Fuzzy Categorical Planning: Autonomous Goal Satisfaction with Graded Semantic Constraints

2026-01-27

AI Summary

This work addresses the challenge of handling fuzzy predicates—such as “sufficiently stable”—in natural language planning, whose graded semantics are incompatible with existing category-theoretic planners that rely solely on hard constraints. To bridge this gap, the paper introduces Fuzzy Categorical Planning (FCP), the first framework integrating fuzzy logic with categorical planning. FCP models action applicability via degrees in [0,1], composes plan quality using Łukasiewicz t-norms, and preserves pullback-based executability checks. It further incorporates a residual operator to enable bidirectional search and leverages large language models (LLMs) combined with k-sample median aggregation for robust mapping from natural language descriptions to graded applicability scores. Evaluated on RecipeNLG-Subs and PDDL3 benchmarks, FCP significantly reduces hard constraint violations and improves success rates over pure LLM and ReAct baselines.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• fuzzy planning
• graded constraints
• natural-language planning
• semantic vagueness
• goal satisfaction

Innovation

• Fuzzy Category-theoretic Planning
• Graded Semantic Constraints
• t-norm Composition
• Pullback Verification
• Residuum-based Backward Search