# Knowledge Reasoning via Jointly Modeling Knowledge Graphs and Soft Rules
## 4 Experiments and Results
### Link Prediction
#### 4.2.4 Main Results  
The results for all compared methods on the FB15K, DB100K, and FB15K-sparse test sets are presented in Tables 3 and 4. We utilize the mean reciprocal rank or HITS@N value for each test triple, with N = 1, 3, 10, as paired data. The experimental results show that (1) Iterlogic-E outperforms numerous strong baselines in most cases. This result shows that Iterlogic-E can achieve excellent accuracy. (2) Iterlogic-E significantly outperforms \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Method**} & \multicolumn{6}{c}{**FB15K**} & \multicolumn{6}{c}{**DB100K**} \\ \cline{3-10}  & & **MRR** & **HITS@1** & **HITS@3** & **HITS@10** & **MRR** & **HITS@1** & **HITS@3** & **HITS@10** \\ \hline
1 & TransE [22] & 0.380 & 0.231 & 0.472 & 0.641 & 0.111 & 0.016 & 0.164 & 0.270 \\
2 & DistMult [25] & 0.654 & 0.546 & 0.733 & 0.824 & 0.233 & 0.115 & 0.301 & 0.448 \\
3 & HolE [28] & 0.524 & 0.402 & 0.613 & 0.739 & 0.260 & 0.182 & 0.309 & 0.4118 \\
4 & ComplEx [26] & 0.627 & 0.550 & 0.671 & 0.766 & 0.272 & 0.218 & 0.303 & 0.362 \\
5 & ANALOGY [27] & 0.725 & 0.646 & 0.785 & 0.854 & 0.252 & 0.143 & 0.323 & 0.427 \\
6 & ComplEx-NNE [47] & 0.727 & 0.659 & 0.772 & 0.845 & 0.298 & 0.229 & 0.330 & 0.426 \\
7 & ComplEx-CAS [48] & - & - & - & 0.866 & - & - & - & - \\
8 & Rotate [24] & 0.664 & 0.551 & 0.751 & 0.841 & 0.327 & 0.200 & 0.417 & 0.526 \\
9 & HAKE [41] & 0.408 & 0.312 & 0.463 & 0.579 & - & - & - & - \\
10 & CAKE [40] & 0.741 & 0.646 & 0.825 & 0.896 & - & - & - & - \\
11 & R-GCN+ [29] & 0.696 & 0.601 & 0.760 & 0.842 & - & - & - & - \\
12 & ConvE [30] & 0.745 & 0.670 & 0.801 & 0.873 & - & - & - & - \\
13 & DPMPN [49] & 0.764 & 0.726 & 0.784 & 0.834 & - & - & - & - \\ \hline
14 & BLP [50] & 0.242 & 0.151 & 0.269 & 0.424 & - & - & - & - \\
15 & MLN [21] & 0.321 & 0.210 & 0.370 & 0.550 & - & - & - & - \\ \hline
16 & PTransE [51] & 0.679 & 0.565 & 0.768 & 0.855 & 0.195 & 0.063 & 0.278 & 0.416 \\
17 & KALE [42] & 0.518 & 0.382 & 0.606 & 0.756 & 0.249 & 0.100 & 0.346 & 0.497 \\
18 & Complex\({}^{\rm R}\)[52] & - & - & - & - & 0.253 & 0.167 & 0.294 & 0.420 \\
19 & TARE [44] & 0.781 & 0.617 & 0.728 & 0.842 & - & - & - & - \\
20 & RUGE [45] & 0.768 & 0.703 & 0.815 & 0.865 & 0.246 & 0.129 & 0.325 & 0.433 \\
21 & ComplEx-NNE+AER [47] & 0.801 & 0.757 & 0.829 & 0.873 & 0.311 & 0.249 & 0.339 & 0.426 \\
22 & IterE [16] & 0.576 & 0.443 & 0.665 & 0.818 & 0.274 & 0.215 & 0.299 & 0.386 \\
23 & pLogicNet [46] & 0.776 & 0.706 & 0.817 & 0.885 & - & - & - & - \\
24 & SoLE [17] & 0.801 & 0.764 & 0.821 & 0.867 & 0.306 & 0.248 & 0.328 & 0.418 \\
25 & SLRE [18] & 0.810 & 0.774 & 0.829 & 0.871 & 0.340 & 0.261 & 0.372 & 0.490 \\
26 & LogicNN [43] & 0.766 & - & - & 0.874 & - & - & - & - \\ \hline  & Iterlogic-E(ComplEx) & 0.814 & 0.778 & 0.835 & 0.873 & 0.374 & **0.301** & 0.409 & 0.509 \\  & Iterlogic-E(RotatE) & **0.837** & **0.794** & **0.868** & **0.904** & **0.387** & 0.287 & **0.449** & **0.559** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Link prediction results on the test sets of FB15K and DB100K. The boldface scores are the best results, and “-” indicates the missing scores not reported in the literature. The first batch of baselines includes embedding-based models, which rely only on triples seen in the KGs. The middle batch of baselines includes the rule-based reasoning methods. The last batch of baselines further incorporates logical rules and embeddings. the basic models that use triples alone, and the improvement comes from the ability to learn the conclusions obtained by soft rules. (3) Iterlogic-E also outperforms many baselines that incorporate logical rules, including SoLE and IterE, indicating its superiority in reducing the noise of candidate conclusions. (4) IterE can only enhance sparse entities, so the experimental results are much lower than those of other baseline models. However, Iterlogic-E is also effective on the FB15K-sparse test set. (5) In DB100K, the improvements over SLRE and SoLE are more substantial than those in FB15K.