Neuro-Symbolic Learning for Predictive Process Monitoring via Two-Stage Logic Tensor Networks with Rule Pruning

Existing approaches for predictive process monitoring are sub-symbolic, meaning that they learn correlations between descriptive features and a target feature fully based on data, e.g., predicting the surgical needs of a patient based on historical events and biometrics. However, such approaches fail to incorporate domain-specific process constraints (knowledge), e.g., surgery can only be planned if the patient was released more than a week ago, limiting the adherence to compliance and providing less accurate predictions. In this paper, we present a neuro-symbolic approach for predictive process monitoring, leveraging Logic Tensor Networks (LTNs) to inject process knowledge into predictive models. The proposed approach follows a structured pipeline consisting of four key stages: 1) feature extraction; 2) rule extraction; 3) knowledge base creation; and 4) knowledge injection. Our evaluation shows that, in addition to learning the process constraints, the neuro-symbolic model also achieves better performance, demonstrating higher compliance and improved accuracy compared to baseline approaches across all compliance-aware experiments.

Process anomaly detection is an important application of process mining for identifying deviations from the normal behavior of a process. Neural network-based methods have recently been applied to this task, learning directly from event logs without requiring a predefined process model. However, since anomaly detection is a purely statistical task, these models fail to incorporate human domain knowledge. As a result, rare but conformant traces are often misclassified as anomalies due to their low frequency, which limits the effectiveness of the detection process. Recent developments in the field of neuro-symbolic AI have introduced Logic Tensor Networks (LTN) as a means to integrate symbolic knowledge into neural networks using real-valued logic. In this work, we propose a neuro-symbolic approach that integrates domain knowledge into neural anomaly detection using LTN and Declare constraints. Using autoencoder models as a foundation, we encode Declare constraints as soft logical guiderails within the learning process to distinguish between anomalous and rare but conformant behavior. Evaluations on synthetic and real-world datasets demonstrate that our approach improves F1 scores even when as few as 10 conformant traces exist, and that the choice of Declare constraint and by extension human domain knowledge significantly influences performance gains.

Machine learning models are predominantly evaluated through predictive performance metrics such as ranking quality, prediction error, or classification accuracy. While these metrics effectively quantify how closely predictions match the ground truth, they do not assess whether model outputs respect predefined logical or domain-specific constraints. In high-stakes applications, including healthcare, finance, and autonomous systems, logical consistency can be as critical as predictive accuracy, yet no standard metric captures this dimension. We introduce the Rule Violation Score (RVS), a complementary evaluation metric that quantifies the extent to which a predictive model respects a given set of logical rules, independently of predictive accuracy. RVS treats hard rules (strict constraints) and soft rules (statistical regularities) differently, can be evaluated on any dataset and on any predictive model expressed over a relational vocabulary, and can be computed using SQL queries that are automatically generated for Horn rules. Beyond evaluating models, RVS can also evaluate the logical consistency of training datasets and help identify poorly defined rules. We evaluate RVS on three benchmarks covering knowledge graph link prediction and relational regression, including rule-based, embedding-based, and neuro-symbolic predictive models. Our results demonstrate that two models achieving comparable predictive accuracy can exhibit substantially different levels of logical compliance, revealing differences in model behavior that standard metrics fail to capture.