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

Fabrizio De Santis, Gyunam Park, Francesco Zanichelli
June, 2026
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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.

Type
Conference paper
Publication
Advances in Knowledge Discovery and Data Mining - 30th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2026, Hong Kong, China, June 9-12, 2026, Proceedings, Part II

Practical problem

Banks, hospitals and manufacturers want to predict how a running case will end, for example whether a patient will develop complications or a loan will be rejected, from the event records their systems collect. Deep learning predictors learn correlations from past cases but know nothing about the mandatory rules that govern the process, such as a transfer requiring prior identity verification, and such rules are rarely violated in training data yet critical in live operation. Earlier attempts to inject knowledge handle only control-flow rules, add them only at the input or output, and cannot cope with noisy or conflicting rules. Simply adding logical rules to a neural model can even backfire, because the model satisfies the rules trivially instead of learning to predict.

Research questions

  1. Does injecting domain knowledge as logical constraints improve predictive performance compared to purely data-driven approaches?
  2. What do the two-stage optimization and the rule pruning mechanism contribute to model performance?
  3. How well does the approach generalize to compliance-constrained scenarios with few compliant training examples?

Contributions

  • A scheme for extracting and categorizing process knowledge into control-flow, temporal and payload features and rules, formalized in Linear Temporal Logic (LTL) and first-order logic using Declare mining, SLA compliance analysis and statistical correlations.
  • A neuro-symbolic outcome classifier for predictive process monitoring built on Logic Tensor Networks (LTN) with LSTM or Transformer backbones, separating data axioms from knowledge axioms.
  • A two-stage optimization: weighted axiom loss (0.8 data, 0.2 knowledge) during pretraining, then rule pruning with an analytic gating score from mean and variance of rule satisfaction, followed by fine-tuning on the pruned knowledge base.
  • A compliance-aware evaluation protocol that enriches test sets with rule-compliant traces, used alongside a standard temporal split.
  • An open-source implementation on GitHub (FabrizioDeSantis/NeSy-PPM).

Key findings

  • On a temporal split of Sepsis, BPIC2012, BPIC2017 and Traffic fines, Two-Stage variants beat LSTM and Transformer baselines on every log; F1 improves by 5.23% on Sepsis (LSTM to Two-Stage-L) and 10.26% on BPIC2012 (Transformer to Two-Stage-T).
  • Adding knowledge axioms without weighting or pruning (LTN-NoP) collapses performance to 18.79% and 19.18% F1 on Sepsis, below data-only LTN (69.10%), whereas Two-Stage-L reaches 75.82% F1 and Two-Stage-T 75.63%.
  • On the compliance-aware test set with only 4% compliant training traces (Sepsis), Two-Stage-L reaches 89.96% F1 versus 73.26% for LSTM and 37.52% for LTN-NoP-L; on BPIC2012 Two-Stage-T reaches 64.23% versus 55.61% for the Transformer.
  • LSTM backbones do better on short traces (Sepsis and Traffic fines, maximum length 13 and 10) and Transformers on longer traces (BPIC2012 and BPIC2017, maximum length 40 and 20).
  • Gains shrink on data-rich logs: on Traffic fines F1 improves by only 1.1% and 0.38%, so knowledge injection pays off mainly when training data or compliant examples are scarce.