# Fuzzy Categorical Planning: Autonomous Goal Satisfaction with Graded Semantic Constraints

arXiv: https://arxiv.org/abs/2601.20021 · HTML: https://mlsanity.com/paper/2601.20021/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Builds on (most cited first, 15 of 15)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Language Models as Zero-Shot Planners: Extracting Actionable Knowledge for Embodied Agents](https://mlsanity.com/paper/2201.07207/) (2022)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [PlanBench: An Extensible Benchmark for Evaluating Large Language Models on Planning and Reasoning about Change](https://mlsanity.com/paper/2206.10498/) (2022)
- [On the Planning Abilities of Large Language Models : A Critical Investigation](https://mlsanity.com/paper/2305.15771/) (2023)
- [ReWOO: Decoupling Reasoning from Observations for Efficient Augmented Language Models](https://mlsanity.com/paper/2305.18323/) (2023)
- [Ask Me Anything: A simple strategy for prompting language models](https://mlsanity.com/paper/2210.02441/) (2022)
- [The LAMA Planner: Guiding Cost-Based Anytime Planning with Landmarks](https://mlsanity.com/paper/1401.3839/) (2014)
- [Double-Ended Synthesis Planning with Goal-Constrained Bidirectional Search](https://mlsanity.com/paper/2407.06334/) (2024)
- [NL2Plan: Robust LLM-Driven Planning from Minimal Text Descriptions](https://mlsanity.com/paper/2405.04215/) (2024)
- [Soft Goals Can Be Compiled Away](https://mlsanity.com/paper/1401.3491/) (2014)
- [Learning to Substitute Ingredients in Recipes](https://mlsanity.com/paper/2302.07960/) (2023)
- [Retro*: Optimizing LLMs for Reasoning-Intensive Document Retrieval](https://mlsanity.com/paper/2509.24869/) (2025)

## Abstract (arXiv)

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.