Monitoring Data-aware Temporal Properties (Extended Version)

2026-05-14

AI Summary

This work addresses the challenge of verifying data-aware temporal properties in complex, heterogeneous AI-driven dynamic systems whose internal specifications are often opaque and thus resistant to traditional model-checking techniques. To this end, the paper proposes a proactive runtime monitoring framework capable of verifying Linear Temporal Logic over finite traces with Mixed Theories (LTLfMT), which integrates arbitrary SMT theories. The approach combines automata-theoretic methods for handling temporal structure with SMT-based reasoning for first-order data constraints. Its principal contribution lies in establishing, for the first time, a decidable fragment of LTLfMT that includes linear arithmetic and uninterpreted functions, and in developing a foundational architecture that balances theoretical rigor with practical applicability. Preliminary evaluations on data-aware business processes and read-only database-driven systems demonstrate the feasibility and potential of the proposed method.

Abstract

Dynamic systems in AI are often complex and heterogeneous, so that an internal specification is not accessible and verification techniques such as model checking are not applicable. Monitoring is in such cases an attractive alternative, as it evaluates desirable properties along traces generated by an unknown dynamic system. In this work, we consider anticipatory monitoring of linear-time properties enriched with an arbitrary SMT theory over finite traces (LTLfMT). Anticipatory monitoring in this setting is highly challenging, as the monitoring state depends on both the trace prefix seen so far and all its possible finite continuations. Under reasonable assumptions on the background theory, we present and formally prove the correctness of a novel foundational framework for monitoring properties in an expressive fragment of LTLfMT. The framework combines automata-theoretic methods to handle the temporal aspects of the logic, with automated reasoning techniques to address the first-order dimension. Moreover, we identify for the first time decidable fragments of this monitoring problem that are practically relevant as they combine linear arithmetic with uninterpreted functions, which covers e.g. data-aware business processes and dynamic systems operating over a read-only database. Feasibility is witnessed by a prototype implementation and preliminary evaluation.

Problem

• monitoring
• LTLfMT
• dynamic systems
• temporal properties
• SMT theory

Innovation

• anticipatory monitoring
• LTLfMT
• automata-theoretic methods
• SMT-based reasoning
• decidable fragments