Fuzzy Categorical Planning: Autonomous Goal Satisfaction with Graded Semantic Constraints

TL;DR

This paper introduces Fuzzy Category-theoretic Planning (FCP), a novel approach that incorporates graded semantic constraints into planning, enabling more nuanced and flexible goal satisfaction in natural-language planning tasks.

Contribution

FCP extends category-theoretic planning by integrating fuzzy logic to handle graded applicability, combining language grounding with compositional plan quality assessment.

Findings

FCP improves success rates on recipe planning benchmarks.

FCP reduces violations of hard constraints compared to baselines.

FCP remains competitive with classical PDDL3 planners.

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.