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* OWL 2 RL — Table 9: Schema vocabulary rules (scm-*)
*
* Implements rules scm-cls, scm-op, scm-dp, scm-eqc1/2, scm-eqp1/2, scm-sco, scm-spo,
* scm-dom1/2, scm-rng1/2, scm-hv, scm-svf1/2, scm-avf1/2, scm-int, scm-uni.
*
* These rules exclusively operate on the schema (TBox) and propagate subclass/subproperty
* relationships, domain/range constraints, and restriction-based subsumption.
*
* @see https://www.w3.org/TR/owl2-profiles/#Reasoning_in_OWL_2_RL_and_RDF_Graphs_using_Rules
* @see Table 9 — https://www.w3.org/TR/owl2-profiles/#tab-rules-schema
*/
import * as rdfjs from '@rdfjs/types';
import DataFactory from '@rdfjs/data-model';
import { TripleIndex } from '../../triple-index.js';
import { InferenceResult, infer } from '../../reasoner.js';
import { RDF, RDFS, OWL, rdf, rdfs, owl } from '../vocabulary.js';
const { namedNode } = DataFactory;
function makeTriple(subject: rdfjs.Quad_Subject, predicate: rdfjs.Quad_Predicate, object: rdfjs.Quad_Object): rdfjs.Quad {
return DataFactory.quad(subject, predicate, object);
}
/**
* Single-quad schema rules that fire once per incoming quad.
*
* Rules applied:
* - scm-cls: c type owl:Class → c subClassOf c, c equivalentClass c, c subClassOf owl:Thing,
* owl:Nothing subClassOf c
* - scm-op: p type owl:ObjectProperty → p subPropertyOf p, p equivalentProperty p
* - scm-dp: p type owl:DatatypeProperty → p subPropertyOf p, p equivalentProperty p
* - scm-eqc1: c1 equivalentClass c2 → c1 subClassOf c2 AND c2 subClassOf c1
* - scm-eqp1: p1 equivalentProperty p2 → p1 subPropertyOf p2 AND p2 subPropertyOf p1
* - scm-int: c intersectionOf list → c subClassOf each component
* - scm-uni: c unionOf list → each component subClassOf c
*
* @see https://www.w3.org/TR/owl2-profiles/#tab-rules-schema
*/
export function* schemaSingleQuad(quad: rdfjs.Quad, index: TripleIndex): Iterable<InferenceResult> {
const { subject, predicate, object } = quad;
const predicateIri = predicate.value;
// scm-cls: every owl:Class gets reflexive subClassOf/equivalentClass + bounds
if (predicateIri === RDF.type && object.value === OWL.Class) {
yield infer(makeTriple(subject, rdfs.subClassOf, subject as rdfjs.Quad_Object), 'scm-cls', quad);
yield infer(makeTriple(subject, owl.equivalentClass, subject as rdfjs.Quad_Object), 'scm-cls', quad);
yield infer(makeTriple(subject, rdfs.subClassOf, owl.Thing), 'scm-cls', quad);
yield infer(makeTriple(owl.Nothing, rdfs.subClassOf, subject as rdfjs.Quad_Object), 'scm-cls', quad);
}
// scm-op: every owl:ObjectProperty gets reflexive subPropertyOf/equivalentProperty
if (predicateIri === RDF.type && object.value === OWL.ObjectProperty) {
yield infer(makeTriple(subject, rdfs.subPropertyOf, subject as rdfjs.Quad_Object), 'scm-op', quad);
yield infer(makeTriple(subject, owl.equivalentProperty, subject as rdfjs.Quad_Object), 'scm-op', quad);
}
// scm-dp: every owl:DatatypeProperty gets reflexive subPropertyOf/equivalentProperty
if (predicateIri === RDF.type && object.value === OWL.DatatypeProperty) {
yield infer(makeTriple(subject, rdfs.subPropertyOf, subject as rdfjs.Quad_Object), 'scm-dp', quad);
yield infer(makeTriple(subject, owl.equivalentProperty, subject as rdfjs.Quad_Object), 'scm-dp', quad);
}
// scm-eqc1: c1 equivalentClass c2 → c1 subClassOf c2 AND c2 subClassOf c1
if (predicateIri === OWL.equivalentClass) {
yield infer(makeTriple(subject, rdfs.subClassOf, object), 'scm-eqc1', quad);
yield infer(makeTriple(object as rdfjs.Quad_Subject, rdfs.subClassOf, subject as rdfjs.Quad_Object), 'scm-eqc1', quad);
}
// scm-eqp1: p1 equivalentProperty p2 → p1 subPropertyOf p2 AND p2 subPropertyOf p1
if (predicateIri === OWL.equivalentProperty) {
yield infer(makeTriple(subject, rdfs.subPropertyOf, object), 'scm-eqp1', quad);
yield infer(makeTriple(object as rdfjs.Quad_Subject, rdfs.subPropertyOf, subject as rdfjs.Quad_Object), 'scm-eqp1', quad);
}
// scm-int: intersectionOf → each component is a superclass
if (predicateIri === OWL.intersectionOf) {
for (const member of walkRdfList(object.value, index)) {
yield infer(makeTriple(subject, rdfs.subClassOf, member), 'scm-int', quad);
}
}
// scm-uni: unionOf → each component is a subclass
if (predicateIri === OWL.unionOf) {
for (const member of walkRdfList(object.value, index)) {
yield infer(makeTriple(member as rdfjs.Quad_Subject, rdfs.subClassOf, subject as rdfjs.Quad_Object), 'scm-uni', quad);
}
}
}
/**
* Join-based schema rules that require scanning the full index.
*
* Rules applied:
* - scm-sco: c1 subClassOf c2, c2 subClassOf c3 → c1 subClassOf c3
* - scm-eqc2: c1 subClassOf c2, c2 subClassOf c1 → c1 equivalentClass c2
* - scm-spo: p1 subPropertyOf p2, p2 subPropertyOf p3 → p1 subPropertyOf p3
* - scm-eqp2: p1 subPropertyOf p2, p2 subPropertyOf p1 → p1 equivalentProperty p2
* - scm-dom1: p domain c1, c1 subClassOf c2 → p domain c2
* - scm-dom2: p2 domain c, p1 subPropertyOf p2 → p1 domain c
* - scm-rng1: p range c1, c1 subClassOf c2 → p range c2
* - scm-rng2: p2 range c, p1 subPropertyOf p2 → p1 range c
* - scm-hv: c1 hasValue v on p1, c2 hasValue v on p2, p1 subPropertyOf p2 → c1 subClassOf c2
* - scm-svf1: c1 someValuesFrom d1 on p, c2 someValuesFrom d2 on p, d1 subClassOf d2 → c1 subClassOf c2
* - scm-svf2: c1 someValuesFrom d on p1, c2 someValuesFrom d on p2, p1 subPropertyOf p2 → c1 subClassOf c2
* - scm-avf1: c1 allValuesFrom d1 on p, c2 allValuesFrom d2 on p, d1 subClassOf d2 → c1 subClassOf c2
* - scm-avf2: c1 allValuesFrom d on p1, c2 allValuesFrom d on p2, p1 subPropertyOf p2 → c2 subClassOf c1
*
* @see https://www.w3.org/TR/owl2-profiles/#tab-rules-schema
*/
export function* schemaJoin(index: TripleIndex): Iterable<InferenceResult> {
// scm-sco: c1 subClassOf c2, c2 subClassOf c3 → c1 subClassOf c3
for (const [class1Iri, superClasses] of index.byPredSubj.get(RDFS.subClassOf) ?? []) {
for (const class2 of superClasses) {
for (const class3 of index.getObjects(RDFS.subClassOf, class2.value)) {
if (class3.value !== class1Iri) {
yield infer(
makeTriple(namedNode(class1Iri), rdfs.subClassOf, class3),
'scm-sco',
makeTriple(namedNode(class1Iri), rdfs.subClassOf, class2),
makeTriple(class2 as rdfjs.Quad_Subject, rdfs.subClassOf, class3),
);
}
}
}
}
// scm-eqc2: c1 subClassOf c2 AND c2 subClassOf c1 → c1 equivalentClass c2
for (const [class1Iri, superClasses] of index.byPredSubj.get(RDFS.subClassOf) ?? []) {
const class1Term = namedNode(class1Iri);
for (const class2 of superClasses) {
if (index.has(RDFS.subClassOf, class2.value, class1Iri)) {
yield infer(
makeTriple(class1Term, owl.equivalentClass, class2),
'scm-eqc2',
makeTriple(class1Term, rdfs.subClassOf, class2),
makeTriple(class2 as rdfjs.Quad_Subject, rdfs.subClassOf, class1Term),
);
}
}
}
// scm-spo: p1 subPropertyOf p2, p2 subPropertyOf p3 → p1 subPropertyOf p3
for (const [property1Iri, superProperties] of index.byPredSubj.get(RDFS.subPropertyOf) ?? []) {
for (const property2 of superProperties) {
for (const property3 of index.getObjects(RDFS.subPropertyOf, property2.value)) {
if (property3.value !== property1Iri) {
yield infer(
makeTriple(namedNode(property1Iri), rdfs.subPropertyOf, property3),
'scm-spo',
makeTriple(namedNode(property1Iri), rdfs.subPropertyOf, property2),
makeTriple(property2 as rdfjs.Quad_Subject, rdfs.subPropertyOf, property3),
);
}
}
}
}
// scm-eqp2: p1 subPropertyOf p2, p2 subPropertyOf p1 → p1 equivalentProperty p2
for (const [property1Iri, superProperties] of index.byPredSubj.get(RDFS.subPropertyOf) ?? []) {
const property1Term = namedNode(property1Iri);
for (const property2 of superProperties) {
if (index.has(RDFS.subPropertyOf, property2.value, property1Iri)) {
yield infer(
makeTriple(property1Term, owl.equivalentProperty, property2),
'scm-eqp2',
makeTriple(property1Term, rdfs.subPropertyOf, property2),
makeTriple(property2 as rdfjs.Quad_Subject, rdfs.subPropertyOf, property1Term),
);
}
}
}
// scm-dom1: p domain c1, c1 subClassOf c2 → p domain c2
for (const [propertyIri, domainClasses] of index.byPredSubj.get(RDFS.domain) ?? []) {
const propertyTerm = namedNode(propertyIri);
for (const class1 of domainClasses) {
for (const class2 of index.getObjects(RDFS.subClassOf, class1.value)) {
yield infer(
makeTriple(propertyTerm, rdfs.domain, class2),
'scm-dom1',
makeTriple(propertyTerm, rdfs.domain, class1),
makeTriple(class1 as rdfjs.Quad_Subject, rdfs.subClassOf, class2),
);
}
}
}
// scm-dom2: p2 domain c, p1 subPropertyOf p2 → p1 domain c
for (const [property2Iri, domainClasses] of index.byPredSubj.get(RDFS.domain) ?? []) {
for (const domainClass of domainClasses) {
for (const property1 of index.getSubjects(RDFS.subPropertyOf, property2Iri)) {
yield infer(
makeTriple(property1 as rdfjs.Quad_Subject, rdfs.domain, domainClass),
'scm-dom2',
makeTriple(namedNode(property2Iri), rdfs.domain, domainClass),
makeTriple(property1 as rdfjs.Quad_Subject, rdfs.subPropertyOf, namedNode(property2Iri)),
);
}
}
}
// scm-rng1: p range c1, c1 subClassOf c2 → p range c2
for (const [propertyIri, rangeClasses] of index.byPredSubj.get(RDFS.range) ?? []) {
const propertyTerm = namedNode(propertyIri);
for (const class1 of rangeClasses) {
for (const class2 of index.getObjects(RDFS.subClassOf, class1.value)) {
yield infer(
makeTriple(propertyTerm, rdfs.range, class2),
'scm-rng1',
makeTriple(propertyTerm, rdfs.range, class1),
makeTriple(class1 as rdfjs.Quad_Subject, rdfs.subClassOf, class2),
);
}
}
}
// scm-rng2: p2 range c, p1 subPropertyOf p2 → p1 range c
for (const [property2Iri, rangeClasses] of index.byPredSubj.get(RDFS.range) ?? []) {
for (const rangeClass of rangeClasses) {
for (const property1 of index.getSubjects(RDFS.subPropertyOf, property2Iri)) {
yield infer(
makeTriple(property1 as rdfjs.Quad_Subject, rdfs.range, rangeClass),
'scm-rng2',
makeTriple(namedNode(property2Iri), rdfs.range, rangeClass),
makeTriple(property1 as rdfjs.Quad_Subject, rdfs.subPropertyOf, namedNode(property2Iri)),
);
}
}
}
// scm-hv: c1 hasValue v on p1, c2 hasValue v on p2, p1 subPropertyOf p2 → c1 subClassOf c2
for (const [class1Iri, values1] of index.byPredSubj.get(OWL.hasValue) ?? []) {
const class1Term = namedNode(class1Iri);
const properties1 = index.getObjects(OWL.onProperty, class1Iri);
for (const value1 of values1) {
for (const class2 of index.getSubjects(OWL.hasValue, value1.value)) {
if (class2.value === class1Iri) continue;
const properties2 = index.getObjects(OWL.onProperty, class2.value);
for (const property1 of properties1) {
for (const property2 of properties2) {
if (index.has(RDFS.subPropertyOf, property1.value, property2.value)) {
yield infer(
makeTriple(class1Term, rdfs.subClassOf, class2 as rdfjs.Quad_Object),
'scm-hv',
makeTriple(class1Term, namedNode(OWL.hasValue), value1),
makeTriple(class1Term, namedNode(OWL.onProperty), property1),
makeTriple(class2 as rdfjs.Quad_Subject, namedNode(OWL.hasValue), value1),
makeTriple(class2 as rdfjs.Quad_Subject, namedNode(OWL.onProperty), property2),
makeTriple(property1 as rdfjs.Quad_Subject, rdfs.subPropertyOf, property2),
);
}
}
}
}
}
}
// scm-svf1: c1 someValuesFrom d1 on p, c2 someValuesFrom d2 on p, d1 subClassOf d2 → c1 subClassOf c2
// scm-svf2: c1 someValuesFrom d on p1, c2 someValuesFrom d on p2, p1 subPropertyOf p2 → c1 subClassOf c2
for (const [class1Iri, fillers1] of index.byPredSubj.get(OWL.someValuesFrom) ?? []) {
const class1Term = namedNode(class1Iri);
const properties1 = index.getObjects(OWL.onProperty, class1Iri);
for (const filler1 of fillers1) {
// scm-svf1: same property, filler1 subClassOf filler2
for (const class2 of index.getSubjects(OWL.someValuesFrom, filler1.value)) {
if (class2.value === class1Iri) continue;
const properties2 = index.getObjects(OWL.onProperty, class2.value);
for (const property1 of properties1) {
for (const property2 of properties2) {
if (property1.value === property2.value) {
yield infer(
makeTriple(class1Term, rdfs.subClassOf, class2 as rdfjs.Quad_Object),
'scm-svf1',
makeTriple(class1Term, namedNode(OWL.someValuesFrom), filler1),
makeTriple(class1Term, namedNode(OWL.onProperty), property1),
makeTriple(class2 as rdfjs.Quad_Subject, namedNode(OWL.someValuesFrom), filler1),
makeTriple(class2 as rdfjs.Quad_Subject, namedNode(OWL.onProperty), property2),
);
}
}
}
}
// scm-svf2: same filler, property1 subPropertyOf property2
for (const class2 of index.getSubjects(OWL.someValuesFrom, filler1.value)) {
if (class2.value === class1Iri) continue;
const properties2 = index.getObjects(OWL.onProperty, class2.value);
for (const property1 of properties1) {
for (const property2 of properties2) {
if (index.has(RDFS.subPropertyOf, property1.value, property2.value)) {
yield infer(
makeTriple(class1Term, rdfs.subClassOf, class2 as rdfjs.Quad_Object),
'scm-svf2',
makeTriple(class1Term, namedNode(OWL.someValuesFrom), filler1),
makeTriple(class1Term, namedNode(OWL.onProperty), property1),
makeTriple(class2 as rdfjs.Quad_Subject, namedNode(OWL.someValuesFrom), filler1),
makeTriple(class2 as rdfjs.Quad_Subject, namedNode(OWL.onProperty), property2),
makeTriple(property1 as rdfjs.Quad_Subject, rdfs.subPropertyOf, property2),
);
}
}
}
}
}
}
// scm-avf1: c1 allValuesFrom d1 on p, c2 allValuesFrom d2 on p, d1 subClassOf d2 → c1 subClassOf c2
// scm-avf2: c1 allValuesFrom d on p1, c2 allValuesFrom d on p2, p1 subPropertyOf p2 → c2 subClassOf c1 (contravariant)
for (const [class1Iri, fillers1] of index.byPredSubj.get(OWL.allValuesFrom) ?? []) {
const class1Term = namedNode(class1Iri);
const properties1 = index.getObjects(OWL.onProperty, class1Iri);
for (const filler1 of fillers1) {
// scm-avf1: filler1 subClassOf filler2, same property → c1 subClassOf c2
for (const filler2 of index.getObjects(RDFS.subClassOf, filler1.value)) {
for (const class2 of index.getSubjects(OWL.allValuesFrom, filler2.value)) {
if (class2.value === class1Iri) continue;
const properties2 = index.getObjects(OWL.onProperty, class2.value);
for (const property1 of properties1) {
for (const property2 of properties2) {
if (property1.value === property2.value) {
yield infer(
makeTriple(class1Term, rdfs.subClassOf, class2 as rdfjs.Quad_Object),
'scm-avf1',
makeTriple(class1Term, namedNode(OWL.allValuesFrom), filler1),
makeTriple(class1Term, namedNode(OWL.onProperty), property1),
makeTriple(class2 as rdfjs.Quad_Subject, namedNode(OWL.allValuesFrom), filler2),
makeTriple(class2 as rdfjs.Quad_Subject, namedNode(OWL.onProperty), property2),
makeTriple(filler1 as rdfjs.Quad_Subject, rdfs.subClassOf, filler2),
);
}
}
}
}
}
// scm-avf2: same filler, p1 subPropertyOf p2 → c2 subClassOf c1 (contravariant)
for (const class2 of index.getSubjects(OWL.allValuesFrom, filler1.value)) {
if (class2.value === class1Iri) continue;
const properties2 = index.getObjects(OWL.onProperty, class2.value);
for (const property1 of properties1) {
for (const property2 of properties2) {
if (index.has(RDFS.subPropertyOf, property1.value, property2.value)) {
yield infer(
makeTriple(class2 as rdfjs.Quad_Subject, rdfs.subClassOf, class1Term),
'scm-avf2',
makeTriple(class1Term, namedNode(OWL.allValuesFrom), filler1),
makeTriple(class1Term, namedNode(OWL.onProperty), property1),
makeTriple(class2 as rdfjs.Quad_Subject, namedNode(OWL.allValuesFrom), filler1),
makeTriple(class2 as rdfjs.Quad_Subject, namedNode(OWL.onProperty), property2),
makeTriple(property1 as rdfjs.Quad_Subject, rdfs.subPropertyOf, property2),
);
}
}
}
}
}
}
}
function walkRdfList(listHeadIri: string, index: TripleIndex): rdfjs.Quad_Object[] {
const firstNodes = index.getObjects(RDF.first, listHeadIri);
if (firstNodes.size === 0) return [];
const [first] = firstNodes;
const restNodes = index.getObjects(RDF.rest, listHeadIri);
if (restNodes.size === 0) return [first];
const [rest] = restNodes;
if (rest.value === RDF.nil) return [first];
return [first, ...walkRdfList(rest.value, index)];
}
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