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package uk.ac.ox.cs.rsacomb.approximation
import org.semanticweb.owlapi.apibinding.OWLManager
import org.semanticweb.owlapi.model.{IRI => _, _}
import tech.oxfordsemantic.jrdfox.logic.expression.{Resource, IRI}
import scala.collection.mutable.Map
import scalax.collection.Graph
import scalax.collection.GraphPredef._, scalax.collection.GraphEdge._
import scalax.collection.GraphTraversal._
import uk.ac.ox.cs.rsacomb.ontology.RSAOntology
import uk.ac.ox.cs.rsacomb.ontology.Ontology
import uk.ac.ox.cs.rsacomb.util.DataFactory
object Upperbound {
private val manager = OWLManager.createOWLOntologyManager()
private val factory = manager.getOWLDataFactory()
}
/** Approximation algorithm that mantains completeness for CQ answering.
*
* The input OWL 2 ontology is assumed to be normalized and the output
* ontology is guaranteed to be in RSA.
*
* The algorithm is performed in three steps:
* 1. the ontology is reduced to ALCHOIQ by discarding any axiom
* that is not in the language;
* 2. the ontology is further reduced to Horn-ALCHOIQ by shifting
* axioms with disjunction on the rhs;
* 3. the ontology is approximated to RSA by manipulating its
* dependency graph.
*
* @see [[uk.ac.ox.cs.rsacomb.converter.Normalizer]]
*/
class Upperbound(implicit fresh: DataFactory)
extends Approximation[RSAOntology] {
/** Simplify conversion between Java and Scala collections */
import uk.ac.ox.cs.rsacomb.implicits.JavaCollections._
/** Simplify conversion between OWLAPI and RDFox concepts */
// import uk.ac.ox.cs.rsacomb.implicits.RDFox._
/** Main entry point for the approximation algorithm */
def approximate(ontology: Ontology): RSAOntology =
toRSA(
new Ontology(
ontology.origin,
ontology.axioms map chooseDisjunct,
ontology.datafiles
)
)
/** Choose a single disjunct
*
* This is a very naïve way of getting rid of disjunction preserving
* completeness of CQ answering.
*/
private def chooseDisjunct(axiom: OWLLogicalAxiom): OWLLogicalAxiom =
axiom match {
case a: OWLSubClassOfAxiom => {
val sub = a.getSubClass.getNNF
val sup = a.getSuperClass.getNNF
sup match {
case sup: OWLObjectUnionOf =>
Upperbound.factory.getOWLSubClassOfAxiom(sub, sup.asDisjunctSet.head)
case _ => axiom
}
}
case _ => axiom
}
/** Approximate a Horn-ALCHOIQ ontology to RSA
*
* This is done by gathering those existential axioms that prevent
* the ontology dependency graph from being tree-shaped and constant
* skolemize them.
*
* @param ontology the set of axioms to approximate.
* @return the approximated RSA ontology
*/
private def toRSA(ontology: Ontology): RSAOntology = {
/* Compute the dependency graph for the ontology */
val (graph, nodemap) = ontology.dependencyGraph
/* Define node colors for the graph visit */
sealed trait NodeColor
case object Unvisited extends NodeColor
case object Visited extends NodeColor
case object ToSkolem extends NodeColor
/* Keep track of node colors during graph visit */
var color = Map.from[Resource, NodeColor](
graph.nodes.toOuter.map(k => (k, Unvisited))
)
for {
component <- graph.componentTraverser().map(_ to Graph)
edge <- component
.outerEdgeTraverser(component.nodes.head)
.withKind(BreadthFirst)
} yield {
val source = edge._1
val target = edge._2
color(source) match {
case Unvisited | Visited => {
color(target) match {
case Unvisited =>
color(source) = Visited;
color(target) = Visited
case Visited =>
color(source) = ToSkolem
case ToSkolem =>
color(source) = Visited
}
}
case ToSkolem => {}
}
}
val toSkolem = color.collect { case (resource: IRI, ToSkolem) =>
nodemap(resource.getIRI)
}.toList
// Force constant skolemization by introducing a fresh individual
// (singleton class).
val skolemized = toSkolem flatMap { (axiom) =>
import uk.ac.ox.cs.rsacomb.implicits.RSAAxiom._
axiom.toTriple match {
case Some((subclass, role, filler)) => {
val skolem = Upperbound.factory.getOWLNamedIndividual(
s"i_${axiom.toString.hashCode}"
)
val cls = fresh.getOWLClass
List(
Upperbound.factory.getOWLSubClassOfAxiom(
subclass,
Upperbound.factory.getOWLObjectSomeValuesFrom(role, cls)
),
Upperbound.factory.getOWLSubClassOfAxiom(
cls,
Upperbound.factory.getOWLObjectOneOf(skolem)
),
Upperbound.factory.getOWLClassAssertionAxiom(filler, skolem)
)
}
case None => List()
}
}
/* Substitute selected axioms with their "skolemized" version */
RSAOntology(
ontology.origin,
ontology.axioms diff toSkolem concat skolemized,
ontology.datafiles
)
}
// val edges1 = Seq('A ~> 'B, 'B ~> 'C, 'C ~> 'D, 'D ~> 'H, 'H ~>
// 'G, 'G ~> 'F, 'E ~> 'A, 'E ~> 'F, 'B ~> 'E, 'F ~> 'G, 'B ~> 'F,
// 'C ~> 'G, 'D ~> 'C, 'H ~> 'D)
// val edges2 = Seq('I ~> 'M, 'I ~> 'L, 'L ~> 'N, 'M ~> 'N)
// val edges3 = Seq('P ~> 'O)
// val graph = Graph.from(edges = edges1 ++ edges2 ++ edges3)
}
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