W3C

Web Ontology Language (OWL) Test Cases

W3C Working Draft 17 February 2003

This version:
http://www.w3.org/TR/2003/WD-owl-test-20030217/
Latest version:
http://www.w3.org/TR/owl-test/
Previous version:
http://www.w3.org/TR/2002/WD-owl-test-20021024/
Editors:
Jeremy J. Carroll, HP <jjc@hpl.hp.com>
Jos De Roo, AGFA,<jos.deroo@agfa.com>

The tests of this document are also available in these non-normative formats: Zip archive of approved tests, Zip archive of proposed tests, the test web site.


Abstract

This document contains and presents test cases for the Web Ontology Language (OWL) approved by the Web Ontology Working Group. Many of the test cases illustrate the correct usage of the Web Ontology Language (OWL), and the formal meaning of its constructs. Other test cases illustrate the resolution of issues considered by the working group. Conformance for OWL documents and OWL document checkers is specified.

Status of this document

This section describes the status of this document at the time of its publication. ther documents may supersede this document. The latest status of this document series is maintained at the W3C.

This is a Working Draft of "OWL Test Cases" for review by members of the W3C and other interested parties in the general public. The approved test cases in this document represent the consensus of the Web Ontology Working Group as at 30th January 2003. Feedback is particular welcome on the new conformance statements. The test cases described in this document (both approved and proposed) are still in development, and may be updated, replaced, negated or obsoleted at any time. Each test may be edited or have a change of status according to the process specified below. Further tests are being added. An editors' version of this document, with the latest tests, can be found at http://www.w3.org/2002/03owlt/editors-draft/snapshot. Despite this flux, the working group would value implementor feedback on the tests both in this document and those found in the editors' version.

This document is subsidiary to the normative definition of the Web Ontology Language [OWL Abstract Syntax and Semantics]).

Publication as a Working Draft does not imply endorsement by the W3C Membership. This is a draft document and may be updated, replaced or obsoleted by other documents at any time. It is inappropriate to cite this document as other than "work in progress". A list of current W3C Recommendations and other technical documents can be found at http://www.w3.org/TR.

Patent disclosures relevant to this specification may be found on the Working Group's public patent disclosure page.

Comments on this document should be sent to public-webont-comments@w3.org, a mailing list with a public archive. General discussion of related technology is welcome in www-rdf-logic@w3.org (archive).

This document has been produced as part of the W3C Semantic Web Activity (Activity Statement) following the procedures set out for the W3C Process. The document has been written by the Web Ontology Working Group. The goals of the Web Ontology working group are discussed in the Web Ontology Working Group charter.


Table of Contents


1. Introduction

As part of the definition of the Web Ontology Language (OWL) the Web Ontology Working Group provides a set of test cases. This document contains those test cases. They are intended to provide examples for, and clarification of, the normative definition of OWL found in [OWL Abstract Syntax and Semantics] to which this document is subsiduary.

This document describes the various types of test used and the format in which the tests are presented. Alternative formats of the test collection are provided. These are intended to be suitable for use by OWL developers in test harnesses, possibly as part of a test driven development process, such as Extreme Programming [XP]. The format of the Manifest files used as part of these alternative formats is described.

This document describes the process for conflict resolution and errata related to these tests.

In the non-normative appendices, this document also describes the process for creation and approval of these tests.

Further appendices show further proposed tests that are awaiting resolution by the working group.

1.1. Conformance and Scope

Various conformance levels are defined in this document in terms of [OWL Abstract Syntax and Semantics].

However, the test cases do not constitute a conformance test suite for OWL.

The tests illustrate issue resolutions, and illustrate the use and meaning of the terms in the OWL namespace.

There are other miscellaneous tests: some arising in the literature, and in preexisting systems; others intending to show the difficulty of complete implementations of OWL Full.

2. Deliverables (Normative)

The deliverables included as part of the test cases are:

Note: Other files can be found under the top URL of the web-site which are not part of the deliverable.

[[EDITORS' NOTE: Do we need index files for the web site that clarify which parts are part of the deliverable and which are not?]]

2.1. Normative Status

Of the deliverables the only normative tests are those included in this document. All other deliverables, are informative. Moreover, the recommendation document is informative except for the conformance statements, the test data (specified in RDF/XML [RDF/XML Syntax]), and the supporting documentation.

3. Test Types (Normative)

Each test consists of either one or more RDF/XML documents and a Manifest file. Tests of one document indicate some property of that document when viewed as an OWL knowledge base. Tests of two or more documents indicate a relationship between the two documents when viewed as OWL knowledge bases.

The Manifest file is named ManifestNNN.rdf (The NNN is replaced by the test number). It contains metadata (in RDF) indicating the test type, and describing the test.

3.1. Tests for Incorrect Use of OWL Namespace

These tests use one document. It is named badNNN.rdf. This document includes a use of the OWL namespace with a local name that is not defined by the OWL recommendation.

Note: These tests are intended to help migration from DAML+OIL [DAML+OIL], since the local names chosen are defined in the DAML+OIL namespace.

3.2. Entailment Tests

These tests use two documents. One is named premisesNNN.rdf, the other is named conclusionsNNN.rdf. The conclusions are entailed by the premises. Such entailment is defined by the OWL semantics [OWL Abstract Syntax and Semantics], (see also OWL Full entailment).

3.3. Non-Entailment Tests

These tests use two documents. One is named premisesNNN.rdf, the other is named nonconclusionsNNN.rdf. The nonconclusions are not entailed by the premises. Such entailment is defined by the OWL semantics [OWL Abstract Syntax and Semantics], (see also OWL Full entailment).

3.4. True Tests

These tests use one document. It is named conclusionsNNN.rdf. The conclusions follow from the OWL semantics [OWL Abstract Syntax and Semantics]. These tests are a special case of the entailment tests in which the premises are empty.

3.5. OWL for OWL

These tests use one document. It is named conclusionsNNN.rdf. These are a special case of true tests. The conclusions follow from the OWL Full semantics [OWL Abstract Syntax and Semantics]. The tests are intended to illustrate how OWL Full can be used to describe its own properties and classes.

3.6. Consistency Tests

These tests use one document. It is named consistentNNN.rdf. The document is consistent as defined by the OWL Semantics [OWL Abstract Syntax and Semantics], (see also OWL Full consistency).

3.7. Inconsistency Tests

These tests use one document. It is named inconsistentNNN.rdf. The document is not consistent as defined by the OWL semantics [OWL Abstract Syntax and Semantics], (see also OWL Full consistency).

3.8. Import Entailment Tests

These tests use more than two documents. One is named premisesNNN.rdf, another is named conclusionsNNN.rdf, the rest have names beginning supportNNN.rdf. The support documents are in the imports closure of the premises document. The conclusions are entailed by the imports closure of the premises. Such entailment is defined by the OWL semantics [OWL Abstract Syntax and Semantics], (see also OWL Full entailment).

3.9. Import Level Tests

These tests use two documents. One is named importsNNN.rdf, the other is named mainNNN.rdf. These tests indicate the interaction between owl:imports and the sublanguage levels of the main document.

4. Conformance (Normative)

4.1. Document Conformance

4.1.1. Syntactic Conformance

An OWL Full document is an RDF/XML document [RDF/XML Syntax], for which the corresponding RDF graph [RDF Concepts] does not use any URI references starting with the prefix http://www.w3.org/2002/07/owl# except those found in the [RDF Schema for OWL].

An OWL DL document is an OWL Full document such that the imports closure [OWL Abstract Syntax and Semantics] of the corresponding RDF graph [RDF Concepts] is an OWL DL ontology in RDF graph form.

An OWL Lite document is an OWL Full document such that the imports closure [OWL Abstract Syntax and Semantics] of the corresponding RDF graph [RDF Concepts] is an OWL Lite ontology in RDF graph form.

4.1.2. Semantic Conformance

A consistent OWL document is an OWL Full document for which the corresponding RDF graph [RDF Concepts] is consistent according to the [OWL Abstract Syntax and Semantics].

4.2. Document Checker Conformance

This section uses the words MUST, MUST NOT, SHOULD and MAY as in [RFC 2119].

4.2.1. Syntax Checker

An OWL syntax checker takes a document as input, and outputs one word being one of Lite, DL, Full, Other.

The output MUST conform with the following:

Lite
The input document is an OWL Lite document.
DL
The input document is an OWL DL document but not an OWL Lite document.
Full
The input document is an OWL Full document but not an OWL DL document.
Other
The input document is not an OWL Full document.

An OWL syntax checker SHOULD report network errors occurring during the computation of the imports closure.

4.2.2. Consistency Checker

An OWL consistency checker takes a document as input, and outputs one word being Consistent, Inconsistent, or Unknown.

Five different conformance classes of OWL consistency checker are defined.

An OWL consistency checker MUST NOT output Consistent unless the input document is a consistent OWL document.

An OWL consistency checker MUST NOT output Inconsistent unless the input document is not a consistent OWL document.

An OWL consistency checker SHOULD report network errors occurring during the computation of the imports closure.

An OWL Lite consistency checker is an OWL consistency checker that takes an OWL Lite document as input.

An OWL DL consistency checker is an OWL consistency checker that takes an OWL DL document as input.

An OWL Full consistency checker is an OWL consistency checker that takes an OWL Full document as input.

Note: Every OWL Full consistency checker is also an OWL DL consistency checker. Every OWL DL consistency checker is also an OWL Lite consistency checker. Every OWL Lite consistency checker can be trivially transformed into an OWL Full consistency checker.

The different levels are intended to be used to indicate the intended domain of a consistency checker.

Note: there are trivial implementations of these consistency checkers; for example, one which always outputs Unknown.

A complete OWL Lite consistency checker is an OWL consistency checker that takes an OWL Lite document as input, and is logically complete with respect to [OWL Abstract Syntax and Semantics] over the set of all OWL Lite documents.

A complete OWL DL consistency checker is an OWL consistency checker that takes an OWL DL document as input, and is logically complete with respect to [OWL Abstract Syntax and Semantics] over the set of all OWL DL documents.

Note: Complete OWL DL consistency checkers and Complete OWL Lite consistency checkers MAY return Unknown on an OWL DL document or OWL Lite document in the case where a resource limit has been exceeded.

5. Testing an OWL Implementation (Informative)

5.1. OWL Syntax Checkers

An OWL syntax checker when presented with any of the test files must return the indicated result.

5.2. OWL Consistency Checker

An OWL Lite consistency checker, when presented with a file from an OWL Lite consistency test, must output Consistent or Unknown.

An OWL DL consistency checker, when presented with a file from an OWL DL or OWL Lite consistency test, must output Consistent or Unknown.

An OWL Full consistency checker, when presented with a file from an OWL Full, OWL DL or OWL Lite consistency test, must output Consistent or Unknown.

The corresponding inconsistency tests must result in output of Inconsistent or Unknown.

A complete OWL Lite consistency checker or a complete OWL DL consistency checker should not return Unknown on the relevant consistency or inconsistency tests.

6. Manifest Files (Informative)

The Manifest file follows the RDF schema developed for the RDF Test Cases [RDF Test Cases].

This is augmented by a few new properties and types which are declared in the OWL Test Ontology, found at http://www.w3.org/2002/03owlt/testOntology.

Specifically each test has its own Manifest file, and is identified from the URI reference formed from the Manifest file's URL with a fragment test.

The test has one rdf:type explicit, and this is one of:

otest:NotOwlFeatureTest
A test for the incorrect us of OWL namespace.
otest:PositiveEntailmentTest
An entailment test.
otest:NegativeEntailmentTest
A non-entailment test.
otest:TrueTest
A true test.
otest:OWLforOWL
An OWL for OWL test.
otest:ConsistencyTest
A consistency test.
otest:InconsistencyTest
An inconsistency test.
otest:ImportEntailmentTest
An import entailment test.
otest:ImportLevelTest
An import level test.

Where otest is bound to http://www.w3.org/2002/03owlt/testOntology# and rtest is bound to http://www.w3.org/2000/10/rdf-tests/rdfcore/testSchema#.

The name of the original author of the test is shown using a dc:creator property, see [Dublin Core].

A description of the test is given (using XHTML markup [XHTML]) as the value of the rtest:description property.

An issue, if any, from the OWL Issues list [OWL Issues], is the value of a rtest:issue property.

An appropriate language feature, from the OWL namespace, if any, is the value of the otest:feature property.

The input documents with the test data are found as the value of the rtest:inputDocument property or as the value of both the rtest:premiseDocument and the rtest:conclusionDocument. The support files for import entailment tests and import level tests are found as the values of otest:importedPremiseDocument.

The conformance level associated with both files and tests are given with the otest:level property. The value for each document and test is one of otest:Full, otest:DL, otest:Lite or otest:Other (documents only).

7. The OWL Tests (Normative)

7.1. By Function

7.1.1. owl:AllDifferent

FullPositive Entailment Test:001
Description: (informative) <AllDifferent/Manifest001#test>
using AllDifferent to derive differentFrom
N3 format is informative.
FullPremises: <AllDifferent/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/AllDifferent/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/AllDifferent/premises001" >

    <owl:AllDifferent> 
      <owl:distinctMembers rdf:parseType="Collection">
        <first:Person rdf:about="#Fred" />
        <first:Person rdf:about="#Wilma" />
        <first:Person rdf:about="#Barney" />
        <first:Person rdf:about="#Betty" />
      </owl:distinctMembers>
    </owl:AllDifferent> 

</rdf:RDF>
_:a rdf:type owl:AllDifferent .
first:Fred rdf:type first:Person .
first:Wilma rdf:type first:Person .
first:Barney rdf:type first:Person .
first:Betty rdf:type first:Person .
_:b rdf:first first:Betty .
_:b rdf:rest rdf:nil .
_:b rdf:type rdf:List .
_:c rdf:first first:Barney .
_:c rdf:rest _:b .
_:c rdf:type rdf:List .
_:d rdf:first first:Wilma .
_:d rdf:rest _:c .
_:d rdf:type rdf:List .
_:e rdf:first first:Fred .
_:e rdf:rest _:d .
_:e rdf:type rdf:List .
_:a owl:distinctMembers _:e .
FullConclusions: <AllDifferent/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/AllDifferent/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/AllDifferent/conclusions001" >

    <rdf:Description rdf:about="premises001#Barney">
        <owl:differentFrom rdf:resource="premises001#Fred"/>
    </rdf:Description>

</rdf:RDF>
first:Barney owl:differentFrom first:Fred .

7.1.2. owl:FunctionalProperty

FullPositive Entailment Test:001
Description: (informative) <FunctionalProperty/Manifest001#test>
If prop belongs to owl:FunctionalProperty, and subject denotes a resource and has two outgoing prop arcs, then the objects of these arcs have the same denotation.
N3 format is informative.
FullPremises: <FunctionalProperty/premises001>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xmlns:first="http://www.w3.org/2002/03owlt/FunctionalProperty/premises001#" 
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/premises001" >
    <owl:FunctionalProperty rdf:ID="prop"/>
    <rdf:Description rdf:ID="subject">
      <first:prop rdf:resource="#object1" />
      <first:prop rdf:resource="#object2" />
    </rdf:Description>
</rdf:RDF>
first:prop rdf:type owl:FunctionalProperty .
first:subject first:prop first:object1 .
first:subject first:prop first:object2 .
FullConclusions: <FunctionalProperty/conclusions001>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/conclusions001" >
    <rdf:Description rdf:about="premises001#object1">
      <owl:sameIndividualAs rdf:resource="premises001#object2" />
    </rdf:Description>
</rdf:RDF>
first:object1 owl:sameIndividualAs first:object2 .

FullPositive Entailment Test:002
Description: (informative) <FunctionalProperty/Manifest002#test>
If prop belongs to owl:FunctionalProperty, and subject denotes a resource and has two outgoing prop arcs, then the objects of these arcs have the same denotation. Hence an arc originating in object1 can be copied to object2.
N3 format is informative.
Namespaces:
@prefix eg: <http://www.example.org/> .
FullPremises: <FunctionalProperty/premises002>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xmlns:eg ="http://www.example.org/"
  xmlns:first="http://www.w3.org/2002/03owlt/FunctionalProperty/premises002#" 
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/premises002" >
    <owl:FunctionalProperty rdf:ID="prop"/>
    <rdf:Description rdf:ID="subject">
      <first:prop>
          <rdf:Description rdf:ID="object1">
            <eg:prop2>value</eg:prop2>
          </rdf:Description>
      </first:prop>
      <first:prop rdf:resource="#object2" />
    </rdf:Description>
</rdf:RDF>
first:prop rdf:type owl:FunctionalProperty .
first:object1 eg:prop2 "value" .
first:subject first:prop first:object1 .
first:subject first:prop first:object2 .
FullConclusions: <FunctionalProperty/conclusions002>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:eg ="http://www.example.org/"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/conclusions002" >
    <rdf:Description rdf:about="premises002#object2" >
        <eg:prop2>value</eg:prop2>
    </rdf:Description>
</rdf:RDF>
first:object2 eg:prop2 "value" .

FullPositive Entailment Test:003
Description: (informative) <FunctionalProperty/Manifest003#test>
If prop is an owl:FunctionalProperty, then its inverse is an owl:InverseFunctionalProperty.
N3 format is informative.
FullPremises: <FunctionalProperty/premises003>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/premises003" >
    <owl:FunctionalProperty rdf:ID="prop">
      <owl:inverseOf rdf:resource="#inv"/>
    </owl:FunctionalProperty>
</rdf:RDF>
first:prop rdf:type owl:FunctionalProperty .
first:prop owl:inverseOf first:inv .
FullConclusions: <FunctionalProperty/conclusions003>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/conclusions003" >
    <owl:InverseFunctionalProperty rdf:about="premises003#inv"/>
</rdf:RDF>
first:inv rdf:type owl:InverseFunctionalProperty .

FullPositive Entailment Test:004
Description: (informative) <FunctionalProperty/Manifest004#test>
If the range of prop is a singleton set then it is necessarily functional, (i.e. every member of its domain has a single value) and so it is an owl:FunctionalProperty.
N3 format is informative.
FullPremises: <FunctionalProperty/premises004>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"  
  xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/premises004" >
    <owl:ObjectProperty rdf:ID="prop">
      <rdfs:range rdf:resource="#Singleton"/>
    </owl:ObjectProperty>
    <rdfs:Class rdf:ID="Singleton">
      <owl:oneOf rdf:parseType="Collection">
          <rdf:Description/>
      </owl:oneOf>
    </rdfs:Class>
</rdf:RDF>
first:prop rdf:type owl:ObjectProperty .
first:prop rdfs:range first:Singleton .
first:Singleton rdf:type rdfs:Class .
_:a rdf:first _:b .
_:a rdf:rest rdf:nil .
_:a rdf:type rdf:List .
first:Singleton owl:oneOf _:a .
FullConclusions: <FunctionalProperty/conclusions004>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/FunctionalProperty/conclusions004" >
    <owl:FunctionalProperty rdf:about="premises004#prop"/>
</rdf:RDF>
first:prop rdf:type owl:FunctionalProperty .

7.1.3. owl:InverseFunctionalProperty

FullPositive Entailment Test:001
Description: (informative) <InverseFunctionalProperty/Manifest001#test>
If prop belongs to owl:InverseFunctionalProperty, and object denotes a resource and has two incoming prop arcs, then the subjects of these arcs have the same denotation.
N3 format is informative.
FullPremises: <InverseFunctionalProperty/premises001>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xmlns:first="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises001#" 
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises001" >
    <owl:InverseFunctionalProperty rdf:ID="prop"/>
    <rdf:Description rdf:ID="subject1">
      <first:prop rdf:resource="#object" />
    </rdf:Description>
    <rdf:Description rdf:ID="subject2">
      <first:prop rdf:resource="#object" />
    </rdf:Description>
</rdf:RDF>
first:prop rdf:type owl:InverseFunctionalProperty .
first:subject1 first:prop first:object .
first:subject2 first:prop first:object .
FullConclusions: <InverseFunctionalProperty/conclusions001>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/conclusions001" >
    <rdf:Description rdf:about="premises001#subject1">
      <owl:sameIndividualAs rdf:resource="premises001#subject2" />
    </rdf:Description>
</rdf:RDF>
first:subject1 owl:sameIndividualAs first:subject2 .

FullPositive Entailment Test:002
Description: (informative) <InverseFunctionalProperty/Manifest002#test>
If prop belongs to owl:InverseFunctionalProperty, and object denotes a resource and has two incoming prop arcs, then the subjects of these arcs have the same denotation. Hence an arc originating in subject1 can be copied to subject2.
N3 format is informative.
Namespaces:
@prefix eg: <http://www.example.org/> .
FullPremises: <InverseFunctionalProperty/premises002>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xmlns:eg ="http://www.example.org/"
  xmlns:first="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises002#" 
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises002" >
    <owl:InverseFunctionalProperty rdf:ID="prop"/>
    <rdf:Description rdf:ID="subject1" >
      <first:prop rdf:resource="#object" />
      <eg:prop2>value</eg:prop2>
    </rdf:Description>
    <rdf:Description rdf:ID="subject2" >
      <first:prop rdf:resource="#object" />
    </rdf:Description>
</rdf:RDF>
first:prop rdf:type owl:InverseFunctionalProperty .
first:subject1 first:prop first:object .
first:subject1 eg:prop2 "value" .
first:subject2 first:prop first:object .
FullConclusions: <InverseFunctionalProperty/conclusions002>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:eg ="http://www.example.org/"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/conclusions002" >
    <rdf:Description rdf:about="premises002#subject2" >
      <eg:prop2>value</eg:prop2>
    </rdf:Description>
</rdf:RDF>
first:subject2 eg:prop2 "value" .

FullPositive Entailment Test:003
Description: (informative) <InverseFunctionalProperty/Manifest003#test>
If prop is an owl:InverseFunctionalProperty, then its inverse is an owl:FunctionalProperty.
N3 format is informative.
FullPremises: <InverseFunctionalProperty/premises003>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises003" >
    <owl:InverseFunctionalProperty rdf:ID="prop">
      <owl:inverseOf rdf:resource="#inv"/>
    </owl:InverseFunctionalProperty>
</rdf:RDF>
first:prop rdf:type owl:InverseFunctionalProperty .
first:prop owl:inverseOf first:inv .
FullConclusions: <InverseFunctionalProperty/conclusions003>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/conclusions003" >
    <owl:FunctionalProperty rdf:about="premises003#inv"/>
</rdf:RDF>
first:inv rdf:type owl:FunctionalProperty .

FullPositive Entailment Test:004
Description: (informative) <InverseFunctionalProperty/Manifest004#test>
If the domain of prop is a singleton set then it is necessarily inverse functional, (i.e. every member of its range is the value of a single item) so it is an owl:InverseFunctionalProperty.
N3 format is informative.
FullPremises: <InverseFunctionalProperty/premises004>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"  
  xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/premises004" >
    <owl:ObjectProperty rdf:ID="prop">
      <rdfs:domain rdf:resource="#Singleton"/>
    </owl:ObjectProperty>
    <rdfs:Class rdf:ID="Singleton">
      <owl:oneOf rdf:parseType="Collection">
          <rdf:Description/>
      </owl:oneOf>
    </rdfs:Class>
</rdf:RDF>
first:prop rdf:type owl:ObjectProperty .
first:prop rdfs:domain first:Singleton .
first:Singleton rdf:type rdfs:Class .
_:a rdf:first _:b .
_:a rdf:rest rdf:nil .
_:a rdf:type rdf:List .
first:Singleton owl:oneOf _:a .
FullConclusions: <InverseFunctionalProperty/conclusions004>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  xmlns:owl ="http://www.w3.org/2002/07/owl#"
  xml:base="http://www.w3.org/2002/03owlt/InverseFunctionalProperty/conclusions004" >
    <owl:InverseFunctionalProperty rdf:about="premises004#prop"/>
</rdf:RDF>
first:prop rdf:type owl:InverseFunctionalProperty .

7.1.4. owl:Nothing

FullInconsistent document.001
Description: (informative) <Nothing/Manifest001#test>
The triple asserts something of type Nothing, however that is the empty class.
N3 format is informative.
FullInconsistent: <Nothing/inconsistent001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#">

  <owl:Nothing/>
</rdf:RDF>
_:a rdf:type owl:Nothing .

FullPositive Entailment Test:002
Description: (informative) <Nothing/Manifest002#test>
There is one empty owl:Class, and it is often called Nothing.
N3 format is informative.
FullPremises: <Nothing/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    >


</rdf:RDF>
FullConclusions: <Nothing/conclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#">

   <owl:Class>
      <owl:oneOf rdf:parseType="Collection"/>
      <owl:sameClassAs  rdf:resource="http://www.w3.org/2002/07/owl#Nothing" />
   </owl:Class>

</rdf:RDF>
_:a rdf:type owl:Class .
_:a owl:oneOf rdf:nil .
_:a owl:sameClassAs owl:Nothing .

7.1.5. owl:SymmetricProperty

FullPositive Entailment Test:001
Description: (informative) <SymmetricProperty/Manifest001#test>
A simple illustration of symmetric properties.
N3 format is informative.
FullPremises: <SymmetricProperty/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/SymmetricProperty/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/SymmetricProperty/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/SymmetricProperty/premises001" >

    <rdf:Description rdf:about="premises001#Ghent">
        <first:path rdf:resource="premises001#Antwerp"/>
    </rdf:Description>

    <owl:SymmetricProperty rdf:about="premises001#path"/>

</rdf:RDF>
first:Ghent first:path first:Antwerp .
first:path rdf:type owl:SymmetricProperty .
FullConclusions: <SymmetricProperty/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/SymmetricProperty/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/SymmetricProperty/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/SymmetricProperty/conclusions001" >

    <rdf:Description rdf:about="premises001#Antwerp">
        <first:path rdf:resource="premises001#Ghent"/>
    </rdf:Description>

</rdf:RDF>
first:Antwerp first:path first:Ghent .

7.1.6. owl:TransitiveProperty

FullPositive Entailment Test:001
Description: (informative) <TransitiveProperty/Manifest001#test>
A simple illustration of transitivity.
N3 format is informative.
FullPremises: <TransitiveProperty/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/TransitiveProperty/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/TransitiveProperty/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/TransitiveProperty/premises001" >

    <rdf:Description rdf:about="premises001#Antwerp">
        <first:path rdf:resource="premises001#Amsterdam"/>
    </rdf:Description>

    <rdf:Description rdf:about="premises001#Ghent">
        <first:path rdf:resource="premises001#Antwerp"/>
    </rdf:Description>

    <owl:TransitiveProperty rdf:about="premises001#path"/>

</rdf:RDF>
first:Antwerp first:path first:Amsterdam .
first:Ghent first:path first:Antwerp .
first:path rdf:type owl:TransitiveProperty .
FullConclusions: <TransitiveProperty/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/TransitiveProperty/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/TransitiveProperty/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/TransitiveProperty/conclusions001" >

    <rdf:Description rdf:about="premises001#Ghent">
        <first:path rdf:resource="premises001#Amsterdam"/>
    </rdf:Description>

</rdf:RDF>
first:Ghent first:path first:Amsterdam .

7.1.7. owl:allValuesFrom

LitePositive Entailment Test:001
Description: (informative) <allValuesFrom/Manifest001#test>
A simple example.
N3 format is informative.
LitePremises: <allValuesFrom/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/allValuesFrom/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/allValuesFrom/premises001" >
    <owl:Class rdf:ID="r">
      <rdfs:subClassOf>
        <owl:Restriction>
            <owl:onProperty rdf:resource="#p"/>
            <owl:allValuesFrom rdf:resource="#c"/>
        </owl:Restriction>
      </rdfs:subClassOf>
    </owl:Class>
    <owl:ObjectProperty rdf:ID="p"/>
    <owl:Class rdf:ID="c"/>
    <first:r rdf:ID="i">
       <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Thing"/>
       <first:p>
         <owl:Thing rdf:ID="o" />
       </first:p>
    </first:r>
</rdf:RDF>
first:r rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:allValuesFrom first:c .
first:r rdfs:subClassOf _:a .
first:p rdf:type owl:ObjectProperty .
first:c rdf:type owl:Class .
first:i rdf:type first:r .
first:i rdf:type owl:Thing .
first:o rdf:type owl:Thing .
first:i first:p first:o .
LiteConclusions: <allValuesFrom/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:first="http://www.w3.org/2002/03owlt/allValuesFrom/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/allValuesFrom/conclusions001" >
    <first:c rdf:about="premises001#o">
       <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Thing"/>
    </first:c>
</rdf:RDF>
first:o rdf:type first:c .
first:o rdf:type owl:Thing .

LiteNegative Entailment Test:002
Description: (informative) <allValuesFrom/Manifest002#test>
See allValuesFrom.
N3 format is informative.
LitePremises: <allValuesFrom/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/allValuesFrom/premises002#"
    xml:base="http://www.w3.org/2002/03owlt/allValuesFrom/premises002" >
    <owl:Class rdf:ID="r">
      <rdfs:subClassOf>
        <owl:Restriction>
            <owl:onProperty rdf:resource="#p"/>
            <owl:allValuesFrom rdf:resource="#c"/>
        </owl:Restriction>
      </rdfs:subClassOf>
    </owl:Class>
    <owl:ObjectProperty rdf:ID="p"/>

    <owl:Class rdf:ID="c"/>
    <first:r rdf:ID="i">
      <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Thing"/>
    </first:r>
</rdf:RDF>
first:r rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:allValuesFrom first:c .
first:r rdfs:subClassOf _:a .
first:p rdf:type owl:ObjectProperty .
first:c rdf:type owl:Class .
first:i rdf:type first:r .
first:i rdf:type owl:Thing .
LiteConclusions: <allValuesFrom/nonconclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/allValuesFrom/premises002#"
    xmlns:second="http://www.w3.org/2002/03owlt/allValuesFrom/nonconclusions002#"
    xml:base="http://www.w3.org/2002/03owlt/allValuesFrom/nonconclusions002" >
    <owl:Thing rdf:about="premises002#i">
        <first:p>
           <first:c rdf:nodeID="o" />
         </first:p>
    </owl:Thing>
    <owl:Thing rdf:nodeID="o" />
</rdf:RDF>
first:i rdf:type owl:Thing .
_:a rdf:type first:c .
first:i first:p _:a .
_:a rdf:type owl:Thing .

7.1.8. owl:cardinality

LitePositive Entailment Test:001
Description: (informative) <cardinality/Manifest001#test>
An owl:cardinality constraint is simply shorthand for a pair of owl:minCardinality and owl:maxCardinality constraints.
N3 format is informative.
LitePremises: <cardinality/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/premises001" >
    <owl:Class rdf:ID="c">
      <rdfs:subClassOf>
          <rdf:Description>
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="#p"/>
                   <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >1</owl:cardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </rdf:Description>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:ID="p"/>
</rdf:RDF>
first:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:cardinality "1"^^xsd:nonNegativeInteger  .
_:b rdf:first _:a .
_:b rdf:rest rdf:nil .
_:b rdf:type rdf:List .
_:c owl:intersectionOf _:b .
first:c rdfs:subClassOf _:c .
first:p rdf:type owl:ObjectProperty .
LiteConclusions: <cardinality/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/conclusions001" >
    <owl:Class rdf:about="premises001#c">
      <rdfs:subClassOf>
          <rdf:Description>
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="premises001#p"/>
                   <owl:maxCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >1</owl:maxCardinality>
                </owl:Restriction>
                <owl:Restriction>
                   <owl:onProperty rdf:resource="premises001#p"/>
                   <owl:minCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >1</owl:minCardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </rdf:Description>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:about="premises001#p"/>
</rdf:RDF>
first:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:maxCardinality "1"^^xsd:nonNegativeInteger  .
_:b rdf:type owl:Restriction .
_:b owl:onProperty first:p .
_:b owl:minCardinality "1"^^xsd:nonNegativeInteger  .
_:c rdf:first _:b .
_:c rdf:rest rdf:nil .
_:c rdf:type rdf:List .
_:d rdf:first _:a .
_:d rdf:rest _:c .
_:d rdf:type rdf:List .
_:e owl:intersectionOf _:d .
first:c rdfs:subClassOf _:e .
first:p rdf:type owl:ObjectProperty .

LitePositive Entailment Test:002
Description: (informative) <cardinality/Manifest002#test>
An owl:cardinality constraint is simply shorthand for a pair of owl:minCardinality and owl:maxCardinality constraints.
N3 format is informative.
LitePremises: <cardinality/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/premises002" >    
    <owl:Class rdf:about="conclusions002#c">
      <rdfs:subClassOf>
          <rdf:Description>
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="conclusions002#p"/>
                   <owl:maxCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >1</owl:maxCardinality>
                </owl:Restriction>
                <owl:Restriction>
                   <owl:onProperty rdf:resource="conclusions002#p"/>
                   <owl:minCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >1</owl:minCardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </rdf:Description>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:about="conclusions002#p"/>
</rdf:RDF>
second:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty second:p .
_:a owl:maxCardinality "1"^^xsd:nonNegativeInteger  .
_:b rdf:type owl:Restriction .
_:b owl:onProperty second:p .
_:b owl:minCardinality "1"^^xsd:nonNegativeInteger  .
_:c rdf:first _:b .
_:c rdf:rest rdf:nil .
_:c rdf:type rdf:List .
_:d rdf:first _:a .
_:d rdf:rest _:c .
_:d rdf:type rdf:List .
_:e owl:intersectionOf _:d .
second:c rdfs:subClassOf _:e .
second:p rdf:type owl:ObjectProperty .
LiteConclusions: <cardinality/conclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/conclusions002" >
    <owl:Class rdf:ID="c">
      <rdfs:subClassOf>
          <rdf:Description>
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="#p"/>
                   <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >1</owl:cardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </rdf:Description>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:ID="p"/>
</rdf:RDF>
second:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty second:p .
_:a owl:cardinality "1"^^xsd:nonNegativeInteger  .
_:b rdf:first _:a .
_:b rdf:rest rdf:nil .
_:b rdf:type rdf:List .
_:c owl:intersectionOf _:b .
second:c rdfs:subClassOf _:c .
second:p rdf:type owl:ObjectProperty .

DLPositive Entailment Test:003
Description: (informative) <cardinality/Manifest003#test>
An owl:cardinality constraint is simply shorthand for a pair of owl:minCardinality and owl:maxCardinality constraints.
N3 format is informative.
DLPremises: <cardinality/premises003>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/premises003" >
    <owl:Class rdf:ID="c">
      <rdfs:subClassOf>
          <rdf:Description>
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="#p"/>
                   <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >2</owl:cardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </rdf:Description>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:ID="p"/>
</rdf:RDF>
first:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:cardinality "2"^^xsd:nonNegativeInteger  .
_:b rdf:first _:a .
_:b rdf:rest rdf:nil .
_:b rdf:type rdf:List .
_:c owl:intersectionOf _:b .
first:c rdfs:subClassOf _:c .
first:p rdf:type owl:ObjectProperty .
DLConclusions: <cardinality/conclusions003>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/conclusions003" >
    <owl:Class rdf:about="premises003#c">
      <rdfs:subClassOf>
          <rdf:Description>
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="premises003#p"/>
                   <owl:maxCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >2</owl:maxCardinality>
                </owl:Restriction>
                <owl:Restriction>
                   <owl:onProperty rdf:resource="premises003#p"/>
                   <owl:minCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >2</owl:minCardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </rdf:Description>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:about="premises003#p"/>
</rdf:RDF>
first:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:maxCardinality "2"^^xsd:nonNegativeInteger  .
_:b rdf:type owl:Restriction .
_:b owl:onProperty first:p .
_:b owl:minCardinality "2"^^xsd:nonNegativeInteger  .
_:c rdf:first _:b .
_:c rdf:rest rdf:nil .
_:c rdf:type rdf:List .
_:d rdf:first _:a .
_:d rdf:rest _:c .
_:d rdf:type rdf:List .
_:e owl:intersectionOf _:d .
first:c rdfs:subClassOf _:e .
first:p rdf:type owl:ObjectProperty .

DLPositive Entailment Test:004
Description: (informative) <cardinality/Manifest004#test>
An owl:cardinality constraint is simply shorthand for a pair of owl:minCardinality and owl:maxCardinality constraints.
N3 format is informative.
DLPremises: <cardinality/premises004>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/premises004" >    
    <owl:Class rdf:about="conclusions004#c">
      <rdfs:subClassOf>
          <rdf:Description>
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="conclusions004#p"/>
                   <owl:maxCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >2</owl:maxCardinality>
                </owl:Restriction>
                <owl:Restriction>
                   <owl:onProperty rdf:resource="conclusions004#p"/>
                   <owl:minCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >2</owl:minCardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </rdf:Description>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:about="conclusions004#p"/>
</rdf:RDF>
second:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty second:p .
_:a owl:maxCardinality "2"^^xsd:nonNegativeInteger  .
_:b rdf:type owl:Restriction .
_:b owl:onProperty second:p .
_:b owl:minCardinality "2"^^xsd:nonNegativeInteger  .
_:c rdf:first _:b .
_:c rdf:rest rdf:nil .
_:c rdf:type rdf:List .
_:d rdf:first _:a .
_:d rdf:rest _:c .
_:d rdf:type rdf:List .
_:e owl:intersectionOf _:d .
second:c rdfs:subClassOf _:e .
second:p rdf:type owl:ObjectProperty .
DLConclusions: <cardinality/conclusions004>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/conclusions004" >
    <owl:Class rdf:ID="c">
      <rdfs:subClassOf>
          <rdf:Description>
             <owl:intersectionOf rdf:parseType="Collection">
                <owl:Restriction>
                   <owl:onProperty rdf:resource="#p"/>
                   <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
                   >2</owl:cardinality>
                </owl:Restriction>
              </owl:intersectionOf>
           </rdf:Description>
       </rdfs:subClassOf>
     </owl:Class>
     <owl:ObjectProperty rdf:ID="p"/>
</rdf:RDF>
second:c rdf:type owl:Class .
_:a rdf:type owl:Restriction .
_:a owl:onProperty second:p .
_:a owl:cardinality "2"^^xsd:nonNegativeInteger  .
_:b rdf:first _:a .
_:b rdf:rest rdf:nil .
_:b rdf:type rdf:List .
_:c owl:intersectionOf _:b .
second:c rdfs:subClassOf _:c .
second:p rdf:type owl:ObjectProperty .

FullPositive Entailment Test:005
Description: (informative) <cardinality/Manifest005#test>
An owl:cardinality constraint is simply shorthand for a pair of owl:minCardinality and owl:maxCardinality constraints.
N3 format is informative.
FullPremises: <cardinality/premises005>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/premises005" >
    <owl:Restriction  rdf:ID="c">
      <owl:onProperty rdf:resource="#p"/>
      <owl:cardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
       >1</owl:cardinality>
    </owl:Restriction>
</rdf:RDF>
first:c rdf:type owl:Restriction .
first:c owl:onProperty first:p .
first:c owl:cardinality "1"^^xsd:nonNegativeInteger  .
FullConclusions: <cardinality/conclusions005>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/cardinality/conclusions005" >
    <rdf:Description rdf:about="premises005#c">
      <owl:intersectionOf rdf:parseType="Collection">
         <owl:Restriction>
            <owl:onProperty rdf:resource="premises005#p"/>
            <owl:maxCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
             >1</owl:maxCardinality>
          </owl:Restriction>
          <owl:Restriction>
          <owl:onProperty rdf:resource="premises005#p"/>
          <owl:minCardinality
 rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger"
           >1</owl:minCardinality>
       </owl:Restriction>
     </owl:intersectionOf>
   </rdf:Description>
</rdf:RDF>
_:a rdf:type owl:Restriction .
_:a owl:onProperty first:p .
_:a owl:maxCardinality "1"^^xsd:nonNegativeInteger  .
_:b rdf:type owl:Restriction .
_:b owl:onProperty first:p .
_:b owl:minCardinality "1"^^xsd:nonNegativeInteger  .
_:c rdf:first _:b .
_:c rdf:rest rdf:nil .
_:c rdf:type rdf:List .
_:d rdf:first _:a .
_:d rdf:rest _:c .
_:d rdf:type rdf:List .
first:c owl:intersectionOf _:d .

7.1.9. owl:complementOf

FullPositive Entailment Test:001
Description: (informative) <complementOf/Manifest001#test>
complementOf is a SymmetricProperty.
N3 format is informative.
FullPremises: <complementOf/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/complementOf/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/complementOf/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/complementOf/premises001" >

    <rdf:Description rdf:about="premises001#A">
        <owl:complementOf rdf:resource="premises001#B"/>
    </rdf:Description>

</rdf:RDF>
first:A owl:complementOf first:B .
FullConclusions: <complementOf/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/complementOf/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/complementOf/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/complementOf/conclusions001" >

    <rdf:Description rdf:about="premises001#B">
        <owl:complementOf rdf:resource="premises001#A"/>
    </rdf:Description>

</rdf:RDF>
first:B owl:complementOf first:A .

7.1.10. owl:differentFrom

FullPositive Entailment Test:001
Description: (informative) <differentFrom/Manifest001#test>
differentFrom is a SymmetricProperty.
N3 format is informative.
FullPremises: <differentFrom/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/differentFrom/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/differentFrom/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/differentFrom/premises001" >

    <rdf:Description rdf:about="premises001#a">
        <owl:differentFrom rdf:resource="premises001#b"/>
    </rdf:Description>

</rdf:RDF>
first:a owl:differentFrom first:b .
FullConclusions: <differentFrom/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/differentFrom/premises001#"
    xmlns:second="http://www.w3.org/2002/03owlt/differentFrom/conclusions001#"
    xml:base="http://www.w3.org/2002/03owlt/differentFrom/conclusions001" >

    <rdf:Description rdf:about="premises001#b">
        <owl:differentFrom rdf:resource="premises001#a"/>
    </rdf:Description>

</rdf:RDF>
first:b owl:differentFrom first:a .

FullPositive Entailment Test:002
Description: (informative) <differentFrom/Manifest002#test>
using distinctMembers to derive differentFrom
N3 format is informative.
FullPremises: <differentFrom/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/differentFrom/premises002#"
    xml:base="http://www.w3.org/2002/03owlt/differentFrom/premises002" >

    <owl:AllDifferent> 
      <owl:distinctMembers rdf:parseType="Collection">
        <first:Person rdf:about="#Fred" />
        <first:Person rdf:about="#Wilma" />
        <first:Person rdf:about="#Barney" />
        <first:Person rdf:about="#Betty" />
      </owl:distinctMembers>
    </owl:AllDifferent> 

</rdf:RDF>
_:a rdf:type owl:AllDifferent .
first:Fred rdf:type first:Person .
first:Wilma rdf:type first:Person .
first:Barney rdf:type first:Person .
first:Betty rdf:type first:Person .
_:b rdf:first first:Betty .
_:b rdf:rest rdf:nil .
_:b rdf:type rdf:List .
_:c rdf:first first:Barney .
_:c rdf:rest _:b .
_:c rdf:type rdf:List .
_:d rdf:first first:Wilma .
_:d rdf:rest _:c .
_:d rdf:type rdf:List .
_:e rdf:first first:Fred .
_:e rdf:rest _:d .
_:e rdf:type rdf:List .
_:a owl:distinctMembers _:e .
FullConclusions: <differentFrom/conclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/differentFrom/premises002#"
    xml:base="http://www.w3.org/2002/03owlt/differentFrom/conclusions002" >

    <rdf:Description rdf:about="premises002#Barney">
        <owl:differentFrom rdf:resource="premises002#Wilma"/>
    </rdf:Description>

</rdf:RDF>
first:Barney owl:differentFrom first:Wilma .

7.1.11. owl:disjointWith

DLPositive Entailment Test:001
Description: (informative) <disjointWith/Manifest001#test>
Disjoint classes have different members.
N3 format is informative.
DLPremises: <disjointWith/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:first="http://www.w3.org/2002/03owlt/disjointWith/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/disjointWith/premises001" >
   <owl:Class rdf:ID="A">
      <owl:disjointWith>
           <owl:Class rdf:ID="B"/>
      </owl:disjointWith>
   </owl:Class>
   <first:A rdf:ID="a"/>
   <owl:Thing rdf:about="#a"/>
   <first:B rdf:ID="b"/>
   <owl:Thing rdf:about="#b"/>
</rdf:RDF>
first:A rdf:type owl:Class .
first:B rdf:type owl:Class .
first:A owl:disjointWith first:B .
first:a rdf:type first:A .
first:a rdf:type owl:Thing .
first:b rdf:type first:B .
first:b rdf:type owl:Thing .
DLConclusions: <disjointWith/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/disjointWith/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/disjointWith/conclusions001" >
    <owl:Thing rdf:about="premises001#a">
       <owl:differentFrom>
          <owl:Thing rdf:about="premises001#b"/>
       </owl:differentFrom>
    </owl:Thing>
</rdf:RDF>
first:a rdf:type owl:Thing .
first:b rdf:type owl:Thing .
first:a owl:differentFrom first:b .

FullPositive Entailment Test:002
Description: (informative) <disjointWith/Manifest002#test>
Disjoint classes have different members; OWL Full.
N3 format is informative.
FullPremises: <disjointWith/premises002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/disjointWith/premises002#"
    xml:base="http://www.w3.org/2002/03owlt/disjointWith/premises002" >

   <rdf:Description rdf:ID="A">
      <owl:disjointWith>
           <rdf:Description rdf:ID="B"/>
      </owl:disjointWith>
   </rdf:Description>
   <first:A rdf:ID="a"/>
   <first:B rdf:ID="b"/>

</rdf:RDF>
first:A owl:disjointWith first:B .
first:a rdf:type first:A .
first:b rdf:type first:B .
FullConclusions: <disjointWith/conclusions002>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xml:base="http://www.w3.org/2002/03owlt/disjointWith/conclusions002" >
    <rdf:Description rdf:about="premises002#a">
       <owl:differentFrom rdf:resource="premises002#b"/>
    </rdf:Description>
</rdf:RDF>
first:a owl:differentFrom first:b .

7.1.12. owl:distinctMembers

FullPositive Entailment Test:001
Description: (informative) <distinctMembers/Manifest001#test>
using distinctMembers to derive differentFrom
N3 format is informative.
FullPremises: <distinctMembers/premises001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/distinctMembers/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/distinctMembers/premises001" >

    <owl:AllDifferent> 
      <owl:distinctMembers rdf:parseType="Collection">
        <first:Person rdf:about="#Fred" />
        <first:Person rdf:about="#Wilma" />
        <first:Person rdf:about="#Barney" />
        <first:Person rdf:about="#Betty" />
      </owl:distinctMembers>
    </owl:AllDifferent> 

</rdf:RDF>
_:a rdf:type owl:AllDifferent .
first:Fred rdf:type first:Person .
first:Wilma rdf:type first:Person .
first:Barney rdf:type first:Person .
first:Betty rdf:type first:Person .
_:b rdf:first first:Betty .
_:b rdf:rest rdf:nil .
_:b rdf:type rdf:List .
_:c rdf:first first:Barney .
_:c rdf:rest _:b .
_:c rdf:type rdf:List .
_:d rdf:first first:Wilma .
_:d rdf:rest _:c .
_:d rdf:type rdf:List .
_:e rdf:first first:Fred .
_:e rdf:rest _:d .
_:e rdf:type rdf:List .
_:a owl:distinctMembers _:e .
FullConclusions: <distinctMembers/conclusions001>
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:first="http://www.w3.org/2002/03owlt/distinctMembers/premises001#"
    xml:base="http://www.w3.org/2002/03owlt/distinctMembers/conclusions001" >

    <rdf:Description rdf:about="premises001#Fred">
        <owl:differentFrom rdf:resource="premises001#Barney"/>
    </rdf:Description>

</rdf:RDF>
first:Fred owl:differentFrom first:Barney .

7.1.13. owl:imports

FullImport Entailment Test:001
Description: (informative) <imports/Manifest001#test>
If a document imports another document, then it entails anything that is entailed by the conjunction of the two documents.
N3 format is informative.
Namespaces:
@prefix ont: <http://www.w3.org/2002/03owlt/imports/support001-A#> .
Fullhttp://www.w3.org/2002/03owlt/imports/premises001 <imports/premises001>
<rdf:RDF
    xmlns:rdf='http://www.w3.org/1999/02/22-rdf-syntax-ns#'
    xmlns:rdfs='http://www.w3.org/2000/01/rdf-schema#'
    xmlns:owl='http://www.w3.org/2002/07/owl#'
    xmlns:ont='http://www.w3.org/2002/03owlt/imports/support001-A#'
    xml:base='http://www.w3.org/2002/03owlt/imports/premises001' >

    <rdf:Description rdf:about=''>
        <owl:imports rdf:resource='http://www.w3.org/2002/03owlt/imports/support001-A'/>
    </rdf:Description>

    <ont:Man rdf:about='http://example.org/data#Socrates'/>

</rdf:RDF>
<imports/premises001> owl:imports <imports/support001-A> .
<http://example.org/data#Socrates> rdf:type ont:Man .
LiteImported Premises <imports/support001-A>
<rdf:RDF
    xmlns:rdf='http://www.w3.org/1999/02/22-rdf-syntax-ns#'
    xmlns:rdfs='http://www.w3.org/2000/01/rdf-schema#'
    xmlns:owl='http://www.w3.org/2002/07/owl#'
    xml:base='http://www.w3.org/2002/03owlt/imports/support001-A' >

    <owl:Ontology rdf:about=''/>

    <owl:Class rdf:ID='Man'>
        <rd