# Nomological Deductive Reasoning for Trustworthy, Human-Readable, and Actionable AI Outputs
## 3 Current XAI State of the Art
### Explanator Formats
#### 3.1.3 Rule-Based Explanations  
Rule-based explanations are a popular type of explanation technique in data mining, machine learning and Artificial Intelligence by which regularities in data are identified through various rule-extraction techniques. These regularities are mostly presented in the form of the IF-THEN rule, sometimes with AND/OR operators, as illustrated in Figure 4, which is an example decision list that was created using the Titanic data set available in R for the task of predicting whether the passenger survived the Titanic tragedy based on his or her features, such as age (adult or child), gender (male or female), passenger class (first, second, third, or crew) [63]. The \"it\" statements express a set of features comparable to the model's inputs, and the \"then\" statements correspond to the predicted outcome corresponding to the conditions stated by \"if\".  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Learning Task** & **Explanation Example** & **Reference** \\ \hline \multirow{8}{*}{Knowledge graph completion (link prediction)} & Prediction: & \\  & World War I—entity involved—German empire & \\  & Explanation: & \\  & World War I—commanders—[PERSON] & \\  & [PERSON]—commands—German Empire & [57] \\  & Supported by: & \\  & Falkland Wars—entities involved—United Kingdom & \\  & Falkland Wars—commanders—[PERSON] & \\  & [PERSON]—commands—United Kingdom & \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._  
Figure 4: Example of rule-based explanations. Source: [64].  
Among the current XAI methods, this approach provides high interpretability of black boxes [37; 64] even if some improvements can be added if analyzed from the holistic perspective of the logic and theory of explanation. The key methods used to provide such explanations are the following:  
**Decision Trees**[65]: One of the oldest and most intuitive methods for model explanation. Decision trees split input data into various branches based on specific features, making them highly interpretable. These trees provide explicit rules that explain how a decision is made.  
**Anchors**[66]: Anchors generate simple, understandable decision rules that are highly accurate in specific regions of the input space. These rules are based on the important features that \"anchor\" the decision in a given region of the input space.  
**Scalable Rule Lists and Rule Sets**[67; 68; 69]: These methods extract human-readable decision rules directly from a model. They are often used with ensemble methods like decision forests or other machine learning algorithms that rely on multiple decision-making processes.  
Various other methods such as Discriminative Patterns [70], MYCIN [71], Fuzzy Inference Systems [72], Automated Reasoning [73], Genetic Rule Extraction (G-REX) [74], Global to Local eXplainer (GLocalX) [75], Mimic Rule Explanation (MRE) [76] and many others exist, as detailed in [37]; these have the capacity to generate explanatory rules of the decision made by the model, although the form may be in some other type than _IF...THEN_.