A Subjective Logic-based method for runtime confidence updates in safety arguments

Assurance arguments provide a clear and structured way to explain why stakeholders should trust that a system satisfies certain properties, yet widely used notations, e.g.Goal Structuring Notation (GSN), typically lack an operational semantics for deriving assurance confidence. Existing approaches address structure and soundness but largely reason over truth values, not over confidence in the justification of claims. Subjective Logic (SL) offers a calculus of belief, disbelief, and uncertainty with operators for combining opinions, enabling confidence propagation under incomplete, conflicting, or subjective evidence. However, existing SL-based approaches do not provide a uniform, compositional semantics that covers all argument elements and relations to enable overall confidence assessment. We propose a confidence semantics that represents argument elements as SL opinions and maps relations between elements to SL operators modelling how confidence flows, effectively turning the argument into an analyzable confidence network. The approach provides explicit warrants, principled handling of context, preserved provenance, and compatibility with GSN, along with practical guidance using an exemplary assurance confidence assessment.

We study certified runtime monitoring of past-time signal temporal logic (ptSTL) from visual observations under partial observability. The monitor must infer safety-relevant quantities from images and provide finite-sample guarantees, while being \emph{reusable}: once trained and calibrated, it should certify any formula in a target fragment without per-formula retraining. For fragments induced by a finite dictionary of temporal atoms, we prove that the \emph{semantic basis}, the vector of atom robustness scores, is the minimum prediction target within the class of monotone, 1-Lipschitz reusable interfaces: any formula is evaluated by a deterministic decoder derived from the parse tree, and a single conformal calibration pass certifies the entire fragment with no union bound. We also introduce a \emph{rolling prediction monitor} that predicts only current predicate values and reconstructs temporal history online; this is easier to learn but grows conservative at long horizons. On a pedestrian-crossroad benchmark, rolling achieves tighter certified bounds at short horizons while the semantic-basis monitor is up to 4-times tighter at long horizons. We validate the presented monitors on real-world Waymo driving data, where both monitors satisfy the conformal coverage guarantee empirically.

Runtime guardrails act before irreversible tool calls, but their guarantees depend on what policy state is representable, what a judge observes, and whether intervention changes future behavior. We separate three questions. First, relative to fixed oracle predicates, a deterministic gate enforces exactly the nonempty safety policies whose good prefixes its register model recognizes; policy nontriviality is undecidable with two decrementable counters but in PSPACE for a separable monotone fragment. Second, under a fixed exogenous law, Neyman-Pearson gives the exact false-block/miss frontier and conformal calibration gives a finite-sample marginal certificate, possibly via block-all. Third, once blocking changes future proposals, static scores and ungated trajectories need not identify the closed-loop frontier; a specified finite controlled model instead yields an occupancy program. Bounded representation attacks add a robustness margin, so benign calibration alone does not transfer. Experiments target these distinctions through static diagnostics, controlled-model enumeration, representation rewrites, and paired closed-loop reruns.