FlexTempRule: Interpretable Time Series Classification via Learning Flexible Temporal Logic Rules

Interpretable time series classification is a significant task for safety-critical systems, as it can help experts gain insight of the system behaviors, especially when the model is intrinsically interpretable and provides intuitive yet rigorous rationales that reflect its actual execution. However, existing rule-based approaches either fail to guarantee model–rationale consistency or restrict the evaluation scope of each learned logical rule to a predefined fixed interval. These limitations inevitably hinder the capture of flexible temporal correlation properties that may be satisfied at different regions across time series. In this paper, we propose a novel neuro-symbolic model called FlexTempRule, which supports adaptive learning of both fixed and slidable temporal logic rules to achieve interpretable time series classification with model-consistent rationales. Specifically, the time series is first dynamically divided into patches of varying lengths, expecting that the boundary points do not break temporal continuity. Then, three types of temporal logic rules with different degrees of sliding flexibility, as well as statistical features, are automatically learned and adaptively weighted to form advanced features for classification. Comprehensive experiments on real-world univariate and multivariate datasets in safety-critical domains show that FlexTempRule attains superior accuracy among rule-based baselines and competitive performance against other interpretable methods. More importantly, discriminative temporal logic rules are explicitly provided, along with their flexibility nature, thereby enhancing user trust in the model and deepening understanding of specific scenarios.