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diff --git a/src/main/scala/rsacomb/CanonicalModel.scala b/src/main/scala/rsacomb/CanonicalModel.scala
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+++ b/src/main/scala/rsacomb/CanonicalModel.scala
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+package rsacomb
+
+import org.semanticweb.owlapi.model.{OWLObjectInverseOf, OWLObjectProperty}
+import org.semanticweb.owlapi.model.{
+  OWLClass,
+  // OWLObjectProperty,
+  OWLSubObjectPropertyOfAxiom,
+  // OWLObjectPropertyExpression,
+  OWLObjectSomeValuesFrom,
+  OWLSubClassOfAxiom
+}
+
+import tech.oxfordsemantic.jrdfox.logic.datalog.{
+  Rule,
+  BodyFormula,
+  TupleTableAtom,
+  Negation
+}
+import tech.oxfordsemantic.jrdfox.logic.expression.{
+  Term,
+  Variable,
+  // Resource,
+  IRI
+}
+
+import suffix.{Empty, Forward, Backward, Inverse}
+
+class CanonicalModel(val ontology: RSAOntology) extends RSAAxiom {
+
+  // Makes working with IRIs less painful
+  import RDFoxUtil._
+
+  val named: List[Rule] =
+    ontology.individuals.map(a =>
+      Rule.create(TupleTableAtom.rdf(a, IRI.RDF_TYPE, RSA.Named))
+    )
+
+  val rolesAdditionalRules: List[Rule] = {
+    // Given a role (predicate) compute additional logic rules
+    def additional(pred: String): Seq[Rule] = {
+      val varX = Variable.create("X")
+      val varY = Variable.create("Y")
+      for (
+        (hSuffix, bSuffix) <- List(
+          (Empty, Forward),
+          (Empty, Backward),
+          (Inverse, Forward + Inverse),
+          (Inverse, Backward + Inverse),
+          (Backward + Inverse, Forward),
+          (Forward + Inverse, Backward),
+          (Backward, Forward + Inverse),
+          (Forward, Backward + Inverse)
+        )
+      )
+        yield Rule.create(
+          TupleTableAtom.rdf(varX, pred :: hSuffix, varY),
+          TupleTableAtom.rdf(varX, pred :: bSuffix, varY)
+        )
+    }
+    // Compute additional rules per role
+    ontology.roles
+      .collect { case prop: OWLObjectProperty => prop }
+      .map(_.getIRI.getIRIString)
+      .flatMap(additional)
+  }
+
+  private lazy val topAxioms: List[Rule] = {
+    val varX = Variable.create("X")
+    val varY = Variable.create("Y")
+    val concepts = ontology.concepts.map(c => {
+      Rule.create(
+        TupleTableAtom.rdf(varX, IRI.RDF_TYPE, IRI.THING),
+        TupleTableAtom.rdf(varX, IRI.RDF_TYPE, c.getIRI)
+      )
+    })
+    val roles = ontology.roles.map(r => {
+      val name = r match {
+        case x: OWLObjectProperty => x.getIRI.getIRIString
+        case x: OWLObjectInverseOf =>
+          x.getInverse.getNamedProperty.getIRI.getIRIString :: Inverse
+      }
+      Rule.create(
+        List(
+          TupleTableAtom.rdf(varX, IRI.RDF_TYPE, IRI.THING),
+          TupleTableAtom.rdf(varY, IRI.RDF_TYPE, IRI.THING)
+        ),
+        List(TupleTableAtom.rdf(varX, name, varY))
+      )
+    })
+    concepts ::: roles
+  }
+
+  private val equalityAxioms: List[Rule] = {
+    val varX = Variable.create("X")
+    val varY = Variable.create("Y")
+    val varZ = Variable.create("Z")
+    List(
+      Rule.create(
+        TupleTableAtom.rdf(varX, RSA.EquivTo, varX),
+        TupleTableAtom.rdf(varX, IRI.RDF_TYPE, IRI.THING)
+      ),
+      Rule.create(
+        TupleTableAtom.rdf(varY, RSA.EquivTo, varX),
+        TupleTableAtom.rdf(varX, RSA.EquivTo, varY)
+      ),
+      Rule.create(
+        TupleTableAtom.rdf(varX, RSA.EquivTo, varZ),
+        TupleTableAtom.rdf(varX, RSA.EquivTo, varY),
+        TupleTableAtom.rdf(varY, RSA.EquivTo, varZ)
+      )
+    )
+  }
+
+  val rules: List[Rule] = {
+    // Compute rules from ontology axioms
+    val rules = ontology.axioms.flatMap(_.accept(RuleGenerator))
+    // Return full set of rules
+    rules ::: rolesAdditionalRules ::: topAxioms ::: equalityAxioms ::: named
+  }
+
+  object RuleGenerator
+      extends RDFoxAxiomConverter(
+        Variable.create("X"),
+        ontology.unsafeRoles,
+        SkolemStrategy.None,
+        Empty
+      ) {
+
+    private def rules1(axiom: OWLSubClassOfAxiom): List[Rule] = {
+      val unfold = ontology.unfold(axiom).toList
+      // Fresh Variables
+      val v0 = RSA.rsa("v0_" ++ RSA.hashed(axiom))
+      val varX = Variable.create("X")
+      // Predicates
+      val atomA: TupleTableAtom = {
+        val cls = axiom.getSubClass.asInstanceOf[OWLClass].getIRI
+        TupleTableAtom.rdf(varX, IRI.RDF_TYPE, cls)
+      }
+      def predIN(t: Term): TupleTableAtom = {
+        TupleTableAtom.rdf(
+          t,
+          RSA.rsa("IN"),
+          RSA.rsa(unfold.hashCode.toString)
+        )
+      }
+      def notIn(t: Term): Negation = Negation.create(predIN(t))
+      val roleRf: TupleTableAtom = {
+        val visitor =
+          new RDFoxPropertyExprConverter(varX, v0, Forward)
+        axiom.getSuperClass
+          .asInstanceOf[OWLObjectSomeValuesFrom]
+          .getProperty
+          .accept(visitor)
+          .head
+      }
+      val atomB: TupleTableAtom = {
+        val cls = axiom.getSuperClass
+          .asInstanceOf[OWLObjectSomeValuesFrom]
+          .getFiller
+          .asInstanceOf[OWLClass]
+          .getIRI
+        TupleTableAtom.rdf(v0, IRI.RDF_TYPE, cls)
+      }
+      // TODO: To be consistent with the specifics of the visitor we are
+      // returning facts as `Rule`s with true body. While this is correct
+      // there is an easier way to import facts into RDFox. Are we able to
+      // do that?
+      val facts = unfold.map(x => Rule.create(predIN(x)))
+      val rules = List(
+        Rule.create(roleRf, atomA, notIn(varX)),
+        Rule.create(atomB, atomA, notIn(varX))
+      )
+      facts ++ rules
+    }
+
+    private def rules2(axiom: OWLSubClassOfAxiom): List[Rule] = {
+      val roleR =
+        axiom.getSuperClass
+          .asInstanceOf[OWLObjectSomeValuesFrom]
+          .getProperty
+      if (ontology.confl(roleR) contains roleR) {
+        // Fresh Variables
+        val v0 = RSA.rsa("v0_" ++ RSA.hashed(axiom))
+        val v1 = RSA.rsa("v1_" ++ RSA.hashed(axiom))
+        val v2 = RSA.rsa("v2_" ++ RSA.hashed(axiom))
+        // Predicates
+        def atomA(t: Term): TupleTableAtom = {
+          val cls = axiom.getSubClass.asInstanceOf[OWLClass].getIRI
+          TupleTableAtom.rdf(t, IRI.RDF_TYPE, cls)
+        }
+        def roleRf(t1: Term, t2: Term): TupleTableAtom = {
+          val visitor =
+            new RDFoxPropertyExprConverter(t1, t2, Forward)
+          roleR.accept(visitor).head
+        }
+        def atomB(t: Term): TupleTableAtom = {
+          val cls = axiom.getSuperClass
+            .asInstanceOf[OWLObjectSomeValuesFrom]
+            .getFiller
+            .asInstanceOf[OWLClass]
+            .getIRI
+          TupleTableAtom.rdf(t, IRI.RDF_TYPE, cls)
+        }
+        //Rules
+        List(
+          Rule.create(roleRf(v0, v1), atomA(v0)),
+          Rule.create(atomB(v1), atomA(v0)),
+          Rule.create(roleRf(v1, v2), atomA(v1)),
+          Rule.create(atomB(v2), atomA(v1))
+        )
+      } else {
+        List()
+      }
+    }
+
+    private def rules3(axiom: OWLSubClassOfAxiom): List[Rule] = {
+      val cycle = ontology.cycle(axiom).toList
+      val roleR =
+        axiom.getSuperClass
+          .asInstanceOf[OWLObjectSomeValuesFrom]
+          .getProperty
+      // Fresh Variables
+      val v1 = RSA.rsa("v1_" ++ RSA.hashed(axiom))
+      // Predicates
+      def atomA(t: Term): TupleTableAtom = {
+        val cls = axiom.getSubClass.asInstanceOf[OWLClass].getIRI
+        TupleTableAtom.rdf(t, IRI.RDF_TYPE, cls)
+      }
+      def roleRf(t: Term): TupleTableAtom = {
+        val visitor =
+          new RDFoxPropertyExprConverter(t, v1, Forward)
+        roleR.accept(visitor).head
+      }
+      val atomB: TupleTableAtom = {
+        val cls = axiom.getSuperClass
+          .asInstanceOf[OWLObjectSomeValuesFrom]
+          .getFiller
+          .asInstanceOf[OWLClass]
+          .getIRI
+        TupleTableAtom.rdf(v1, IRI.RDF_TYPE, cls)
+      }
+      cycle.flatMap { x =>
+        List(
+          Rule.create(roleRf(x), atomA(x)),
+          Rule.create(atomB, atomA(x))
+        )
+      }
+    }
+
+    override def visit(axiom: OWLSubClassOfAxiom): List[Rule] = {
+      if (axiom.isT5) {
+        // TODO: get role in T5 axiom
+        // Assuming one role here
+        val role = axiom.objectPropertyExpressionsInSignature(0)
+        if (ontology.unsafeRoles contains role) {
+          val visitor =
+            new RDFoxAxiomConverter(
+              Variable.create("X"),
+              ontology.unsafeRoles,
+              SkolemStrategy.Standard(axiom.toString),
+              Forward
+            )
+          axiom.accept(visitor)
+        } else {
+          rules1(axiom) ::: rules2(axiom) ::: rules3(axiom)
+        }
+      } else {
+        // Fallback to standard OWL to LP translation
+        super.visit(axiom)
+      }
+    }
+
+    override def visit(axiom: OWLSubObjectPropertyOfAxiom): List[Rule] = {
+      val varX = Variable.create("X")
+      val visitorF = new RDFoxAxiomConverter(
+        varX,
+        ontology.unsafeRoles,
+        SkolemStrategy.None,
+        Forward
+      )
+      val visitorB = new RDFoxAxiomConverter(
+        varX,
+        ontology.unsafeRoles,
+        SkolemStrategy.None,
+        Backward
+      )
+      axiom.accept(visitorB) ::: axiom.accept(visitorF)
+    }
+
+  }
+
+}