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

Fabrizio De Santis; Gyunam Park; Francesco Zanichelli

cs.AIMar 27, 2026

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

Authors: Fabrizio De Santis, Gyunam Park, Francesco Zanichelli

Organizations: University of Parma, Parma, Italy · Eindhoven University of Technology, Eindhoven, Netherlands

Abstract

Predictive modeling on sequential event data is critical for fraud detection and healthcare monitoring. Existing data-driven approaches learn correlations from historical data but fail to incorporate domain-specific sequential constraints and logical rules governing event relationships, limiting accuracy and regulatory compliance. For example, healthcare procedures must follow specific sequences, and financial transactions must adhere to compliance rules. We present a neuro-symbolic approach integrating domain knowledge as differentiable logical constraints using Logic Networks (LTNs). We formalize control-flow, temporal, and payload knowledge using Linear Temporal Logic and first-order logic. Our key contribution is a two-stage optimization strategy addressing LTNs' tendency to satisfy logical formulas at the expense of predictive accuracy. The approach uses weighted axiom loss during pretraining to prioritize data learning, followed by rule pruning that retains only consistent, contributive axioms based on satisfaction dynamics. Evaluation on four real-world event logs shows that domain knowledge injection significantly improves predictive performance, with the two-stage optimization proving essential knowledge (without it, knowledge can severely degrade performance). The approach excels particularly in compliance-constrained scenarios with limited compliant training examples, achieving superior performance compared to purely data-driven baselines while ensuring adherence to domain constraints.

Figures & tables

Figure 1: Binary classification using LTN: loan applications (constants

\mathcal{C}

) are evaluated by predicate

A

(neural network) to determine approval. Variables

x_{+}

and

x_{-}

represent positive and negative classes, aggregated by universal quantifiers

\forall

to compute satisfaction.

Figure 2: The pipeline followed in the approach, which consists of feature extraction, rule extraction, knowledge base creation and injection, rule pruning, and then the creation of the neuro-symbolic model leveraging the LTN framework.

Method	Sepsis		BPIC2012		BPIC2017		Traffic fines
Method	Accuracy	F1	Accuracy	F1	Accuracy	F1	Accuracy	F1
LSTM	88.69 $\pm$ 0.92	70.59 $\pm$ 1.31	52.47 $\pm$ 0.77	52.44 $\pm$ 0.74	70.16 $\pm$ 0.41	69.47 $\pm$ 0.44	67.34 $\pm$ 0.42	66.93 $\pm$ 0.28
TRF	90.11 $\pm$ 0.47	73.80 $\pm$ 0.36	52.29 $\pm$ 0.58	51.86 $\pm$ 0.92	71.15 $\pm$ 0.25	70.74 $\pm$ 0.22	67.81 $\pm$ 0.11	67.34 $\pm$ 0.14
Two-Stage-L	89.39 $\pm$ 0.47	75.82 $\pm$ 0.92	60.33 $\pm$ 0.86	57.25 $\pm$ 0.38	70.69 $\pm$ 0.89	70.67 $\pm$ 0.89	68.44 $\pm$ 0.43	68.20 $\pm$ 0.38
Two-Stage-T	91.30 $\pm$ 0.11	75.63 $\pm$ 0.99	65.27 $\pm$ 0.27	62.12 $\pm$ 0.39	72.30 $\pm$ 0.11	72.16 $\pm$ 0.16	67.94 $\pm$ 0.11	67.72 $\pm$ 0.08

Table 1: RQ1: Performance on temporal split comparing purely data-driven baselines with knowledge-enhanced variants. Results show mean and standard deviation over 5 seeds.

Method	Sepsis		BPIC2012		BPIC2017		Traffic fines
Method	Accuracy	F1	Accuracy	F1	Accuracy	F1	Accuracy	F1
LTN-Data-L	82.56 $\pm$ 4.52	69.10 $\pm$ 4.22	54.24 $\pm$ 0.63	53.18 $\pm$ 0.63	69.73 $\pm$ 0.07	69.71 $\pm$ 0.07	67.59 $\pm$ 0.60	67.31 $\pm$ 0.56
LTN-Data-T	81.09 $\pm$ 6.25	66.79 $\pm$ 4.65	57.17 $\pm$ 1.13	55.40 $\pm$ 0.77	71.15 $\pm$ 0.25	70.74 $\pm$ 0.22	67.53 $\pm$ 0.19	67.27 $\pm$ 0.1
LTN-NoP-L	21.36 $\pm$ 5.96	18.79 $\pm$ 2.95	54.50 $\pm$ 4.35	45.00 $\pm$ 5.54	69.16 $\pm$ 0.24	66.27 $\pm$ 0.36	59.33 $\pm$ 0.27	46.35 $\pm$ 0.41
LTN-NoP-T	21.69 $\pm$ 7.58	19.18 $\pm$ 4.76	47.47 $\pm$ 6.68	33.82 $\pm$ 2.70	68.54 $\pm$ 0.52	66.09 $\pm$ 0.69	57.57 $\pm$ 0.86	41.78 $\pm$ 1.94
Two-Stage-L	89.39 $\pm$ 0.47	75.82 $\pm$ 0.92	60.33 $\pm$ 0.86	57.25 $\pm$ 0.38	70.69 $\pm$ 0.89	70.67 $\pm$ 0.89	68.44 $\pm$ 0.43	68.20 $\pm$ 0.38

Table 2: RQ2: Ablation study comparing LTN variants on temporal split: Data-only (no knowledge), NoP (knowledge without pruning), and Two-Stage (complete method).

Method	Sepsis		BPIC2012		BPIC2017		Traffic fines
Method	Accuracy	F1	Accuracy	F1	Accuracy	F1	Accuracy	F1
LSTM	81.50 $\pm$ 2.41	73.26 $\pm$ 3.28	53.89 $\pm$ 1.59	53.71 $\pm$ 1.49	65.71 $\pm$ 1.04	65.41 $\pm$ 1.19	77.47 $\pm$ 0.21	76.92 $\pm$ 0.33
TRF	82.74 $\pm$ 1.39	74.66 $\pm$ 1.77	56.16 $\pm$ 0.79	55.61 $\pm$ 0.68	68.77 $\pm$ 0.83	68.54 $\pm$ 0.96	77.39 $\pm$ 0.48	76.85 $\pm$ 0.45
LTN-NoP-L	39.91 $\pm$ 4.83	37.52 $\pm$ 6.51	47.58 $\pm$ 5.82	34.61 $\pm$ 4.53	65.28 $\pm$ 0.05	64.48 $\pm$ 0.02	64.93 $\pm$ 0.05	42.39 $\pm$ 0.11
LTN-NoP-T	34.55 $\pm$ 4.10	30.38 $\pm$ 5.47	63.61 $\pm$ 0.74	53.39 $\pm$ 1.00	62.02 $\pm$ 6.69	60.68 $\pm$ 7.77	65.15 $\pm$ 0.09	42.74 $\pm$ 0.22
Two-Stage-L	91.47 $\pm$ 2.82	89.96 $\pm$ 2.96	62.88 $\pm$ 0.80	60.07 $\pm$ 0.49	75.53 $\pm$ 0.35	74.66 $\pm$ 0.22	78.36 $\pm$ 0.52	77.76 $\pm$ 0.59

Table 3: RQ3: Performance on compliance-aware test set. Models must generalize to scenarios emphasizing rule-compliant behavior with limited compliant training examples.

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Compliance-Aware Predictive Process Monitoring: A Neuro-Symbolic Approach

Fabrizio De Santis, Gyunam Park, Wil M. P. van der Aalst, Francesco Zanichelli

University of Parma, Parma, Italy · Eindhoven University of Technology, Eindhoven, Netherlands · RWTH Aachen University, Aachen, Germany

Predictive Process Monitoring Neurosymbolic Learning

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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.

Abstract

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