OWL ⊨ SKOS ⊨ SHACL derivation chain

Motivation

Evaluating column classification or ontology-grounded pretraining requires the type system, the constraints that exercise it, the relational schema, and the populated data to be mutually consistent. When those are versioned independently — a glossary in one place, DDL in another, corpus regenerated ad hoc — drift silently contaminates downstream measurement. The derivation chain treats them as one function of a versioned OWL artifact, so a commit hash identifies a coherent (ontology, vocabulary, shapes, schema, corpus) tuple.

Formulation

Let Ω be a realized OWL 2 ontology, BFO 2020 / CCO-grounded and HermiT-certified [Motik, Patel-Schneider & Grau 2012; Arp, Smith & Spear 2015]. The published faces are entailed, never independently authored:

Ω ⊨ V(Ω) ⊨ S(Ω) → R(Ω) → X(Ω, V, R)

• V(Ω) is the SKOS ConceptScheme [Miles & Bechhofer 2009]: every concept’s defining class exists in Ω. skos:prefLabel / altLabel / definition / scopeNote / example are annotation properties on that class — retrieval text, not a parallel taxonomy.
• S(Ω) is the SHACL Core shapes graph [Knublauch & Kontokostas 2017]. Every sh:targetClass names a realized OWL class; some restrictions become sh:minCount ≥ 1; exactly n becomes min = max = n; fillers become sh:class. Value enumerations (sh:in) correspond to SKOS labels — that is SKOS ⊨ SHACL.
• R(Ω) is the relational projection: loadable SQL (tables, keys, foreign keys) lowered from the certified OWL by kvasir, with a plan that cites class and property IRIs per relation. The schema is a view of Ω, not a catalog of generation templates.
• X(Ω, V, R) is the populated corpus — textbook chapters and rows that conform to R with column labels drawn from V.

Aegir’s scripts/check_triad_entailment.py measures the three entailments mechanically (OWL ⊨ SKOS, OWL ⊨ SHACL, SKOS ⊨ SHACL). Realization (scripts/realize_sdg.py) is merge → HermiT certificate → DDL → shapes.ttl.

Implementation notes

The chain lives in Ægir and publishes through the corpora/ submodule (sdg-corpora). Two properties make it operational. First, content-hashed run identity: identical certified inputs produce bit-identical DDL and shapes in a directory named by their fingerprint. Second, blind release: a tagged SHARE-tier package includes ontology, SKOS, SHACL, and populated tables, but holds back the per-column class reference. Downstream classifiers — Atelier for independent scoring, Ægir for lift — see values and vocabulary only.

Hand-authored axiom families and a fixed template catalog were an early scaffold. They are retired: the live ontology is content-derived from input passages, membrane-gated (parse → HermiT → OntoClean), and projected outward. Counts of classes, concepts, and tables are properties of a given snapshot, not the method.

Status

The triad and the relational lowering are the published contract. Atlas and Qdrant are views of the same OWL, rebuilt from it. Cross-entity foreign keys are earned from content, not name-matched from a family table.

References

• Motik, B., Patel-Schneider, P. F., Grau, B. C. (2012). OWL 2 Web Ontology Language Direct Semantics. W3C Recommendation.
• Arp, R., Smith, B., Spear, A. (2015). Building Ontologies with Basic Formal Ontology. MIT Press.
• Miles, A., Bechhofer, S. (2009). SKOS Simple Knowledge Organization System Reference. W3C Recommendation.
• Knublauch, H., Kontokostas, D. (2017). Shapes Constraint Language (SHACL). W3C Recommendation.
• Common Core Ontologies (CCO). github.com/CommonCoreOntology/CommonCoreOntologies.