This paper addresses the problem of suffix prediction in Business Process Management (BPM) by proposing a Neuro-Symbolic Predictive Process Monitoring (PPM) approach that integrates data-driven learning with temporal logic-based prior knowledge. While recent approaches leverage deep learning models for suffix prediction, they often fail to satisfy even basic logical constraints due to the lack of explicit integration of domain knowledge during training. We propose a novel method to incorporate Linear Temporal Logic over finite traces (LTLf) into the training process of autoregressive sequence predictors. Our approach introduces a differentiable logical loss function, defined using a soft approximation of LTLf semantics and the Gumbel-Softmax trick, which can be combined with standard predictive losses. This ensures that the model learns to generate suffixes that are both accurate and logically consistent. Experimental evaluation on three real-world datasets shows that our method improves suffix prediction accuracy and compliance with temporal constraints. We also introduce two variants of the logic loss (local and global) and demonstrate their effectiveness under noisy and realistic settings. While developed in the context of BPM, our framework is applicable to any symbolic sequence generation task and contributes to advancing Neuro-Symbolic AI.

翻译：本文针对业务流程管理（BPM）中的后缀预测问题，提出了一种融合数据驱动学习与基于时序逻辑先验知识的神经符号化预测性过程监控（PPM）方法。当前方法虽然利用深度学习模型进行后缀预测，但由于在训练过程中未显式整合领域知识，常无法满足基础逻辑约束。我们提出一种创新方法，将有限迹线性时序逻辑（LTLf）融入自回归序列预测器的训练过程。该方法通过基于LTLf语义的软近似与Gumbel-Softmax技巧，定义了可微分的逻辑损失函数，并能与标准预测损失协同优化，从而确保模型生成的既准确又符合逻辑一致性的后缀。在三个真实数据集上的实验表明，本方法提升了后缀预测精度与时序约束满足度。我们还提出了逻辑损失的两种变体（局部与全局），并验证了其在含噪及现实场景下的有效性。尽管本框架面向BPM场景开发，但可推广至任何符号序列生成任务，为神经符号化人工智能的发展作出贡献。