of all other argument relations, as shown in Table 1. We expanded the graph based on nodes unrelated to the arguments.  
The results of the experiments are shown in Table 2. ACP-ARG scored the highest in both the new development and test sets. The performance of the model based on the ACP-ARG graph suggests that using all the information related to the question is not always correct. This suggests that it is efficient and effective when using the specific knowledge graph that the question requires and that the arguments of an AMR graph can provide significant evidence for retrieving the knowledge graph. According to ACP-ARG-mini, the amount of knowledge should be considered even when using arguments from the AMR graph. The model using the ACP-nonARG graph demonstrated inability in the reasoning process.