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* OWL 2 RL — Table 7: Class axiom rules (cax-*)
*
* Implements rules cax-sco, cax-eqc1, cax-eqc2, cax-dw, and cax-adc.
*
* @see https://www.w3.org/TR/owl2-profiles/#Reasoning_in_OWL_2_RL_and_RDF_Graphs_using_Rules
* @see Table 7 — https://www.w3.org/TR/owl2-profiles/#tab-rules-class-axioms
*/
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 class axiom rules that fire once per incoming quad.
*
* Rules applied:
* - cax-sco: x type c1, c1 subClassOf c2 → x type c2
* - cax-eqc1: x type c1, c1 equivalentClass c2 → x type c2
* - cax-eqc2: x type c2, c1 equivalentClass c2 → x type c1
* - cax-dw: x type c1, c1 disjointWith c2, x type c2 → inconsistency
*
* @see https://www.w3.org/TR/owl2-profiles/#tab-rules-class-axioms
*/
export function* classAxiomSingleQuad(quad: rdfjs.Quad, index: TripleIndex): Iterable<InferenceResult> {
const { subject, predicate, object } = quad;
const predicateIri = predicate.value;
const subjectIri = subject.value;
const objectIri = object.value;
if (predicateIri === RDF.type) {
// cax-sco: x type c1, c1 subClassOf c2 → x type c2
for (const superClass of index.getObjects(RDFS.subClassOf, objectIri)) {
yield infer(
makeTriple(subject, rdf.type, superClass),
'cax-sco',
quad,
makeTriple(object as rdfjs.Quad_Subject, namedNode(RDFS.subClassOf), superClass),
);
}
// cax-eqc1/2: x type c1, c1 equivalentClass c2 → x type c2 (and vice versa)
for (const equivalentClass of index.getObjects(OWL.equivalentClass, objectIri)) {
yield infer(
makeTriple(subject, rdf.type, equivalentClass),
'cax-eqc1',
quad,
makeTriple(object as rdfjs.Quad_Subject, namedNode(OWL.equivalentClass), equivalentClass),
);
}
for (const equivalentClass of index.getSubjects(OWL.equivalentClass, objectIri)) {
yield infer(
makeTriple(subject, rdf.type, equivalentClass as rdfjs.Quad_Object),
'cax-eqc2',
quad,
makeTriple(equivalentClass as rdfjs.Quad_Subject, namedNode(OWL.equivalentClass), object),
);
}
// cax-dw: x type c1, c1 disjointWith c2, x type c2 → inconsistency
for (const disjointClass of index.getObjects(OWL.disjointWith, objectIri)) {
if (index.has(RDF.type, subjectIri, disjointClass.value)) {
yield infer(
makeTriple(owl.Thing, rdfs.subClassOf, owl.Nothing),
'cax-dw',
quad,
makeTriple(object as rdfjs.Quad_Subject, namedNode(OWL.disjointWith), disjointClass),
makeTriple(subject, rdf.type, disjointClass),
);
}
}
for (const disjointClass of index.getSubjects(OWL.disjointWith, objectIri)) {
if (index.has(RDF.type, subjectIri, disjointClass.value)) {
yield infer(
makeTriple(owl.Thing, rdfs.subClassOf, owl.Nothing),
'cax-dw',
quad,
makeTriple(disjointClass as rdfjs.Quad_Subject, namedNode(OWL.disjointWith), object),
makeTriple(subject, rdf.type, disjointClass),
);
}
}
}
if (predicateIri === RDFS.subClassOf) {
// cax-sco propagation: if anything was typed as subject, it is now typed as object
for (const instance of index.getSubjects(RDF.type, subjectIri)) {
yield infer(
makeTriple(instance as rdfjs.Quad_Subject, rdf.type, object),
'cax-sco',
quad,
makeTriple(instance as rdfjs.Quad_Subject, rdf.type, subject as rdfjs.Quad_Object),
);
}
}
if (predicateIri === OWL.equivalentClass) {
// Propagate type for all existing instances of subject → typed as object too
for (const instance of index.getSubjects(RDF.type, subjectIri)) {
yield infer(
makeTriple(instance as rdfjs.Quad_Subject, rdf.type, object),
'cax-eqc1',
quad,
makeTriple(instance as rdfjs.Quad_Subject, rdf.type, subject as rdfjs.Quad_Object),
);
}
for (const instance of index.getSubjects(RDF.type, objectIri)) {
yield infer(
makeTriple(instance as rdfjs.Quad_Subject, rdf.type, subject as rdfjs.Quad_Object),
'cax-eqc2',
quad,
makeTriple(instance as rdfjs.Quad_Subject, rdf.type, object),
);
}
}
}
/**
* Join-based class axiom rules that require scanning the full index.
*
* Rules applied:
* - cax-adc: AllDisjointClasses, any individual typed as two member classes → inconsistency
*
* @see https://www.w3.org/TR/owl2-profiles/#tab-rules-class-axioms
*/
export function* classAxiomJoin(index: TripleIndex): Iterable<InferenceResult> {
for (const [allDisjointIri, listHeads] of index.byPredSubj.get(OWL.members) ?? []) {
if (!index.has(RDF.type, allDisjointIri, OWL.AllDisjointClasses)) continue;
for (const listHead of listHeads) {
const memberClasses = walkRdfList(listHead.value, index);
for (let i = 0; i < memberClasses.length; i++) {
const class1Iri = memberClasses[i].value;
const typedAsClass1 = index.getSubjects(RDF.type, class1Iri);
for (let j = i + 1; j < memberClasses.length; j++) {
const class2Iri = memberClasses[j].value;
for (const instance of typedAsClass1) {
if (index.has(RDF.type, instance.value, class2Iri)) {
yield infer(
makeTriple(owl.Thing, rdfs.subClassOf, owl.Nothing),
'cax-adc',
makeTriple(namedNode(allDisjointIri), rdf.type, namedNode(OWL.AllDisjointClasses)),
makeTriple(namedNode(allDisjointIri), namedNode(OWL.members), listHead),
makeTriple(instance as rdfjs.Quad_Subject, rdf.type, namedNode(class1Iri)),
makeTriple(instance as rdfjs.Quad_Subject, rdf.type, namedNode(class2Iri)),
);
}
}
}
}
}
}
}
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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