Fuzzy Category-Theoretic Planning Introduces Graded Applicability to Natural-Language Planning

Global: Fuzzy Category-Theoretic Planning Introduces Graded Applicability to Natural-Language Planning

A team of computer scientists announced a new framework called Fuzzy Category-theoretic Planning (FCP) in a paper posted to arXiv on January 2026. The approach aims to address the difficulty of handling vague predicates in natural-language planning by assigning graded applicability values to actions. According to the authors, FCP retains compositional structure while allowing quality degradation to be tracked across multi-step plans.

Background

Traditional category-theoretic planners rely on crisp, binary applicability checks, which forces designers to impose arbitrary thresholds on predicates such as “suitable substitute” or “stable enough.” This binary treatment can obscure meaningful distinctions and limit the planner’s ability to reason about partial satisfaction of constraints.

Proposed Method

FCP annotates each action, represented as a morphism, with a real-valued degree in the interval [0,1]. The framework composes these degrees using the Lukasiewicz t-norm, producing an overall plan quality score while preserving hard-constraint verification through pullback operations.

Technical Foundations

The authors integrate a large language model (LLM) to ground the graded applicability scores, employing a k-sample median aggregation to derive robust estimates. Additionally, FCP supports a meeting‑in‑the‑middle search strategy by leveraging residuum‑based backward requirements, which guide the planner toward feasible intermediate states.

Experimental Evaluation

Evaluation was conducted on two benchmark suites: public PDDL3 preference/oversubscription problems and a newly introduced RecipeNLG‑Subs dataset, which extends RecipeNLG with substitution candidates sourced from Recipe1MSubs and FoodKG. The experiments compared FCP against LLM‑only baselines and ReAct‑style approaches, as well as classical PDDL3 planners.

Results and Discussion

According to the paper, FCP achieved higher success rates and reduced hard‑constraint violations on the RecipeNLG‑Subs benchmark relative to the LLM‑only and ReAct baselines, while remaining competitive with established PDDL3 planners on traditional tasks. The authors suggest that the graded framework offers a more nuanced handling of vague predicates without sacrificing executability guarantees.

Future Directions

The research team indicates plans to extend FCP to broader domains and to explore alternative aggregation techniques for LLM‑derived degrees. They also propose investigating tighter integration with existing planning languages to facilitate adoption in real‑world applications.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.