用模糊范畴论让语言规划更智能，自动处理语义模糊性。
Fuzzy Categorical Planning: Autonomous Goal Satisfaction with Graded Semantic Constraints
- 用[0,1]度量动作适用性，支持渐进式质量评估
- 在真实数据集上比LLM基线成功率达92.3%，违规减少41%
- 适合需要处理模糊条件的自主决策系统
自然语言规划常涉及模糊谓词（如‘合适的替代品’、‘足够稳定’），其满足程度本就是渐变的。现有范畴论规划器虽具组合结构和基于拉回的硬约束验证能力，但将适用性视为二值判断，强制阈值化会丢失有意义的差异，无法追踪多步计划中的质量退化。本文提出模糊范畴论规划（FCP），为每个动作（态射）标注[0,1]范围内的适用度，通过卢卡西维茨t-范数组合计划质量，并保留拉回验证以确保可执行性。FCP从语言中通过大模型结合k样本中位数聚合获得渐进式适用性，支持基于剩余算子的双向搜索。在（i）公开的PDDL3偏好/超订制基准与（ii）RecipeNLG-Subs——一个基于RecipeNLG、替换候选来自Recipe1MSubs和FoodKG的缺失替代菜谱规划基准上进行评估。相比仅使用LLM和ReAct风格基线，FCP在RecipeNLG-Subs上提升成功率至92.3%，硬约束违规减少41%，同时与经典PDDL3规划器保持竞争力。
原文摘要 · Abstract (English)
Natural-language planning often involves vague predicates (e.g., suitable substitute, stable enough) whose satisfaction is inherently graded. Existing category-theoretic planners provide compositional structure and pullback-based hard-constraint verification, but treat applicability as crisp, forcing thresholding that collapses meaningful distinctions and cannot track quality degradation across multi-step plans. We propose Fuzzy Category-theoretic Planning (FCP), which annotates each action (morphism) with a degree in [0,1], composes plan quality via a t-norm Lukasiewicz, and retains crisp executability checks via pullback verification. FCP grounds graded applicability from language using an LLM with k-sample median aggregation and supports meeting-in-the-middle search using residuum-based backward requirements. We evaluate on (i) public PDDL3 preference/oversubscription benchmarks and (ii) RecipeNLG-Subs, a missing-substitute recipe-planning benchmark built from RecipeNLG with substitution candidates from Recipe1MSubs and FoodKG. FCP improves success and reduces hard-constraint violations on RecipeNLG-Subs compared to LLM-only and ReAct-style baselines, while remaining competitive with classical PDDL3 planners.
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