FuzzyCell: Differentiable Cell Ontology Reasoning for Graded Cell Type Annotation

*How reliable are single-cell foundation models?* We audit scGPT, Geneformer, CellFM, and scCello on Tabula Sapiens and find that $18.4$ of predictions violate a hard biological constraint encoded in the Cell Ontology ($mathsfCL$): neurons placed in liver, cells assigned simultaneously to mutually exclusive lineages. These errors are invisible to accuracy and F1, yet they follow from elementary reasoning over the formal axioms of $mathsfCL$. The root cause is that annotation is treated as flat classification over a label set. Even methods that do use $mathsfCL$ use only its graph: random walks, hierarchical classifiers, PageRank, post-hoc probability propagation, hierarchy-weighted losses. The axioms themselves, disjointness and role restrictions that state which cell types cannot coexist and where each type must reside, are discarded. We recast annotation as ontology-constrained entity linking. FuzzyCell retrieves candidate types with a pretrained encoder and re-ranks them with a differentiable $$\begin{gathered} mathcalEL\_ \\ bot \end{gathered}$$ reasoner that evaluates $6,165$ extracted axioms, including $214$ asserted disjointness axioms that propagate to $8,246$ effective pairs, inside the training loop. Scoring uses a sigmoidal implication $$\begin{gathered} I\_ \\ sigma \end{gathered}$$ in the family of van Krieken et al., which remains trainable where Goguen and Lukasiewicz implications produce zero gradient on positive-measure regions, and satisfies the fuzzy implication boundary conditions at any finite steepness $s$. On Tabula Sapiens, HLCA, and AIDA v2, FuzzyCell reduces axiom violations by over $80$ and improves Macro-F1 by $7$ to $8$ points over the respective backbone, as a backbone-agnostic module adding under $4$ ms per cell. Gains concentrate in the long tail: median per-type F1 rises $1.0$ on common types and $18.7$ on rare types, and the improvement is recall-led, with macro-recall gaining $8.3$ points against $6.7$ for macro-precision. Ablations isolate the source: switching off the reasoner at fixed checkpoint changes $14$ of predictions, of which corrections outnumber degradations $3.6$ to $1$; removing tissue context costs $1.7$ Macro-F1 while removing $$\begin{gathered} I\_ \\ sigma \end{gathered}$$ costs $4.6$; removing $30$ of axioms at random costs $2.6$. Beyond hard labels, FuzzyCell outputs graded memberships that track differentiation: along two bone marrow trajectories, terminal-type membership correlates with pseudotime at Spearman $rho=0.755$ and $rho=0.648$.