Interactive robot planning requires robots to infer and execute human intentions from natural language instructions that are often ambiguous, incomplete, or underspecified. Although large language models (LLMs) provide a powerful interface for clarification, relying on the generative model to drive an multi-turn conversation can introduce systematic failures. We propose a Bayesian framework that treats clarification as an active learning problem over grounded Signal Temporal Logic (STL) task specifications. Our method uses LLMs to initialize candidate formal specifications and translate informative contrasts into natural-language clarification questions, while Bayesian optimization maintains uncertainty estimation over user intent and selects queries that maximize information gain. After convergence, the inferred STL specification is passed to a formal planner to synthesize a verifiable robot trajectory. Across four simulated and real-world task domains, our approach generally achieves higher task satisfaction and requires fewer clarification rounds than LLM baselines, while helping smaller models close the performance gap against larger reasoning models.

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