A simple DAML ontology with transitive properties, unique properties and unambigous properties.

<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:daml="http://www.daml.org/2000/10/daml-ont#"
  xmlns:xsd ="http://www.w3.org/2000/10/XMLSchema#"
  xmlns:dex ="http://www.daml.org/2001/03/daml+oil-ex#"
  xmlns:exd ="http://www.daml.org/2001/03/daml+oil-ex-dt#"
  xmlns     ="http://www.daml.org/2001/03/daml+oil-ex#"
>

<daml:Ontology rdf:about="">
  <daml:versionInfo>$Id: daml+oil-ex.daml,v 1.9 2001/05/03 16:38:38 mdean Exp $</daml:versionInfo>
  <rdfs:comment>
    An example ontology, with data types taken from XML Schema
  </rdfs:comment>
  <daml:imports rdf:resource="http://www.daml.org/2000/10/daml-ont"/>
</daml:Ontology>

<daml:Class rdf:ID="Man">
  <rdfs:subClassOf rdf:resource="#Male"/>
</daml:Class>

<daml:Class rdf:ID="Animal">
</daml:subclassOf>
</daml:Class>

<daml:Class rdf:ID="Male">
  <rdfs:subClassOf rdf:resource="#Animal"/>
</daml:Class>

<daml:Class rdf:ID="Female">
  <rdfs:subClassOf rdf:resource="#Animal"/>
</daml:Class>

<daml:Class rdf:ID="Woman">
  <rdfs:subClassOf rdf:resource="#Female"/>
</daml:Class>

<daml:ObjectProperty rdf:ID="hasParent">
  <rdfs:domain rdf:resource="#Animal"/>
  <rdfs:range rdf:resource="#Animal"/>
</daml:ObjectProperty>

"hasMother" is a UniqueProperty,^{PDDL version} it is also the sub property of "hasParent".^{PDDL version}

<daml:UniqueProperty rdf:ID="hasMother">
  <rdfs:subPropertyOf rdf:resource="hasParent"/>
  <rdfs:domain rdf:resource="#Animal"/>
  <rdfs:range rdf:resource="#Female"/>
</daml:UniqueProperty>

"isMother" is the inverse of "hasMother",^{PDDL version} so it is an UnambigousProperty.^{PDDL version}

<daml:UnambigousProperty rdf:ID="isMother">
  <daml:inverseOf rdf:resource="#hasMother"/>
  <rdfs:domain rdf:resource="#Female"/>
  <rdfs:range rdf:resource="#Animal"/>
</daml:UnambigousProperty>

"hasAncestor" is a TransitiveProperty.^{PDDL version}

<daml:TransitiveProperty rdf:ID="hasAnsestor">
  <rdfs:domain rdf:resource="#Animal"/>
  <rdfs:range rdf:resource="#Animal"/>
</daml:TransitiveProperty>

</rdf:RDF>

Translated PDDL version of the above DAML ontology

(define (domain animal-ont)

(:types
Animal - object
Male - Animal
Female - Animal
Man - Male
Woman - Female

(:predicates
(hasParent ?an1 - Animal ?an2 - Animal)
(hasMother ?an1 - Animal ?fe2 - Female)
(hasAncestor ?an1 - Animal ?an2 - Animal)
(isMother ?fe1 - Female ?an2 - Animal)
)
)

(:facts
(forall (?ob1 - object ?ob2 - object)
(if (hasMother ?ob1 ?ob2) (hasParent ?ob1 ?ob2))) ^{daml:subPropertyOf}

(forall (?ob1 - object ?ob21 - object ?ob22 - object)
(if (and (hasMother ?ob1 ?ob21) (hasMother ?ob1 ?ob22)) (= ?ob21 ?ob22))) ^{daml:UniqueProperty}

(forall (?ob1 - object ?ob2 - object ?ob3 - object)
(if (and (hasAncestor ?ob1 ?ob2) (hasAncestor ?ob2 ?ob3)) (hasAncestor ?ob1 ?ob3))) ^{daml:TransitiveProperty}

(forall (?ob11 - object ?ob12 - object ?ob2 - object)
(if (and (isMother ?ob11 ?ob2) (isMother ?ob12 ?ob2)) (= ?ob11 ?ob12))) ^{daml:UnambigousProperty}

(forall (?ob1 - object ?ob2 - object)
(if (isMother ?ob1 ?ob2) (hasMother ?ob2 ?ob1))) ^{daml:inverseOf}

)
)