Time Robustness for Point-Based Semantics of Metric Interval Temporal Logic

Time-critical systems must satisfy temporal constraints whose correctness depends not only on event ordering but also on precise timing. Metric Interval Temporal Logic (MITL) provides a formalism to express such requirements. Although robustness has been widely studied under signal-based interpretations, it remains largely unexplored for point-based semantics, where executions are sequences of timestamped facts. In this setting, small timing variations may arbitrarily change Boolean satisfaction, revealing the instability of temporal truth under uncertainty.

We introduce a notion of time robustness for MITL over point-based semantics, interpreting robustness as a margin of validity of temporal interpretations. We define a quantitative semantics and prove soundness with respect to Boolean satisfaction together with a Lipschitz stability property with respect to timestamp perturbations, which induces a metric notion of proximity between interpretations. The semantics admits a polynomial-time evaluation procedure and is illustrated on two case studies (drone surveillance and smart hospital), where robustness empirically correlates with tolerance to temporal noise.