pOTTR: The Basics of Reasonable Ontology Templates

The Basics of Reasonable Ontology Templates

Learn the basics of OTTR

Authors: Leif Harald Karlsen, Martin G. Skjæveland
Issues: https://gitlab.com/ottr/language/pOTTR/issues

1. Introduction

This primer is a lightweight introduction to the basics concepts of OTTR templates. The fundamentals of OTTR are formally defined in mOTTR [1]. The syntax used in this document is stOTTR [3].

1.1. Prefixes

The following prefixes are used throughout the document, and may be used in the text input areas of the interactive examples without declaration.

@prefix rdf: 	<http://www.w3.org/1999/02/22-rdf-syntax-ns#> . 
@prefix rdfs: 	<http://www.w3.org/2000/01/rdf-schema#> . 
@prefix owl: 	<http://www.w3.org/2002/07/owl#> .
@prefix xsd: 	<http://www.w3.org/2001/XMLSchema#> . 
@prefix foaf: 	<http://xmlns.com/foaf/0.1/> . 
@prefix dbp: 	<http://dbpedia.org/ontology/> . 
@prefix ex: 	<http://example.com/ns#> . 
@prefix ottr: 	<http://ns.ottr.xyz/0.4/> . 
@prefix ax: 	<http://tpl.ottr.xyz/owl/axiom/0.1/> . 
@prefix rstr: 	<http://tpl.ottr.xyz/owl/restriction/0.1/> .

2. Templates and Instances

The core concepts in OTTR are templates and instances of templates.

Here are two instances of the template ex:Person, which is listed below. The first instance specifies the 3 arguments: "Ann", "Strong" and <mailto:[email protected]>:

ex:Person("Ann", "Strong", <mailto:[email protected]>) .
ex:Person("Bob", "Brite", <mailto:[email protected]>) .

A template consists of a signature and a pattern. The signature of template specifies its identifier and its parameters. The pattern contains (other) instances and may use the template's parameters as arguments.

This is the ex:Person template. It specifies 3 parameters, ?firstName, ?lastName and ?email, and contains 3 instances of the ottr:Triple template in its pattern. The arguments of an instance must match the parameters of its template.

ex:Person[ ?firstName, ?lastName, ?email ] :: {
  ottr:Triple (_:person, rdf:type, foaf:Person ),
  ottr:Triple (_:person, foaf:firstName, ?firstName ),
  ottr:Triple (_:person, foaf:lastName, ?lastName ),
  ottr:Triple (_:person, foaf:mbox, ?email )
} .

An instance represents a replica of the template pattern where the template's parameters have been replaced by the arguments of the instance. An instance can be expanded by recursively replacing instances with the pattern they represent.

This is the expansion of the example ex:Person instance when we expand to stOTTR [3] syntax:

@prefix dbp: <http://dbpedia.org/ontology/> .
@prefix ex: <http://example.com/ns#> .
@prefix ottr: <http://ns.ottr.xyz/0.4/> .
@prefix ax: <http://tpl.ottr.xyz/owl/axiom/0.1/> .
@prefix rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix owl: <http://www.w3.org/2002/07/owl#> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .

ottr:Triple(_:blank502, rdf:type, foaf:Person) .

ottr:Triple(_:blank502, foaf:lastName, "Strong") .

ottr:Triple(_:blank502, foaf:firstName, "Ann") .

ottr:Triple(_:blank502, foaf:mbox, <mailto:[email protected]>) .

ottr:Triple(_:blank503, rdf:type, foaf:Person) .

ottr:Triple(_:blank503, foaf:lastName, "Brite") .

ottr:Triple(_:blank503, foaf:firstName, "Bob") .

ottr:Triple(_:blank503, foaf:mbox, <mailto:[email protected]>) .

This is the expansion of the instance when we expand to wOTTR [4] syntax, the RDF serialisation format of OTTR:

PREFIX ex: <http://example.com/ns#>
PREFIX dbp: <http://dbpedia.org/ontology/>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX ottr: <http://ns.ottr.xyz/0.4/>
PREFIX ax: <http://tpl.ottr.xyz/owl/axiom/0.1/>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/>
PREFIX foaf: <http://xmlns.com/foaf/0.1/>

_:b0    rdf:type        foaf:Person;
        foaf:lastName   "Strong";
        foaf:firstName  "Ann";
        foaf:mbox       <mailto:[email protected]> .

_:b1    rdf:type        foaf:Person;
        foaf:lastName   "Brite";
        foaf:firstName  "Bob";
        foaf:mbox       <mailto:[email protected]> .

The expansion is done by our reference implementation Lutra. Lutra has special support for instances of the template ottr:Triple and treats them as regular RDF triples.

2.1. Exercise: Getting familiar with the interactive exercise form

This primer contains interactive exercises where you can test and run your solution directly. Usually each exercise contains one input box for template instances, and one box for templates. When clicking the "Run" button at the bottom, the instances in the instance box are expanded using the templates in the template box, or using templates fetched by their IRI or the templates found in the standard library at http://tpl.ottr.xyz, if these options set to true.

One can also change the what should happen when one clicks "Run" by changing "Action" on the same line as "Run", and change the output format to, e.g., stOTTR.

ex:Person("Ann", "Strong", <mailto:ann.strong@gmail.com>) . ex:Person("Bob", "Brite", <mailto:bob.brite@gmail.com>) .

ex:Person[ ?firstName, ?lastName, ?email ] :: { ottr:Triple (_:person, rdf:type, foaf:Person ), ottr:Triple (_:person, foaf:firstName, ?firstName ), ottr:Triple (_:person, foaf:lastName, ?lastName ), ottr:Triple (_:person, foaf:mbox, ?email ) } .

In this exercise we will get familiar with this setup, so do the following:

Click the "Run" button to expand the instances
Add a few more instances of the ex:Person template in the instance-box and click "Run" to expand them
Do some changes in the pattern of the ex:Person template, e.g., change foaf:lastName to foaf:surname, click "Run" and see the effects of the expansion.
Change the output format to stOTTR and click "Run"

2.2. Exercise: Create a new template

Create a template ex:Organization such that the instance below expands to the following RDF graph:

Note that # can be used to add comments.

PREFIX ex: <http://example.com/ns#>
PREFIX dbp: <http://dbpedia.org/ontology/>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX ottr: <http://ns.ottr.xyz/0.4/>
PREFIX ax: <http://tpl.ottr.xyz/owl/axiom/0.1/>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/>
PREFIX foaf: <http://xmlns.com/foaf/0.1/>

_:b0    rdf:type       foaf:Organization;
        foaf:homepage  <http://uio.no>;
        foaf:age       "208"^^xsd:int;
        foaf:name      "University of Oslo" .

ex:Organization("University of Oslo", "208"^^xsd:int, <http://uio.no>) .

ex:Organization[ , , ] :: { # add instances here } .

Solution

ex:Organization[ ?name, ?age, ?url] :: {
    ottr:Triple(_:org, rdf:type, foaf:Organization),
    ottr:Triple(_:org, foaf:name, ?name),
    ottr:Triple(_:org, foaf:age, ?age),
    ottr:Triple(_:org, foaf:homepage, ?url)
} .

2.3. Base templates

A base template is a template with no pattern.

This is an example of a base template:

ex:MyTriple{?s, ?p, ?o} :: BASE .

The process of expanding instances terminates until all instances are instances of base templates. Any further processing of base template instances must be handled by the implementation. In the current specification and implementation, ottr:Triple is the only such base template; and instances of ottr:Triple represent (regular) RDF triples.

It is possible to specify your own base templates, however we do not yet support specifying how such instances are handled, so an instance of a user defined template will simply be "left as is".

2.4. Exercise: Create a base template

Exercise: Declare the ex:Organization template as a base template, expand and see the results.

ex:Organization[ , , ] :: { } .

Solution

ex:Organisation[?name, ?age, ?homepage] :: BASE .

3. Nesting templates

The pattern of a template can contain any template instances, not just instances of ottr:Triple as we have seen in the examples so far. However, cyclic template definitions are not allowed and will result in an error.

The ability to compose templates from existing templates is a powerful feature of OTTR templates which allows templates to hide the complexity of modelling patterns at different levels of abstraction.

3.1. Exercise: Refactoring

Below is the definition of the template ex:Type. (This templates' parameters are typed—ignore this for now, we will learn what types are in the next section.)

Change the templates in the previous exercises to use this template instead of the ottr:Triple instances with rdf:type as argument.

To see what the ex:Type template expands to, we have provided some example instances below.

ex:Type(ex:Per, foaf:Person) . ex:Type(ex:Kari, foaf:Person) . ex:Type(foaf:Person, rdfs:Class) .

ex:Type[ottr:IRI ?individual, ottr:IRI ?type] :: { ottr:Triple(?individual, rdf:type, ?type) } .

Solution

ex:Organization[?name, ?age, ?url] :: {
    ex:Type(_:org, foaf:Organization),
    ottr:Triple(_:org, foaf:name, ?name),
    ottr:Triple(_:org, foaf:age, ?age),
    ottr:Triple(_:org, foaf:homepage, ?url)
} .

3.2. Exercise

The templates below are ill-defined; why?

ex:A(ex:uri) .

ex:A[?x] :: { ex:B(?x) } . ex:B[?x] :: { ex:C(?x) } . ex:C[?x] :: { ex:A(?x) } .

Solution

The templates are ill-defined because there is a cyclic dependency:

Lutra will print these errors:

[ERROR] Cyclic dependency in template http://example.com/ns#A. The template has a cyclic dependency.

[ERROR] Cyclic dependency in template http://example.com/ns#C. The template has a cyclic dependency.

[ERROR] Cyclic dependency in template http://example.com/ns#B. The template has a cyclic dependency.

4. Types

Each template parameter has a type. The type specifies the permissible type or datatype the corresponding argument may have, the argument type must be compatible [1] with the parameter type. In essence, a parameter with type X requires that the type of the argument is X or a subtype of X.

The permissible types are classes from the RDF, RDFS, OWL and XSD vocabularies and specifications, including lists; see rOTTR [2] for the full list and hierarchy.

The default type which is used in case no type is specified, as in the previous examples, is the most general one, rdfs:Resource.

We also check that arguments are consistently typed. This is relevant for arguments where the lexical value does not identify its type, such as for subtypes of ottr:IRI, e.g., owl:Class and owl:ObjectProperty. An argument can not be used in way that forces it to have an illegal or non-existing type, for instance an argument cannot have both the type owl:ObjectProperty and owl:DatatypeProperty.

Types are specified like the following, by setting the type before the parameter variable. Here we extend the ex:Person template seen earlier with types, showing only the signature:

ex:Person[ 
  ottr:IRI ?person, 
  xsd:string ?firstName, 
  xsd:string ?lastName, 
  ottr:IRI ?email ] .

4.1. Exercise

What is the type error?

ex:A[ ottr:IRI ?x ] :: BASE . ex:B [ xsd:string ?x ] :: { ex:A(?x) } .

Solution

Lutra's error message explains:

[ERROR] Type error in template http://example.com/ns#B: incompatible argument and parameter type. The template contains a value ?x : xsd:string which has the type xsd:string and which is used as argument to a parameter with the incompatible type ottr:IRI in instance http://example.com/ns#A(?x : xsd:string) (arg no. 1).

4.2. Exercise

What is the type error?

ex:A[ ottr:IRI ?x ] :: BASE . ex:B [ owl:ObjectProperty ?x ] :: { ex:A(?x) } . ex:C [ owl:AnnotationProperty ?x ] :: { ex:A(?x) } . ex:D [ ?x ] :: { ex:B(?x), ex:C(?x) } .

Solution

Lutra's error message explains:

[ERROR] Type error in template http://example.com/ns#D: incompatible parameter types. The template contains an argument ?x : rdfs:Resource to different parameters with incompatible types: instance http://example.com/ns#B(?x : rdfs:Resource) (arg no. 1) with parameter type owl:ObjectProperty instance http://example.com/ns#C(?x : rdfs:Resource) (arg no. 1) with parameter type owl:AnnotationProperty [ERROR] Type error in template http://example.com/ns#D: incompatible argument and parameter type. The template contains a value ?x : rdfs:Resource which has the type rdfs:Resource and which is used as argument to a parameter with the incompatible type owl:ObjectProperty in instance http://example.com/ns#B(?x : rdfs:Resource) (arg no. 1). [ERROR] Type error in template http://example.com/ns#D: incompatible argument and parameter type. The template contains a value ?x : rdfs:Resource which has the type rdfs:Resource and which is used as argument to a parameter with the incompatible type owl:AnnotationProperty in instance http://example.com/ns#C(?x : rdfs:Resource) (arg no. 1).

4.3. Exercise: Specifying types

Specify reasonable types for the template ex:Organization below. Note, that the template is slightly changed from the above and now includes the IRI of the organisation.

ex:Organization(ex:uio, "University of Oslo", "208"^^xsd:int, <http://uio.no>) .

ex:Organization[?org, ?name, ?age, ?url] :: { ex:Type(?org, foaf:Organization), ottr:Triple(?org, foaf:name, ?name), ottr:Triple(?org, foaf:age, ?age), ottr:Triple(?org, foaf:homepage, ?url) } . ex:Type[ottr:IRI ?individual, ottr:IRI ?type] :: { ottr:Triple(?individual, rdf:type, ?type) } .

Solution

ex:Organization[ottr:IRI ?org, xsd:string ?name, xsd:int ?age, ottr:IRI ?url] :: {
    ex:Type(?org, foaf:Organization),
    ottr:Triple(?org, foaf:name, ?name),
    ottr:Triple(?org, foaf:age, ?age),
    ottr:Triple(?org, foaf:homepage, ?url)
} .

5. NonBlank

A parameter can be specified as nonblank, which means it will not accept a blank node as argument.

A parameter is set to be nonblank by writing ! before the parameter type, e.g., the ottr:Triple, which according to the RDF specification should not allow blank nodes as predicates, can be written as:

ottr:Triple [ ottr:IRI ?subject, ! ottr:IRI ?predicate, rdfs:Resource ?object ] :: BASE .

5.1. Exercise

The following template is ill-defined; why? Can you fix it?

ex:Relative(ex:Bart, ex:hasFather, ex:Homer) . ex:Relative(ex:Bart, ex:hasMother, ex:Marge) .

ex:Relative[ ottr:IRI ?person, ottr:IRI ?relation, ottr:IRI ?other ] :: { ottr:Triple(?person, ?relation, ?other) } .

Solution

Lutra explains:

[ERROR] Inconsistent non-blank parameter flags in template http://example.com/ns#Relative. The template contains a parameter ?relation : ottr:IRI which is not non-blank, but the parameter is used as argument (arg no. 2) to an instance of template http://ns.ottr.xyz/0.4/Triple where the corresponding parameter [?s : rdfs:Resource, !?p : rdfs:Resource, ?o : rdfs:Resource] is non-blank.

6. Optionals and None

A parameter can be specified as optional. This determines how the parameter treats arguments which are equal to the specific IRI ottr:none, which in stOTTR can be written as just none. none is a term that represents a missing or no value.

An instance with none as an argument to a non-optional parameter will be removed in the expansion, while if the parameter is optional, then the instance is not removed. Essentially, optional parameters allow none to be passed on in the expansion.

Note that all the parameters of the ottr:Triple template are non-optional. If want wants to produce triples with none, one can use the base template ottr:NullableTriple.

A parameter is specified as optional by adding ? before its type.

ottr:NullableTriple can be specified as

ottr:NullableTriple[? ottr:IRI ?subject, !? ottr:IRI ?predicate, ? rdfs:Resource ?object ] :: BASE .

6.1. Exercise: Triple vs. NullableTriple

Observe the difference of expanding ottr:Triple and ottr:NullableTriple by changing the pattern of ex:TripleWrapper from using ottr:Triple to using ottr:NullableTriple.

Look closely at the signature of ex:TripleWrapper and make sure you understand it.

ex:TripleWrapper(ex:s1, ex:p1, ex:o1) . ex:TripleWrapper(none, ex:p2, ex:o2) . ex:TripleWrapper(ex:s3, none, ex:o3) . ex:TripleWrapper(ex:s4, ex:p4, none) .

ex:TripleWrapper[ ? ottr:IRI ?s, !? ottr:IRI ?p, ??o ] :: { ottr:Triple(?s, ?p, ?o ) # ottr:NullableTriple(?s, ?p, ?o ) } .

Solution

Here is an explanation of the parameters of the ex:TripleWrapper:

ex:TripleWrapper[ 
  ? ottr:IRI ?s,   # ? = optional, ottr:IRI = type, ?s = parameter
  !? ottr:IRI ?p,  # ? = optional, ! = nonBlank, ottr:IRI = type, ?p = parameter
  ??o              # ? = optional, [no type, means rdfs:Resource], ?o = parameter
] .

If the ottr:TripleWrapper does not contain ottr:NullableTriple in the pattern, the resulting graph will contain no none values (which is shorthand for the IRI ottr:none). This is because none of the parameters of the ottr:Triple template are optional. If using ottr:NullableTriple, ottr:none resources will appear in the resulting expansion, since all of ottr:NullableTriple's parameters are optional.

6.2. Exercise: Optionals

Change the ex:Person template below so the first name is optional, and the instances below expand to the following:

PREFIX ex: <http://example.com/ns#>
PREFIX dbp: <http://dbpedia.org/ontology/>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX ottr: <http://ns.ottr.xyz/0.4/>
PREFIX ax: <http://tpl.ottr.xyz/owl/axiom/0.1/>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/>
PREFIX foaf: <http://xmlns.com/foaf/0.1/>

ex:mary  rdf:type       foaf:Person;
        foaf:lastName   "Stone";
        foaf:mbox       <mailto:[email protected]>;
        foaf:firstName  "Mary" .

ex:smith  rdf:type     foaf:Person;
        foaf:lastName  "Smith";
        foaf:mbox      <mailto:[email protected]> .

ex:Person(ex:mary, "Mary", "Stone", <mailto:mstone@mail.com>) . ex:Person(ex:smith, none, "Smith", <mailto:smith@mail.com>) .

ex:Person[ ottr:IRI ?person, xsd:string ?firstName, xsd:string ?lastName, ottr:IRI ?email ] :: { ex:Type (?person, foaf:Person ), ottr:Triple (?person, foaf:firstName, ?firstName ), ottr:Triple (?person, foaf:lastName, ?lastName ), ottr:Triple (?person, foaf:mbox, ?email ) } . ex:Type[ottr:IRI ?individual, ottr:IRI ?type] :: { ottr:Triple(?individual, rdf:type, ?type) } .

Solution

ex:Person[ ottr:IRI ?person, ? xsd:string ?firstName, xsd:string ?lastName, ottr:IRI ?email ] :: {
  ex:Type (?person, foaf:Person ),
  ottr:Triple (?person, foaf:firstName, ?firstName ),
  ottr:Triple (?person, foaf:lastName, ?lastName ),
  ottr:Triple (?person, foaf:mbox, ?email )
} .

ex:Type[ottr:IRI ?individual, ottr:IRI ?type] :: {
  ottr:Triple(?individual, rdf:type, ?type)
} .

7. Default values

Parameters can specify a default value. The default value is used if the argument is none. The default value can be any term. If the default value is a blank node, a fresh blank node will be used for each instance.

A default value is specified appending the value to the parameter variable separated by =, i.e., ?variable=default.

7.1. Exercise

The template

ax:SubObjectSomeValuesFrom[owl:Class ?class, owl:ObjectProperty ?property, owl:Class ?qualifier ] .

can be used to create OWL axioms of the form \(C \sqsubseteq \exists P . D\)

How would you need to change the signature so that the instance

ax:SubObjectSomeValuesFrom(ex:A, ex:Q, none) .

would produce \(A \sqsubseteq \exists Q . \top\)

Solution

Change the signature to

ax:SubObjectSomeValuesFrom[owl:Class ?class, owl:ObjectProperty ?property, owl:Class ?qualifier = owl:Thing ] .

7.2. Exercise: Setting concrete default values

Change the template ex:Organization to include an extra argument ?loc which states that the organisation is dbp:locatedIn ?loc and which defaults to ex:norway, so that the following instances expand to:

PREFIX ex: <http://example.com/ns#>
PREFIX dbp: <http://dbpedia.org/ontology/>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX ottr: <http://ns.ottr.xyz/0.4/>
PREFIX ax: <http://tpl.ottr.xyz/owl/axiom/0.1/>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/>
PREFIX foaf: <http://xmlns.com/foaf/0.1/>

ex:uio  foaf:homepage  <http://uio.no>;
        foaf:age       "208"^^xsd:int;
        rdf:type       foaf:Organization;
        dbp:locatedIn  ex:norway;
        foaf:name      "University of Oslo" .

ex:google  foaf:homepage  <http://google.com>;
        foaf:age       "21"^^xsd:int;
        rdf:type       foaf:Organization;
        dbp:locatedIn  ex:usa;
        foaf:name      "Google AS" .

ex:Organization(ex:uio, "University of Oslo", "208"^^xsd:int, <http://uio.no>, none) . ex:Organization(ex:google, "Google AS", "21"^^xsd:int, <http://google.com>, ex:usa) .

ex:Organization[ottr:IRI ?org, xsd:string ?name, xsd:int ?age, ottr:IRI ?url] :: { ex:Type(?org, foaf:Organization), ottr:Triple(?org, foaf:name, ?name), ottr:Triple(?org, foaf:age, ?age), ottr:Triple(?org, foaf:homepage, ?url) } . ex:Type[ottr:IRI ?individual, ottr:IRI ?type] :: { ottr:Triple(?individual, rdf:type, ?type) } .

Solution

ex:Organization[ottr:IRI ?org, xsd:string ?name, xsd:int ?age, ottr:IRI ?url, ottr:IRI ?loc=ex:norway] :: {
    ex:Type(?org, foaf:Organization),
    ottr:Triple(?org, foaf:name, ?name),
    ottr:Triple(?org, foaf:age, ?age),
    ottr:Triple(?org, dbp:locatedIn, ?loc),
    ottr:Triple(?org, foaf:homepage, ?url)
} .

7.3. Exercise: Setting blank node default values

Change the template ex:Person so that it generates a fresh blank node if no IRI is provided for the person. The instances below should expand to:

PREFIX ex: <http://example.com/ns#>
PREFIX dbp: <http://dbpedia.org/ontology/>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX ottr: <http://ns.ottr.xyz/0.4/>
PREFIX ax: <http://tpl.ottr.xyz/owl/axiom/0.1/>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/>
PREFIX foaf: <http://xmlns.com/foaf/0.1/>

_:b0    rdf:type        foaf:Person;
        foaf:lastName   "Jones";
        foaf:mbox       <mailto:[email protected]>;
        foaf:firstName  "Ann" .

_:b1    rdf:type        foaf:Person;
        foaf:lastName   "Bright";
        foaf:mbox       <mailto:[email protected]>;
        foaf:firstName  "Bill" .

ex:cindy  rdf:type      foaf:Person;
        foaf:lastName   "Stevens";
        foaf:mbox       <mailto:[email protected]>;
        foaf:firstName  "Cindy" .

ex:Person(none, "Ann", "Jones", <mailto:ann@mail.com>) . ex:Person(none, "Bill", "Bright", <mailto:bill@mail.com>) . ex:Person(ex:cindy, "Cindy", "Stevens", <mailto:cindy@mail.com>) .

ex:Person[ ottr:IRI ?person, ? xsd:string ?firstName, xsd:string ?lastName, ottr:IRI ?email ] :: { ex:Type (?person, foaf:Person ), ottr:Triple (?person, foaf:firstName, ?firstName ), ottr:Triple (?person, foaf:lastName, ?lastName ), ottr:Triple (?person, foaf:mbox, ?email ) } . ex:Type[ottr:IRI ?individual, ottr:IRI ?type] :: { ottr:Triple(?individual, rdf:type, ?type) } .

Solution

ex:Person[ ottr:IRI ?person=_:person, xsd:string ?firstName, xsd:string ?lastName, ottr:IRI ?email ] :: {
  ex:Type (?person, foaf:Person ),
  ottr:Triple (?person, foaf:firstName, ?firstName ),
  ottr:Triple (?person, foaf:lastName, ?lastName ),
  ottr:Triple (?person, foaf:mbox, ?email )
} .

7.4. Exercise: Specifying relationship between organisation and persons

Make a new template ex:Member that takes three arguments:

?org the IRI of an organisation,
?person the IRI of a person,
?relation the IRI of the relationship between the organisation and the person (e.g. foaf:member, ex:employee, ex:associate). It should default to foaf:member.

Add types and other necessary flags to make the template correct. The pattern should contain a single triple instance stating that the ?org is ?relation related to ?person, so that the following instances expands to:

PREFIX ex: <http://example.com/ns#>
PREFIX dbp: <http://dbpedia.org/ontology/>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX ottr: <http://ns.ottr.xyz/0.4/>
PREFIX ax: <http://tpl.ottr.xyz/owl/axiom/0.1/>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/>
PREFIX foaf: <http://xmlns.com/foaf/0.1/>

ex:busAZ  ex:employee  ex:bob .

ex:united_nations  foaf:member  ex:norway .

ex:Member(ex:busAZ, ex:bob, ex:employee) . ex:Member(ex:united_nations, ex:norway, none) .

ex:Member[ ?org, ?person, ?relation ] :: { } .

Solution

ex:Member[ottr:IRI ?org, ottr:IRI ?person, ! ottr:IRI ?relation=foaf:member] :: {
    ottr:Triple(?org, ?relation, ?person)
} .

8. Expansion modes

Instances in a template pattern can be marked with an expansion mode. Expansion modes are used to create multiple instances from arguments which are lists. There are different expansion modes which behave differently when multiple list arguments are in play. The current list of expansion modes are cross, zipMin and zipMax.

An pattern instance is marked by adding the expansion mode like this: cross | [Instance]

The list argument to which the expansion mode is applied must be selected. This is done by adding ++ to the argument like this: ++?argument

8.1. Exercise: Getting acquainted with expansion modes

The template ex:Types below can be used to express that an IRI has multiple classes. This is done by marking the instance ex:Type in the pattern of ex:Types with an expansion mode. The result of expanding the instance below is the following:

PREFIX ex: <http://example.com/ns#>
PREFIX dbp: <http://dbpedia.org/ontology/>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX ottr: <http://ns.ottr.xyz/0.4/>
PREFIX ax: <http://tpl.ottr.xyz/owl/axiom/0.1/>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/>
PREFIX foaf: <http://xmlns.com/foaf/0.1/>

ex:ann  rdf:type  ex:Person;
        rdf:type  ex:Employee .

Essentially, the expansion mode specifies that an instance of ex:Type is created for each element in the list of the second argument of ex:Types. What really happens is that an instance for each element in the cross product of all the arguments to ex:Type is created, temporarily treating all arguments as lists: \(\langle ann \rangle \times \langle Person, Employee \rangle = \{ \langle ann, Person \rangle ,\langle ann, Employee \rangle \}\)

ex:Types(ex:ann, (ex:Person, ex:Employee)) .

ex:Types[ ottr:IRI ?inst, List<ottr:IRI> ?class ] :: { cross | ex:Type(?inst, ++?class) } . ex:Type[ottr:IRI ?individual, ottr:IRI ?type] :: { ottr:Triple(?individual, rdf:type, ?type) } .

Exercises:

Change the signature of ex:Types so that the type of the first parameter is also List<ottr:IRI> and mark the argument ?inst in the pattern with ++. Now change the instance in the input box to
```
ex:Types((ex:ann, ex:bob, ex:cindy, ex:david), (ex:Person, ex:Employee))
```
and see what this expands to.
Keep the setup as in 1., but now change the expansion mode to zipMin and see what happens with the expansion results.
Now change the expansion mode to zipMax and see what happens.

Solution

cross: ⟨ A, B, C ⟩ × ⟨ X, Y ⟩ = { ⟨ A, X ⟩ , ⟨ B, X ⟩ , ⟨ C, X ⟩ , ⟨ A, Y ⟩ , ⟨ B, Y ⟩ , ⟨ C, Y ⟩ }
zipMin zips the lists, but only the size of the shortest list: zipMin(⟨ A, B, C ⟩, ⟨ X, Y ⟩)= { ⟨ A, X ⟩ , ⟨ B, Y ⟩ }.
zipMax zips the lists, and appends shorter lists with none to match the size of the longest list: zipMax(⟨ A, B, C ⟩, ⟨ X, Y ⟩)= { ⟨ A, X ⟩ , ⟨ B, Y ⟩ ⟨ C, none ⟩ }.

8.2. Exercise: Setting expansion modes

Make a new template ex:Members that takes an organisation, a list of individuals (given as IRIs), and a relation as argument and produces a ex:Member instance between the organization and each of the persons in the list. The instances below should expand to:

PREFIX ex: <http://example.com/ns#>
PREFIX dbp: <http://dbpedia.org/ontology/>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX ottr: <http://ns.ottr.xyz/0.4/>
PREFIX ax: <http://tpl.ottr.xyz/owl/axiom/0.1/>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/>
PREFIX foaf: <http://xmlns.com/foaf/0.1/>

ex:fast  ex:employee  ex:ann;
        ex:employee  ex:bob;
        ex:employee  ex:carl .

ex:united_nations  foaf:member  ex:usa;
        foaf:member  ex:germany;
        foaf:member  ex:france;
        foaf:member  ex:norway .

Note the use of optional flag in the signature so that a none value gets passed on to the ex:Member template, which then uses the default value foaf:member.

ex:Members(ex:fast, (ex:ann, ex:bob, ex:carl), ex:employee) . ex:Members(ex:united_nations, (ex:usa, ex:germany, ex:france, ex:norway), none) .

ex:Members[ ottr:IRI ?org, List<ottr:IRI> ?members, !? ottr:IRI ?relation] :: { } . ex:Member[ottr:IRI ?org, ottr:IRI ?person, ! ottr:IRI ?relation=foaf:member] :: { ottr:Triple(?org, ?relation, ?person) } .

Solution

ex:Members[ ottr:IRI ?org, List<ottr:IRI> ?members, !? ottr:IRI ?relation ] :: {
    cross | ex:Member(?org, ++?members, ?relation)
} .

8.3. Exercise (*): Exploiting expansion modes

Make a template ex:Friends with the signature below, that from the given the instances produces the following, i.e., everybody knows everybody.

PREFIX ex: <http://example.com/ns#>
PREFIX dbp: <http://dbpedia.org/ontology/>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX ottr: <http://ns.ottr.xyz/0.4/>
PREFIX ax: <http://tpl.ottr.xyz/owl/axiom/0.1/>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/>
PREFIX foaf: <http://xmlns.com/foaf/0.1/>

ex:ann  foaf:knows  ex:ann;
        foaf:knows  ex:bob;
        foaf:knows  ex:carl .

ex:bob  foaf:knows  ex:ann;
        foaf:knows  ex:bob;
        foaf:knows  ex:carl .

ex:carl  foaf:knows  ex:ann;
        foaf:knows  ex:bob;
        foaf:knows  ex:carl .

ex:Friends((ex:ann, ex:bob, ex:carl)) .

ex:Friends[ List<ottr:IRI> ?friends] :: { } .

Solution

ex:Friends[ List<ottr:IRI> ?friends] :: {
  cross | ottr:Triple(++?friends, foaf:knows, ++?friends)
} .

8.4. Exercise: NamedPizza

The NamedPizza template, published at http://tpl.ottr.xyz/pizza/0.1/NamedPizza, uses lists both with and without expansion modes. The list of toppings is used to create a union of classes using the http://tpl.ottr.xyz/owl/restriction/0.1/ObjectUnionOf template, and to create a instance of http://tpl.ottr.xyz/owl/axiom/0.1/SubObjectSomeValuesFrom for each topping in the list.

Try and make new pizzas and see the results.

@prefix o-pizza: <http://tpl.ottr.xyz/pizza/0.1/> . o-pizza:NamedPizza(ex:Margerita, ex:Italy, (ex:Tomato, ex:Mozzarella)) . o-pizza:NamedPizza(ex:QuattroFormaggi, ex:Italy, (ex:Tomato, ex:Mozzarella, ex:Gorgonzola, ex:Parmesan, ex:Stracchino)) . o-pizza:NamedPizza(ex:Grandiosa, ex:Norway, (ex:Tomato, ex:Cheese, ex:BellPepper, ex:Ham)) . o-pizza:NamedPizza(ex:PepperoniPizza, ottr:none, (ex:Tomato, ex:Cheese, ex:Pepperoni)) .

8.5. Exercise (**): Using multiple expansion modes

Make a template ex:OrganizationMembers with the given signature, that given the instance below expands to the following:

PREFIX ex: <http://example.com/ns#>
PREFIX dbp: <http://dbpedia.org/ontology/>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX ottr: <http://ns.ottr.xyz/0.4/>
PREFIX ax: <http://tpl.ottr.xyz/owl/axiom/0.1/>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX rstr: <http://tpl.ottr.xyz/owl/restriction/0.1/>
PREFIX foaf: <http://xmlns.com/foaf/0.1/>

ex:leif  foaf:knows  ex:leif;
        foaf:knows  ex:daniel;
        foaf:knows  ex:martin .

ex:daniel  foaf:knows  ex:leif;
        foaf:knows  ex:daniel;
        foaf:knows  ex:martin .

ex:martin  foaf:knows  ex:leif;
        foaf:knows  ex:daniel;
        foaf:knows  ex:martin .

ex:leif  rdf:type       foaf:Person;
        foaf:lastName   "Karlsen";
        foaf:mbox       <mailto:[email protected]>;
        foaf:firstName  "Leif Harald" .

ex:daniel  rdf:type     foaf:Person;
        foaf:lastName   "Lupp";
        foaf:mbox       <mailto:[email protected]>;
        foaf:firstName  "Daniel" .

ex:martin  rdf:type     foaf:Person;
        foaf:lastName   "Skjæveland";
        foaf:mbox       <mailto:[email protected]>;
        foaf:firstName  "Martin" .

ex:uio  foaf:homepage  <http://uio.no>;
        rdf:type       foaf:Organization;
        foaf:age       "208"^^xsd:int;
        dbp:locatedIn  ex:norway;
        foaf:name      "University of Oslo";
        ex:employee    ex:leif;
        ex:employee    ex:daniel;
        ex:employee    ex:martin .

ex:OrganizationMembers( ex:uio, "University of Oslo", "208"^^xsd:int, <http://uio.no>, none, ex:employee, (ex:leif, ex:daniel, ex:martin), ("Leif Harald", "Daniel", "Martin"), ("Karlsen", "Lupp", "Skjæveland"), (<mailto:leifhka@ifi.uio.no>, <mailto:danielup@ifi.uio.no>, <mailto:martige@ifi.uio.no>) ) .

ex:OrganizationMembers[ ottr:IRI ?org, xsd:string ?name, xsd:int ?age, ottr:IRI ?url, ? ottr:IRI ?loc, !? ottr:IRI ?relation, List<ottr:IRI> ?members, List<xsd:string> ?memberFirstNames, List<xsd:string> ?memberLastNames, List<ottr:IRI> ?memberMboxes ] :: { } . #### no need to change the templates below this line ex:Type[ottr:IRI ?individual, ottr:IRI ?type] :: { ottr:Triple(?individual, rdf:type, ?type) } . ex:Person[ ottr:IRI ?person=_:person, xsd:string ?firstName, xsd:string ?lastName, ottr:IRI ?email ] :: { ex:Type (?person, foaf:Person ), ottr:Triple (?person, foaf:firstName, ?firstName ), ottr:Triple (?person, foaf:lastName, ?lastName ), ottr:Triple (?person, foaf:mbox, ?email ) } . ex:Organization[ottr:IRI ?org, xsd:string ?name, xsd:int ?age, ottr:IRI ?url, ottr:IRI ?loc=ex:norway] :: { ex:Type(?org, foaf:Organization), ottr:Triple(?org, foaf:name, ?name), ottr:Triple(?org, foaf:age, ?age), ottr:Triple(?org, dbp:locatedIn, ?loc), ottr:Triple(?org, foaf:homepage, ?url) } . ex:Members[ ottr:IRI ?org, List<ottr:IRI> ?members, !? ottr:IRI ?relation ] :: { cross | ex:Member(?org, ++?members, ?relation) } . ex:Member[ottr:IRI ?org, ottr:IRI ?person, ! ottr:IRI ?relation=foaf:member] :: { ottr:Triple(?org, ?relation, ?person) } . ex:Friends[ List<ottr:IRI> ?friends] :: { cross | ottr:Triple(++?friends, foaf:knows, ++?friends) } .

Solution

ex:OrganizationMembers[
    ottr:IRI ?org, xsd:string ?name, xsd:int ?age, ottr:IRI ?url,
    ? ottr:IRI ?loc, !? ottr:IRI ?relation,
    List<ottr:IRI>   ?members,
    List<xsd:string> ?memberFirstNames,
    List<xsd:string> ?memberLastNames,
    List<ottr:IRI>   ?memberMboxes]
:: {
  ex:Organization(?org, ?name, ?age, ?url, ?loc),
  zipMin | ex:Person(++?members, ++?memberFirstNames, ++?memberLastNames, ++?memberMboxes),
  ex:Members(?org, ?members, ?relation),
  ex:Friends(?members) 
} .

9. References

mOTTR: Concepts and Abstract Model for Reasonable Ontology Templates http://spec.ottr.xyz/mOTTR/0.1/
rOTTR: Adapting Reasonable Ontology Templates to RDF http://spec.ottr.xyz/rOTTR/0.2/
stOTTR: Terse Syntax for Reasonable Ontology Templates http://spec.ottr.xyz/stOTTR/0.1/
wOTTR: Web Reasonable Ontology Templates http://spec.ottr.xyz/wOTTR/0.4/

10. Appendix

10.1. WebLutra

The web application that drives the interactive examples in this primer, called WebLutra, uses Lutra, the reference application for OTTR. Both applications are open source and available at http://gitlab.com/ottr/lutra/lutra. If you experience errors or have suggestions for improvements, please take a look at existing issues or file a new issue: http://gitlab.com/ottr/lutra/lutra/issues

Table of Contents

The Basics of Reasonable Ontology Templates

1. Introduction

1.1. Prefixes

2. Templates and Instances

2.1. Exercise: Getting familiar with the interactive exercise form

2.2. Exercise: Create a new template

Solution

2.3. Base templates

2.4. Exercise: Create a base template

Solution

3. Nesting templates

3.1. Exercise: Refactoring

Solution

3.2. Exercise

Solution

4. Types

4.1. Exercise

Solution

4.2. Exercise

Solution

4.3. Exercise: Specifying types

Solution

5. NonBlank

5.1. Exercise

Solution

6. Optionals and None

6.1. Exercise: Triple vs. NullableTriple

Solution

6.2. Exercise: Optionals

Solution

7. Default values

7.1. Exercise

Solution

7.2. Exercise: Setting concrete default values

Solution

7.3. Exercise: Setting blank node default values

Solution

7.4. Exercise: Specifying relationship between organisation and persons

Solution

8. Expansion modes

8.1. Exercise: Getting acquainted with expansion modes

Solution

8.2. Exercise: Setting expansion modes

Solution

8.3. Exercise (*): Exploiting expansion modes

Solution

8.4. Exercise: NamedPizza

8.5. Exercise (**): Using multiple expansion modes

Solution

9. References

10. Appendix

10.1. WebLutra