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Fuzzy Categorical Planning: Autonomous Goal Satisfaction with Graded Semantic Constraints

Shuhui Qu

TL;DR

The paper tackles planning in the presence of vagueness by extending category-theoretic planning with graded action applicability, while preserving crisp executability through pullback verification. It grounds vague predicates with an LLM using k-sample median, and composes plan quality via the Łukasiewicz t-norm, enabling explicit degradation tracking across multi-step plans. A bidirectional search with fuzzy propagation and residuation-based backward requirements enables meeting-in-the-middle planning under graded constraints, with plan acceptance controlled by explicit α-cuts. Empirically, FCP achieves competitive success on PDDL3 preferences/oversubscription and outperforms baselines on RecipeNLG-Subs in terms of feasibility and constraint satisfaction, while showing robustness to aggregation, chunking, and t-norm choices. The work demonstrates a practical pathway to integrate semantic vagueness into symbolic planning for real-world tasks, with implications for natural-language instruction following and mixed-initiative planning.

Abstract

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.

Fuzzy Categorical Planning: Autonomous Goal Satisfaction with Graded Semantic Constraints

TL;DR

The paper tackles planning in the presence of vagueness by extending category-theoretic planning with graded action applicability, while preserving crisp executability through pullback verification. It grounds vague predicates with an LLM using k-sample median, and composes plan quality via the Łukasiewicz t-norm, enabling explicit degradation tracking across multi-step plans. A bidirectional search with fuzzy propagation and residuation-based backward requirements enables meeting-in-the-middle planning under graded constraints, with plan acceptance controlled by explicit α-cuts. Empirically, FCP achieves competitive success on PDDL3 preferences/oversubscription and outperforms baselines on RecipeNLG-Subs in terms of feasibility and constraint satisfaction, while showing robustness to aggregation, chunking, and t-norm choices. The work demonstrates a practical pathway to integrate semantic vagueness into symbolic planning for real-world tasks, with implications for natural-language instruction following and mixed-initiative planning.

Abstract

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.
Paper Structure (52 sections, 13 equations, 2 figures, 2 tables)

This paper contains 52 sections, 13 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Approach.
  3. Evaluation.
  4. Contributions.
  5. Related Work
  6. Classical Planning, Preferences, and Oversubscription
  7. Neural and LLM-Based Planning
  8. Search-Augmented and Structured Reasoning for Planning
  9. Fuzzy Logic and Graded Satisfaction in Planning
  10. Soft Constraints vs. Graded Predicates
  11. Category-Theoretic Structure for Planning and Reasoning
  12. Vagueness in Natural Language and LLM Uncertainty
  13. Fuzzy Category-Theoretic Planning
  14. Fuzzy-Enriched Planning Category
  15. State representation.
  16. ...and 37 more sections

Figures (2)

  • Figure 1: Degradation drivers in FCP. Success rate (%) as a function of plan length, number of missing requirements, number of substitute candidates, and grounding aggregation size $k$ (color denotes the x-axis bin: 1/3/5/7/$>7$ or 1/3/5/7 depending on the factor). Performance degrades sharply with longer plans and more missing items, while varying the number of candidates has minimal impact; increasing $k$ improves robustness up to $k{=}5$ with diminishing returns thereafter.
  • Figure 2: Influence of backbone. FCP maintains high success across backbones (80--92%), with modest gains from stronger models.