## 4 Framework  
For applying rule-based classification, we assume that all attributes of events in \(EL\) are discrete, that is, continuous attributes in an event log have been discretised if needed. For each attribute \(d_{i}\), we define the attribute itemizer function \(it^{a}_{i}:\mathcal{D}\longrightarrow\{0,1\}^{l}\), which maps an attribute \(d_{i}\) into a sequence of \(J\) binary items, obtained by one-hot encoding the value of an attribute within its domain, that is \(it^{a}_{i}(d_{i})=\{dummy_{j}\}_{j=1,\ldots,J}\), with:  
\[dummy_{j}= \begin{cases}1&\text{if }d_{i}=v_{i,j}\\ 0&\text{if }d_{i}\
eq v_{i,j}\end{cases} \]  
The event itemizer \(it^{e}:\mathcal{E}\longrightarrow\{0,1\}^{n}\) maps an event into the set of items derived from its event-level attributes: \(it^{e}(e)=\bigcup_{d_{i}\in e}it^{a}(d_{i})\), with \(d_{i}\in D_{E}\). The trace itemizer \(it^{t}:\mathcal{S}\longrightarrow\{0,1\}^{n}\) maps a trace, possibly incomplete, into the set of items derived from its events and from case-level attributes:  
\[it^{t}(\sigma)=it^{a}(d_{1}),\ldots,it^{a}(d_{\mathbb{C}}),it^{e}(e_{1}), \ldots,it^{e}(e_{n}),\]  
where \(C\) is the number of case-level attributes in \(EL\). Given a prefix length \(L\), we define an item matrix \(T^{L}\) containing, in each row, the items generated by a prefix in an event log:  
\[T^{L}= \begin{bmatrix}it^{t}(pr(\sigma_{1},L))\\ \vdots\\ it^{t}(pr(\sigma_{N},L))\end{bmatrix} \]  
where \(N\) in the number of traces in \(EL\). Let us refer to the columns of \(T^{L}\) as \(\mathcal{X}_{1},\ldots,\mathcal{X}_{p}\). Let us also define a labeling function \(y:\mathcal{S}\longrightarrow\mathcal{Y}\) mapping a trace \(\sigma\in\mathcal{S}\) to its class label \(y(\sigma)\in\mathcal{Y}\), with \(\mathcal{Y}\) being the domain of the class labels. For outcome predictions, \(\mathcal{Y}\) is a finite set of categorical outcomes. Consistently with the literature [10], we consider binary outcomes, i.e., \(\mathcal{Y}=\{0,1\}\). Note that all prefixes generated from a trace \(\sigma\) have the same class label. An outcome classifier \(oc:\mathcal{X}_{1}\times\ldots\times\mathcal{X}_{p}\longrightarrow\mathcal{Y}\) is a function mapping the items of a (possibly incomplete) trace into its class label, that is, \(oc(it^{t}(\sigma))=y\). A machine learning-based (ML-based) classifier (\(mlbc\)) is an \(oc\) developed using machine learning classification techniques, such as a decision tree or an artificial neural network. In other words, an ML-based classifier uses the items \(\mathcal{X}_{p}\) as features to train a model that predicts the outcome label of traces. The literature typically has focused on this type of techniques to solve the outcome prediction task in predictive monitoring [25]. An association rule mining-based (ARM-based) classifier (_armb_) is an _oc_ developed using association rule mining techniques, such as RIPPER [26]. In this paper, we tackle the following two problems:  
* To compare the performance of ML-based classifiers and an ARM-based classifier, in order to assess whether the level of performance achievable in outcome-based process predictive monitoring by rule-based classification is at least comparable with the one achieved by other techniques in the literature;
* Exploiting the intrinsic interpretability of rule-based classifiers, to propose visualisations that foster the interpretability of outcome-based process predictive models at the global level, i.e., generally regarding all the traces in an event log, and at the local level, i.e., specifically for a particular trace in an event log. To tackle the first objective, it is necessary to pre-process an event log into a discrete set of items, as discussed above. A first data preparation step, therefore, concerns the discretisation of the continuous attributes in an event log.