RDFS-Plus Inferencing

AnzoGraph DB includes an inference engine that can create new relationships based on the vocabularies or ontologies in the existing data.

The following example from the W3C Semantic Web Inference documentation illustrates the inference concept:

A data set might include the relationship Flipper isA Dolphin. An ontology might declare that "every Dolphin is also a Mammal." An inference program that understands the notion of "X is also Y" adds the statement Flipper isA Mammal to the set of relationships even though it was not specified in the original data.

When AnzoGraph DB creates inferences, it scans the specified graph for any of the RDFS-plus and supported OWL 2 RL ontologies and generates new triples according to the W3C OWL 2 RL rules, or rules specified with the optional WITH RULES clause. This topic provides instructions for generating inferences with AnzoGraph DB and describes the supported inference vocabularies.

Generating Inferences

AnzoGraph DB generates inferences as a batch command. Run the following command to generate inferences from one or more existing graphs:

CREATE INFERENCES FROM source_graph1 [ source_graph2 ... ] INTO GRAPH target_graph 
  [ WITH RULES 'list_of_rules' ]

Where list_of_rules in the optional WITH RULES clause is any of the following arguments. Specify multiple options in a comma-separated list:

all Run all rules.
rdfsplus Run only the RDFS-plus rules.
rule list List specific rules to run. For a list of available rule names, see Inference Rule Reference below.
-rulename Specify a hyphen (-) in front of a rule name to exclude that rule. For example, -scm-svf2 excludes the scm-svf2 rule.

For example, the following WITH RULES clause runs all of the inference rules except prp-fp and prp-ifp:

... WITH RULES 'all,-prp-fp,-prp-ifp'

When you run the CREATE INFERENCES command, AnzoGraph DB runs rules for each of the RDFS-plus ontologies that it finds in the source graphs, or rules specified with the optional WITH RULES clause, and inserts the inferred triples into the specified target graph.

Certain inference rules are coupled. Specifying either of the rules in the pair automatically runs the coupled rule. The list below describes the paired rules:

  • scm-dom1 and scm-rng1
  • scm-dom2 and scm-rng2
  • prp-inv1 and prp-inv2

In addition, running scm-eqc1 and cax-sco also runs cax-eqc1 and cax-eqc2. And running scm-eqp1 and prp-spo1 also runs prp-eqp1 and prp-eqp2.

Inference Rule Reference

The tables below describe the RDFS-plus rules as well as the additional subset of OWL 2 RL rules that AnzoGraph DB supports.

RDFS-Plus Rules

The tables below define the RDFS-plus inference rules.

Semantics of Class Axioms

Because cax-eqc1 and cax-eqc2 (described in the table below) are implied rules that are coupled with scm-eqc1 and cax-sco, including cax-eqc1 or cax-eqc2 in the WITH RULES clause will result in an invalid inference rule name error. To run the cax-eqc1 and cax-eqc2 rules, specify scm-eqc1 and cax-sco (scm-eqc1,cax-sco) in the WITH RULES clause.

Rule Description IF THEN
cax-eqc1 Two classes are synonymous. T(?c1, owl:equivalentClass, ?c2)
T(?x, rdf:type, ?c1)
T(?x, rdf:type, ?c2)
cax-eqc2 Two classes are synonymous. T(?c1, owl:equivalentClass, ?c2)
T(?x, rdf:type, ?c2)
T(?x, rdf:type, ?c1)
cax-sco Members of a subclass are also members of the superclass. T(?c1, rdfs:subClassOf, ?c2)
T(?x, rdf:type, ?c1)
T(?x, rdf:type, ?c2)

Semantics of Axioms about Properties

Because prp-eqp1 and prp-eqp2 (described in the table below) are implied rules that are coupled with scm-eqp1 and prp-spo1, including prp-eqp1 or prp-eqp2 in the WITH RULES clause will result in an invalid inference rule name error. To run the prp-eqp1 and prp-eqp2 rules, specify scm-eqp1 and prp-spo1 (scm-eqp1,prp-spo1) in the WITH RULES clause.

Rule Description IF THEN
prp-dom Infer the subject's type from the predicate's domain. T(?p, rdfs:domain, ?c)
T(?x, ?p, ?y)
T(?x, rdf:type, ?c)
prp-eqp1 Two properties are synonymous. T(?p1, owl:equivalentProperty, ?p2)
T(?x, ?p1, ?y)
T(?x, ?p2, ?y)
prp-eqp2 Two properties are synonymous. T(?p1, owl:equivalentProperty, ?p2)
T(?x, ?p2, ?y)
T(?x, ?p1, ?y)
prp-fp If predicate p is a functional property, then a subject can be related to only one specific object by p. T(?p, rdf:type, owl:FunctionalProperty)
T(?x, ?p, ?y1)
T(?x, ?p, ?y2)
T(?y1, owl:sameAs, ?y2)
prp-ifp If predicate p is an inverse functional property, then a specific object can be related to only one subject by p. T(?p, rdf:type, owl:InverseFunctionalProperty)
T(?x1, ?p, ?y)
T(?x2, ?p, ?y)
T(?x1, owl:sameAs, ?x2)
prp-inv1 Two properties are the inverse of each other. T(?p1, owl:inverseOf, ?p2)
T(?x, ?p1, ?y)
T(?y, ?p2, ?x)
prp-inv2 Two properties are the inverse of each other. T(?p1, owl:inverseOf, ?p2)
T(?x, ?p2, ?y)
T(?y, ?p1, ?x)
prp-rng Infer the object's type from the predicate's range. T(?p, rdfs:range, ?c)
T(?x, ?p, ?y)
T(?y, rdf:type, ?c)
prp-spo1 Relationships that are described by a subproperty also hold for the superproperty. T(?p1, rdfs:subPropertyOf, ?p2)
T(?x, ?p1, ?y)
T(?x, ?p2, ?y)
prp-symp The inverse is true for a property. T(?p, rdf:type, owl:SymmetricProperty)
T(?x, ?p, ?y)
T(?y, ?p, ?x)
prp-trp Chains of relationships collapse into a single relationship. T(?p, rdf:type, owl:TransitiveProperty)
T(?x, ?p, ?y)
T(?y, ?p, ?z)
T(?x, ?p, ?z)

Semantics of Schema Vocabulary

Rule Description IF THEN
scm-cls Every class is its own subclass and equivalent class, and it is a subclass of owl:Thing. T(?c, rdf:type, owl:Class) T(?c, rdfs:subClassOf, ?c)
T(?c, owl:equivalentClass, ?c)
T(?c, rdfs:subClassOf, owl:Thing)
T(owl:Nothing, rdfs:subClassOf, ?c)
scm-dom1 A property with domain c also has domain c's superclasses. T(?p, rdfs:domain, ?c1)
T(?c1, rdfs:subClassOf, ?c2)
T(?p, rdfs:domain, ?c2)
scm-dom2 A subproperty inherits the domains of the superproperties. T(?p2, rdfs:domain, ?c)
T(?p1, rdfs:subPropertyOf, ?p2)
T(?p1, rdfs:domain, ?c)
scm-eqc1 Equivalent classes are subclasses of each other. T(?c1, owl:equivalentClass, ?c2) T(?c1, rdfs:subClassOf, ?c2)
T(?c2, rdfs:subClassOf, ?c1)
scm-eqc2 If two classes are subclasses, they are also equivalent classes. T(?c1, rdfs:subClassOf, ?c2)
T(?c2, rdfs:subClassOf, ?c1)
T(?c1, owl:equivalentClass, ?c2)
scm-eqp1 Equivalent properties are subproperties of each other. T(?p1, owl:equivalentProperty, ?p2) T(?p1, rdfs:subPropertyOf, ?p2)
T(?p2, rdfs:subPropertyOf, ?p1)
scm-eqp2 If two properties are subproperties, they are also equivalent properties. T(?p1, rdfs:subPropertyOf, ?p2)
T(?p2, rdfs:subPropertyOf, ?p1)
T(?p1, owl:equivalentProperty, ?p2)
scm-rng1 A property with range c also has range c's superclasses. T(?p, rdfs:range, ?c1)
T(?c1, rdfs:subClassOf, ?c2)
T(?p, rdfs:range, ?c2)
scm-rng2 A subproperty inherits the ranges of its superproperties. T(?p2, rdfs:range, ?c)
T(?p1, rdfs:subPropertyOf, ?p2)
T(?p1, rdfs:range, ?c)
scm-sco owl:subClassOf relationships are transitive T(?c1, rdfs:subClassOf, ?c2)
T(?c2, rdfs:subClassOf, ?c3)
T(?c1, rdfs:subClassOf, ?c3)
scm-spo owl:subPropertyOf relationships are transitive. T(?p1, rdfs:subPropertyOf, ?p2)
T(?p2, rdfs:subPropertyOf, ?p3)
T(?p1, rdfs:subPropertyOf, ?p3)

The scm-dp and scm-op schema vocabulary rules are not run. Those rules add significant compute overhead but do not result in meaningful inference results.

OWL 2 RL Rules

The tables below define the subset of OWL 2 RL inference rules that are supported.

Semantics of Equality

Rule Description IF THEN
eq-rep-o Describes the replacement property of the owl:sameAs axiom. T(?o, owl:sameAs, ?o')
T(?s, ?p, ?o)
T(?s, ?p, ?o')
eq-rep-p Describes the replacement property of the owl:sameAs axiom. T(?p, owl:sameAs, ?p')
T(?s, ?p, ?o)
T(?s, ?p', ?o)
eq-rep-s Describes the replacement property of the owl:sameAs axiom. T(?s, owl:sameAs, ?s')
T(?s, ?p, ?o)
T(?s', ?p, ?o)
eq-sym Describes the symmetric property of the owl:sameAs axiom. T(?x, owl:sameAs, ?y) T(?y, owl:sameAs, ?x)
eq-trans Describes the transitive property of the owl:sameAs axiom. T(?x, owl:sameAs, ?y)
T(?y, owl:sameAs, ?z)
T(?x, owl:sameAs, ?z)

Semantics of Schema Vocabulary

Rule Description IF THEN
scm-svf1 A property restriction c1 is a subclass of c2 if they are both someValuesFrom restrictions on the same property and c1's target class is a subclass of c2's target class. T(?c1, owl:someValuesFrom, ?y1)
T(?c1, owl:onProperty, ?p)
T(?c2, owl:someValuesFrom, ?y2)
T(?c2, owl:onProperty, ?p)
T(?y1, rdfs:subClassOf, ?y2)
T(?c1, rdfs:subClassOf, ?c2)
scm-svf2 A property restriction c1 is a subclass of c2 if they are both someValuesFrom restrictions on the same class where c1's target property is a subproperty of c2's target property. T(?c1, owl:someValuesFrom, ?y)
T(?c1, owl:onProperty, ?p1)
T(?c2, owl:someValuesFrom, ?y)
T(?c2, owl:onProperty, ?p2)
T(?p1, rdfs:subPropertyOf, ?p2)
T(?c1, rdfs:subClassOf, ?c2)
scm-int   T(?c, owl:intersectionOf, ?x)
LIST[?x, ?c1, ..., ?cn]
T(?c, rdfs:subClassOf, ?c1)
T(?c, rdfs:subClassOf, ?c2)
...
T(?c, rdfs:subClassOf, ?cn)

Semantics of Classes

Rule Description IF THEN
cls-svf1 At least one object of a property is a member of the specified class. T(?x, owl:someValuesFrom, ?y)
T(?x, owl:onProperty, ?p)
T(?u, ?p, ?v)
T(?v, rdf:type, ?y)
T(?u, rdf:type, ?x)
cls-int1 An instance belongs to every one of the specified classes. T(?c, owl:intersectionOf, ?x)
LIST[?x, ?c1, ..., ?cn]
T(?y, rdf:type, ?c1)
T(?y, rdf:type, ?c2)
...
T(?y, rdf:type, ?cn)
T(?y, rdf:type, ?c)

Inference Example

The following simple example demonstrates the inferences that AnzoGraph DB generates to infer friendships in the sample Tickit data set. The example uses the following subset of triples, and it describes the friend relationships using the owl:TransitiveProperty vocabulary:

# friends.ttl
PREFIX owl: <http://www.w3.org/2002/07/owl#>
<friend> a owl:TransitiveProperty .
<person1>
rdf:type <person>
;<name> "Rafael Taylor"
;<like> "sports","theatre","classical","vegas","musicals"
;<dislike> "jazz","broadway"
;<friend> <person2>,<person4>
.
<person2>
rdf:type <person>
;<name> "Vladimir Humphrey"
;<like> "jazz","classical","vegas","musicals"
;<dislike> "broadway"
;<friend> <person3>
.
<person3>
rdf:type <person>
;<name> "Lars Ratliff"
;<like> "sports","rock","musicals"
;<dislike> "theatre","jazz","opera"
;<friend> <person1>
.
<person4>
rdf:type <person>
;<name> "Barry Roy"
;<like> "theatre"
;<dislike> "sports","jazz","musicals"
;<friend> <person5>
.
<person5>
rdf:type <person>
;<name> "Reagan Hodge"
;<like> "concerts","rock","vegas","musicals"
;<dislike> "jazz","broadway"
;<friend> <person1>
.

Loading friends.ttl into a graph named friends and querying the new graph for a list of friendships produces the following results. The query returns 6 friendships:

SELECT *
FROM <friends>
WHERE { ?person <friend> ?friend . }
ORDER BY ?person
person  | friend
--------+---------
person1 | person4
person1 | person2
person2 | person3
person3 | person1
person4 | person5
person5 | person1
6 rows

The query below generates inferences for the friends graph based on the rules for owl:TransitiveProperty. The query creates the inferences in a graph named more-friends:

CREATE INFERENCES FROM <friends> INTO GRAPH <more-friends>

When the inferencing is complete, the following query returns the friend triples in the more-friends graph. The query filters out triples for which the same person is the subject (?person) and object (?friend):

SELECT *
FROM <more-friends>
WHERE {
  ?person <friend> ?friend.
  FILTER(?person != ?friend).
}
ORDER BY ?person
person  | friend
--------+---------
person1 | person5
person1 | person3
person2 | person5
person2 | person4
person2 | person1
person3 | person5
person3 | person2
person3 | person4
person4 | person2
person4 | person3
person4 | person1
person5 | person2
person5 | person4
person5 | person3
14 rows

Following the OWL 2 RL rules for owl:TransitiveProperty, AnzoGraph DB inferred 8 new friendships from the 6 friendships in the original friend graph.