When May an Agent Stop? Evidence-Carrying Termination for Tool-Using LLMs

An agent whose tool keeps returning nothing useful should stop relying on it. In a retrieval environment with controlled source failures, we separate how agents judge results from what they do. We compare stopping at the same step after longer and shorter runs of results the agent judged useless; this contrast is zero for clock- or deadline-driven stopping. Where we record their judgments, the seven agents we test call a failing source's results useless 97-100% of the time, yet most of them rarely stop on that judgment. Prompt cues change when they stop but not what they stop on. Permission to answer from memory and a reasoning mode can bring early stops regardless of evidence, a stated budget moves the 7-8B models' stops to the deadline, and a stopping rule or call cost in the prompt is followed at most partly. Stopping follows the evidence only when the harness enforces an integration step that makes the agent answer after five consecutive results it judged useless. This step raises failing-source success for every model, keeps the stopping point fixed when the budget doubles, and needs no extra judgment call when the agent states its judgments. A pre-registered replication on 300 fresh questions confirms the dissociation and the rule's effect.

Tool-using LLM agents are usually evaluated by final-answer correctness or LLM judges. Neither captures how an answer was produced. In safety-critical settings, the procedure itself is part of correctness. In this paper, we introduce AgentLTL, a language derived from First-Order Linear Temporal Logic (FO-LTL) that expresses procedural rules over agent traces. It yields a deterministic, judge-free compliance score. In this framework, a single specification drives two usages. The first is harnessing: the constraints score completed traces, or gate tool calls by checking each prefix online, before execution. The second is finetuning: the score serves as a dense reward. On a benchmark spanning ordering, branching, iteration, and grounding, block-and-warn harnessing improves compliance on five of seven models. Finetuning with the same reward yields +38 and +17.5 percentage point gains in accuracy and compliance on held-out patterns, including unseen tool-name aliases. These findings are consistent with the model acquiring procedural structure rather than memorizing surface tool names and procedures.

Safety alignment for large language models (LLMs) in conversational settings is largely framed around whether to answer or refuse a request. In agentic settings, however, the same models must decide whether to act as permission-critical evidence emerges during execution. This creates a distinct challenge: apparent risk, action permissibility, and task competence are easily confounded, making agentic over-refusal difficult to distinguish from ordinary task failure. To address this, we introduce AgentBound, the first four-way counterfactual generation-and-evaluation framework for tool-using agent safety. AgentBound transforms the same executable workflow by independently varying apparent risk and action permissibility, enabling controlled comparisons of risky-looking but authorized tasks and routine-looking but unauthorized tasks. These comparisons jointly diagnose over-refusal and unsafe compliance while controlling for task competence. We instantiate AgentBound as a human-validated 4,000-task evaluation suite with trajectory-based and post-state-based judgments. Across 17 model and harness configurations, high safety frequently coexists with poor authorized-task completion: GPT-5.5 blocks 99.5% of routine-looking unauthorized actions yet completes only 28.7% of risky-looking authorized tasks. We further train a lightweight runtime calibration module that improves authorized-task completion by 18.2% on average across 10 evaluated configurations, while improving unsafe-action blocking by 5.4% on average. These show that effective agentic alignment requires action decisions to track permission-relevant execution evidence, rather than refusal strength alone.