Institutional policies stay in natural language while the systems that check compliance demand machine-readable constraints. Bridging that gap is still done by hand. PolicyKG closes the loop. It is an LLM pipeline that reads a policy PDF, classifies each sentence as an obligation, permission, or prohibition, lifts the label into first-order deontic logic, and emits SHACL constraints. Four stages run on a LangGraph state machine with per-stage validators. The piece that matters most is the Corpus Adapter: a YAML vocabulary registry that grounds LLM predicates in a target ontology. Retargeting to a new domain means swapping the registry, not retraining a model. On the Asian Institute of Technology Policies and Procedures corpus (1,663 sentences, 443 rules), PolicyKG reaches 86.9% deontic classification accuracy (Cohen's kappa = .709). Three annotators independently re-label a 50-item sample and agree at Fleiss' kappa = .844. SHACL shape correctness on a 69-shape subset is F1 = .866. The FOL path handles 79.2% of rules; the rest go through a direct NL-to-SHACL fallback. We audited every one of the 443 rules for second- or higher-order constructs. An automated regex checklist flagged none, and a first-author pass on the 92 FOL-fallback cases confirmed the same. The exact upper 95% Clopper-Pearson bound on the true HOL rate is 0.67%. This is an audit finding for one corpus, not a proof of FOL sufficiency for institutional policy. Swapping the AIT registry for a GDPR registry raises exact property alignment from 1/15 to 11/15 (Fisher's exact p < .001; Cohen's h = 1.53). On the LexDeMod lease-contract benchmark (N = 200), Macro F1 drops to .370 because lease English uses "shall be entitled" for permission -- exactly the vocabulary mismatch registry swap is meant to fix. Repeated runs produce hash-identical SHACL outputs.
SHACL (Shapes Constraint Language) expresses constraints on RDF data by means of so-called shapes. Its central service is validation: verifying whether a data graph complies with a SHACL document. But so far, there are no static analysis services to compare documents. In this paper, we study the following problem: decide whether all graphs that validate one SHACL document also validate another. Unlike previous works that have considered the implication of shape expressions only, we consider documents comprising (recursive) shape definitions and targets. We show that implication (a.k.a. containment) is undecidable under the supported and the stable model semantics, even for the fragment that uses the description logic ALCIO for shape expressions. Under the well-founded semantics, in surprising contrast, it is decidable in single exponential time. Our key technical contribution is a translation of SHACL under the well-founded semantics into the full hybrid mu-calculus, revealing a novel link between well-founded models and a fixed point modal logic, and a worst-case optimal automata-based decision procedure.