A Transparent Fuzzy-Inference Layer for Explainable Knowledge Tracing: Why Prerequisite Graphs Must Be Expert-Supplied, and Which T-Norm to Use

<title>Abstract</title> <p>Deep knowledge tracing (KT) predicts student difficulty accurately but is opaque about the prerequisite concepts a teacher must address. A popular neuro-symbolic remedy attaches a fuzzy prerequisite graph to a KT backbone, assuming the graph can be discovered from interaction logs. We test that assumption and report two principal results. First, a systematic negative result: on the ASSISTments 2009 benchmark, three log-only induction families — transfer entropy, confound-controlled mastery-lift, and semi-supervised expert-seeded classification — all fail to recover expert prerequisites at a usable level; the confound-controlled estimator ranks the 16 expert edges at a median of 3,622 out of 7,144 candidate pairs (chance ≈ 3,572). We trace this failure to an ability/difficulty confound that renders almost all skill pairs positively associated, and we show that the confound replicates on two further datasets (ASSISTments 2012 and Junyi, 25.9 million interactions). This finding concerns log-only induction and is orthogonal to content-based (NLP/LLM) methods. Second, we introduce a reusable, rater-free localisation-audit framework with model-defined ground truth: it measures whether a trained model encodes each expert prerequisite and whether an explanation localises it. The audit shows that the model encodes most prerequisites (12 of 16 on DKT, 11 of 16 on SAKT), whereas post-hoc attribution localises them unreliably (top-3 hit-rate 66% for Integrated Gradients and 61% for occlusion-SHAP on DKT), with occlusion-SHAP collapsing to 27% on a self-attentive model — a graph-grounded fuzzy layer localises reliably regardless of architecture. Our two central contributions are therefore the log-signal limit and the reusable, architecture-independent localisation-audit framework; we deliberately keep the fuzzy exploitation layer (D-FIS) fixed and parameter-free so that it is transparent and auditable by construction, and we compare four fuzzy conjunction operators (product, minimum, Łukasiewicz, drastic), finding that the product t-norm aligns best with the model's true prerequisite effect (positive in 97.6% of bootstrap resamples; permutation p = 0.026). All code and anonymised data are released.</p>