arXiv:2507.03293v1 Announce Type: new Abstract: Large language models (LLMs) have demonstrated promise in reasoning tasks and general decision-making in static environments. In long-term planning tasks, however, errors tend to accumulate, often leading to unsafe or inefficient behavior, limiting their use in general-purpose settings. We propose a modular actor-critic architecture in which an LLM actor is guided by LTLCrit, a trajectory-level LLM critic that communicates via linear temporal logic (LTL). Our setup combines the reasoning strengths of language models with the guarantees of formal logic. The actor selects high-level actions from natural language observations, while the critic analyzes full trajectories and proposes new LTL constraints that shield the actor from future unsafe or inefficient behavior. The architecture supports both fixed, hand-specified safety constraints and adaptive, learned soft constraints that promote long-term efficiency. Our architecture is model-agnostic: any LLM-based planner can serve as the actor, and LTLCrit serves as a logic-generating wrapper. We formalize planning as graph traversal under symbolic constraints, allowing LTLCrit to analyze failed or suboptimal trajectories and generate new temporal logic rules that improve future behavior. We evaluate our system on the Minecraft diamond-mining benchmark, achieving 100% completion rates and improving efficiency compared to baseline LLM planners. Our results suggest that enabling LLMs to supervise each other through logic is a powerful and flexible paradigm for safe, generalizable decision making.