The RDF and OWL Recommendations use the simple types from XML
Schema. This document addresses
three questions left unanswered by
these Recommendations: Which URIref should be used to refer to a
user defined datatype? Which values of which XML Schema simple
types are the same? How to use the problematic
xsd:duration in RDF and OWL?
In addition, we further describe how to
integrate OWL DL with user defined datatypes (in appendix B).
Status of this Document
This editors' draft is for WG consideration and review.
Changes are listed in the
change log.
The remainder of this section is fictitious, and acts as a draft for
the status of a Working Group Note.
This section describes the status of this document at the
time of its publication. Other documents may supersede this
document. A list of current W3C publications and the latest
revision of this technical report can be found in the W3C technical reports index at
http://www.w3.org/TR/.
This document is a Working
Group Note, produced by the Semantic
Web Best Practices and Deployment Working Group, part of the
W3C Semantic Web Activity.
Comments on this document may be sent to
public-swbp-wg@w3.org,
a mailing list with a
public archive.
Publication as a Working Group Note 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.
An overview of the datatype abstraction
used by RDF is found in the [RDF
Concepts and Abstract Syntax]; this is
shared by the [OWL Abstract
Syntax].
The semantics of RDF datatyping and OWL datatyping are
summarized in appendix A.
RDF and OWL allow the use of typed literal values in the
description of resources and ontologies. See the [RDF Primer], and the [OWL Guide] for a more introductory treatments
for RDF
and OWL.
Both the [RDF Semantics] and the
[OWL Semantics] use the
lexical-to-value mapping of the datatype to give the interpretation
(the value) of a typed literal, thus the semantics of typed
literals is given by the type system. The type systems are defined
externally to RDF and OWL, most notably by [XML Schema2].
Concrete syntaxes for typed literals are found in [RDF Syntax], [N-triples], and [N3].
Some questions about XML Schema datatypes in the Semantic Web
are not directly answered by the published W3C Recommendations.
This document considers four of them:
- Within RDF and OWL, how to refer to an XML Schema user defined
simple type with a URI.
- Details of the denotational semantics of the values of the
primitive XML Schema simple types. XML Schema principally gives an
operational semantics. RDF and OWL applications need a denotational
semantics for interoperable behaviour.
- A possible solution to the problems concerning
xsd:duration, which are reported
in [RDF Semantics].
- Appropriate use of numeric types for engineering applications.
While this document can be read from start to finish, many readers
will benefit from skipping sections.
The intended reader is informed about RDF and/or OWL,
and may be a creator or
user of metadata or ontologies, or may be an implementor
of systems that implement the RDF or OWL Recommendations, or
may be the author or editor of related specifications.
The reader who is interested in defining their own datatypes
should read section 2
and maybe
appendix B, which gives
a formal treatment,
in terms of OWL DL and user defined datatypes, that has not been covered by the [OWL Semantics].
The reader who is interested in the correct use of datatypes
should read section 3, concerning
which values are the same, and
section 5 concerning numerics, particularly,
but not exclusively,
for engineering
applications.
Implementors probably should read most of the document:
appendix A summarizes
the formal treatment of datatyping from the recommendations;
section 3 gives an extended discussion
about equality; section 2
discusses the mapping from URIs to user defined types.
Readers most interested in formal semantics
will find most value in
appendix B,
concerning user defined datatypes,
and
section 3
concerning equality. Such readers should start by
reviewing
appendix A, which should be
familiar.
Section 4
on durations, is of more limited interest, but is significant
to any reader who wishes to use, implement
or build on top of
duration datatypes.
In this document we use N3 such as "10"^^xsd:int
following the subset used by the [OWL Test
Cases], with the following namespace prefixes:
@prefix dc: <http://purl.org/dc/elements/1.1/> .
@prefix eg: <http://www.example.org/> .
@prefix egdt: <http://example.org/simpleTypes#> .
@prefix xsd: <http://www.example.org/> .
@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#> .
[XML SCHEMA2] defines facilities for defining simple types to
be used in XML Schema as well as other XML specifications.
It is influenced by earlier work on datatypes such as
[ISO 11404].
[Definition:] An XML Schema
simple type d is characterised by a value space, V(d), which
is a non-empty set, a lexical space, L(d), which is a non-empty set
of Unicode strings, and a set of facets, F(d), each of which
characterizes a value space along independent axes or
dimensions.
XML Schema simple types are divided into disjoint built-in
simple types and derived simple types. Derived datatypes can be
defined
from primitive or existing derived datatypes
by the following three means:
- By
restriction, i.e., by using facets on an
existing type, so as to limit the number of possible values of the
derived type.
- By
union, i.e., to allow values from a list
of simple types.
- By
list, i.e., to define the list type of
an existing simple type.
The following is the definition of a derived simple type (of the
base datatype xsd:integer) which restricts values to integers
greater than or equal to 0 and less than 150, using the facets
minInclusive and maxExclusive.
<xsd:schema ...>
<xsd:simpleType name="humanAge">
<xsd:restriction base="integer">
<xsd:minInclusive value="0">
<xsd:maxExclusive value="150">
</xsd:restriction>
</xsd:simpleType>
...
</xsd:schema>
[XML Schema2] predefines about
forty simple types, the ones suitable for RDF and OWL are listed in
[RDF Semantics].
In addition, XML Schema permits users to refine these builtin
types by taking a restriction including only some of the values or
some of the lexical forms.
As a further example, we may wish to talk about
ages of adults in years, where an adult is over 18. This can be
described as a restriction on the xsd:integer
datatype.
<xsd:schema ...>
<xsd:simpleType name="adultAge">
<xsd:restriction base="integer">
<xsd:minInclusive value="18">
</xsd:restriction>
</xsd:simpleType>
...
</xsd:schema>
In a Semantic Web context this may be used with the objects of
triples of an eg:age property, used, for instance,
when describing some members of a club which is restricted to
adults, e.g. a nightclub or a political party.
We will use this example throughout this section, and assume it
can be retrieved from
http://example.org/simpleTypes.
Within RDF, and RDF reasoning, this additional restriction may
be enough to catch some typos or data entry errors (e.g. putting an
inappropriate value of 0 for the eg:age
property). Within OWL, and OWL reasoning, this may interact with
axioms in the ontology to significantly restrict the possible
interpretations, adding to the modelling power of the language.
This section only deals with the problem of how to refer to such
datatypes.
Their semantics is treated in the appendices.
Appendix A
reviews the semantics of datatypes from the RDF and OWL
recommendations.
Appendix B
describes how to integrate Description Logics (such as the
SHOIN DL, which is the underpinning of OWL DL) with user
defined datatypes.
We will also consider the topic of
the
target namespace
from [XML SCHEMA1].
For clarity, we will consider
two variants on this example. The first has no target namespace,
the second defines one.
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema">
<xs:simpleType name="adultAge">
<xs:restriction base="integer">
<xs:minInclusive value="18">
</xs:restriction>
</xs:simpleType>
...
</xs:schema>
<xs:schema
targetNamespace="http://example.org/ns"
elementFormDefault="qualified"
xmlns:egn="http://example.org/ns"
xmlns:xs="http://www.w3.org/2001/XMLSchema">
<xs:simpleType name="adultAge">
<xs:restriction base="integer">
<xs:minInclusive value="18">
</xs:restriction>
</xs:simpleType>
...
</xs:schema>
The case where the XML Schema has been assembed from multiple schema
documents lies outside the scope of this document.
This case is
discussed in
[XML SCHEMA1]
and explicitly
not discussed in
[XSCD].
When describing a resource with RDF or building an ontology with
OWL, in which a user defined simple XML Schema datatype, such as
adultAge above, what URI should be used to identify
this datatype?
Following XML Schema Component Designators [XSCD]
Example 2B
has URI reference
http://example.org/simpleTypes#xscd(/type::adultAge).
A URI reference for
Example 2C
requires a choice of prefix for the namespace
http://example.org/ns.
A good choice is to use the prefix
used by the schema itself, i.e. egn.
The resulting URI reference for the datatype
is then
http://example.org/simpleTypes#xmlns(egn=http://example.org/ns)xscd(/type::egn:adultAge)
When the schema does not define a prefix for the
target namespace, perhaps by using the default namespace,
then an arbitrary prefix needs to be chosen.
As always with namespace prefixes, it is permitted
to use any prefix of your choice, even when a conventional
prefix is used in the schema document.
XML Schema Component Designators [XSCD]
defines an XPointer scheme that navigates the XML
Schema document to identify any of the schema components using a
fragment. This is very general: fragments are defined that identify
many different aspects of the document, including unnamed simple
types within complex schema.
Our
example 2B becomes:
eg:membersAge rdfs:range <http://example.org/simpleTypes#xscd(/type::adultAge)> .
_:aMember eg:name "Jane Doe" .
_:aMember eg:membersAge "24"^^<http://example.org/simpleTypes#xscd(/type::adultAge)> .
One way of reading the fragment is that it provides full
semantic clarity about what is being identified: the xscd(.)
shows that an XML Schema component is being identified; the /type
indicates that a type is being identified; the ::adultAge shows which
type is being identified.
The above URIrefs cannot be abbreviated as:
eg:membersAge rdfs:range egdt:xscd(/type::adultAge) .
_:aMember eg:name "Jane Doe" .
_:aMember eg:membersAge "24"^^egdt:xscd(/type::adultAge) .
because xscd(/type::adultAge) does not match
the NCName production.
Overall, referring to XML Schema Datatypes
in the manner proposed by the XML Schema Working Group is
a good practice, and will be moreso, when
[XSCD]
reaches Recommendation status.
In cases where the XML Schema is under the control
of a Semantic Web author, the full generality of
[XSCD]
is not needed. This section shows how when defining
your own datatype, derived from an XML Schema type,
it is possible to use a simpler method, by slightly
modifying the schema defining the datatype.
Example 2A becomes:
<xsd:schema ...>
<xsd:simpleType id="adultAge" name="adultAge">
<xsd:restriction base="integer">
<xsd:minInclusive value="18">
</xsd:restriction>
</xsd:simpleType>
...
</xsd:schema>
The difference is that the datatype we wish to use
is not only identified by the @name
attribute, but also by an @id attribute.
While it is technically possibly to use different values
for these two attributes, it would be confusing.
The URI reference
http://example.org/simpleTypes#adultAge can then be used to refer
to the datatype.
In the terminology of [RFC 3986],
the URI http://example.org/simpleTypes#adultAge
identifies a secondary resource. When
http://example.org/simpleTypes is retrieved
as an XML Schema document, with mimetype application/xml,
this may be taken as
a
shorthand
pointer
from the [XPointer
Framework].
This identifies a view on the XML representation of the primary resource
being the XML element with the matching @id attribute.
When used in RDF (see
[RDF Concepts], this URI reference
may be understood with the URI
http://example.org/simpleTypes
as identifying the schema, and the URI
http://example.org/simpleTypes#adultAge
as identifying the datatype itself, a resource defined
or described by the representation identified
by the application/xml retrieval.
It is preferred that no targetNamespace
is given in the schema for this usage.
If there is no @id attribute
with the given name,
the
[XPointer
Framework]
is clear that this is an error:
If no element information item is identified by a shorthand pointer's
NCName, the pointer is in error.
Our example RDF is:
eg:membersAge rdfs:range <http://example.org/simpleTypes#adultAge> .
_:aMember eg:name "Jane Doe" .
_:aMember eg:membersAge "24"^^<http://example.org/simpleTypes#adultAge> .
Or:
eg:membersAge rdfs:range egdt:adultAge .
_:aMember eg:name "Jane Doe" .
_:aMember eg:membersAge "24"^^egdt:adultAge .
As a further example, a club which has members of all ages,
but wishes to have a class of its adult members, could use an OWL expression
like the following (in the
[OWL Abstract Syntax]:
Class(AdultMembers
insersectionOf(
Members
Restriction(eg:membersAge, allValuesFrom(egdt:adultAge)) ) )
When referring to arbitrary user defined datatypes
in arbitrary XML Schema, the
[XSCD] solution is appropriate.
When an
RDF or OWL author or tool
is writing an XML Schema for use with an RDF/XML document,
the @id solution may be preferred.
Two different authors publishing the same information on the
Semantic Web may make different syntactic choices. They then say
the same thing in different ways. This is seen most clearly when
the two documents entail one another as determined by the
[RDF Semantics] or
[OWL Semantics].
One aspect of the syntactic choices facing an author is which
datatypes to use. Even if they use only the built in
[XML SCHEMA2] simple types, there are non-trivial choices, and
different authors may legitimately choose different datatypes. This
section addresses the issue of how implementations of
[RDF Semantics] and
[OWL Semantics] should allow for the different choices of
datatype made by different authors.
What is the relationship between the value spaces of the various
XML Schema built-in simple types when used within RDF and OWL?
Or in other words, when do two literals, which are written down
differently, refer to the same value. For example,
"10"^^xsd:integer and "010"^^xsd:integer
both denote the integer ten.
The most appropriate solution is
that all
primitive XML Schema Datatypes
are treated as having disjoint value spaces.
This
approach is both easy to understand,
and easy to implement.
Formally, in a unary datatype group, value spaces of primitive base
datatypes are required to be defined as disjoint with
each other. For instance, if the value space datatype D1 is a subset of that of the
datatype D2, then D1 and D2 can not be both primitive base datatypes
in a unary datatype group.
In discussing the examples, we presented pairs of literals which
denoted the same value. This relationship of denoting the same
value forms an equivalence relation, which we will write as
~; it is conventionally written as '='
and called equality. It is reflexive, symmetric and transitive.
In terms of the
[RDF Semantics]
(see appendix A.1)
the equivalence relation ~ can
be constructed from the interpretation function IL, in the
following way:
~ = { <x,y> : IL(x)=IL(y), for any x, y ∈ LV }
In terms of
[OWL Semantics] (see appendix A.2), this can be constructed in terms of the
interpretation function ED as:
~ = { <x,y> : ED(x)=ED(y), for any x, y ∈ LV }
A key term we will use in the following examples, is primitive base datatype in a
type system. A recursive definition is:
- Each
built in primitive datatype is its own primitive base
datatype.
- The primitive base datatype of a derived
simple type is the primitive base datatype of its base
datatype.
In other words, the primitive base datatype of a type system is
found by walking up the
restriction tree until reaching a primitive
type. Note that the concept of primitive base datatypes in a type
system is slightly different from the concept of primitive base
datatypes in a unary datatype group.
This is because it is possible that a primitive base datatype of a
type system is not in a datatype map, but its derived datatypes
are. For instance, in Example_B,
xsd:integer is a primitive base datatype in the unary datatype
group G1.
We give two sets of examples.
The first set of examples, depend on comparisons where
the primitive base datatype
is the same. The second set
where the primitive base datatype is not. However,
the second set are intended to be slightly counter-intuitive,
and to illustrate limitations in this approach to comparing
typed literals.
Each example is presented in two ways:
- As a pair of literals which may, or may not, denote the same
value.
- As a possible entailment. Technically the intended entailment
is a D-entailment,
in terms of
[RDF Semantics], or an OWL Full entailment in terms of the
[OWL Semantics]. Similar, slightly longer, OWL DL entailments could be
constructed, illustrating the same issues.
It is uncontested that in
[XML SCHEMA2] a datatype derived
by
restriction refers to a subset of the values of its base
datatype, and not to different values (see
[XML SCHEMA2]).
Hence, two typed literals whose type have the same primitive
base datatype, and whose lexical forms are equivalent, are
equal.
In addition,
[RDF Semantics] explicitly sanctions identification of RDF
plain literals without language tags with corresponding typed
literals with datatype xsd:string.
As a first example "15"^^xsd:byte and
"15.0"^^xsd:decimal both denote the same value,
fifteen. This follows because xsd:byte has primitive
base datatype xsd:decimal.
This licenses the following entailment:
eg:Jane eg:age "15"^^xsd:byte .
entails
eg:Jane eg:age "15.0"^^xsd:decimal .
The same result holds for two types both of which have primitive
base datatype decimal. For example "15"^^xsd:byte and
"15"^^xsd:nonNegativeInteger both denote fifteen, and
the entailment:
eg:Jane eg:age "15"^^xsd:nonNegativeInteger .
entails
eg:Jane eg:age "15"^^xsd:byte .
Note that xsd:byte is not derived from
xsd:nonNegativeInteger, or vice versa, even with
intermediate steps.
xsd:language has primitive base datatype
xsd:string. Thus "en-US"^^xsd:language
and "en-US"^^xsd:string denote the same value, and the
following entailment holds:
eg:doc dc:language "en-US"^^xsd:language .
entails
eg:doc dc:language "en-US"^^xsd:string .
However, despite the language identifier being case insensitive
according to
[RFC 3066], this case insensitivity is not represented in the
datatype, so that "en-US"^^xsd:language and
"en-us"^^xsd:language denote different values and we
have the following non-entailment:
eg:doc dc:language "en-US"^^xsd:language .
does not entail
eg:doc dc:language "en-us"^^xsd:language .
The
[RDF Semantics] says
(in an informative section):
the value space and lexical-to-value
mapping of the XSD datatype xsd:string
sanctions the identification of typed literals with plain literals
without language tags for all character strings which are in the
lexical space of the datatype, since both of them denote the
Unicode character string which is displayed in the literal;
Thus "en-US"^^xsd:string denotes the same as the
plain literal "en-US", and the following two
entailments hold:
eg:doc dc:language "en-US"^^xsd:string .
entails
eg:doc dc:language "en-US" .
eg:doc dc:language "en-US"^^xsd:language .
entails
eg:doc dc:language "en-US" .
When the two typed literals being compared have different
primitive base datatypes,
all the values are assumed
to be different, and entailments do not follow, even
when this is counterintuitive. The
number one for instance can be a float, a double, or a decimal.
Since they all have different primitive base datatypes,
these are all different.
A human age is conventionally given as an integer (number of
years, except for babies). but a float is a plausible alternative
representation. On April 7th 2004,
Jeremy was forty,
"40"^^xsd:integer has a different primitive
basetype to
"40"^^xsd:float, so that, they are not equal
and:
eg:JeremyCarroll eg:ageInYears "40"^^xsd:integer .
does not
entail
eg:JeremyCarroll eg:ageInYears "40"^^xsd:float .
Similarly, float and double
are different primitive base datatypes, and so
superficially similar values,
such as
"1.3"^^xsd:float
and
"1.3"^^xsd:decimal
are different, and:
eg:car eg:engineSizeInLitres "1.3"^^xsd:decimal .
does not
entail
eg:car eg:engineSizeInLitres "1.3"^^xsd:float .
As with float and decimal,
neither float or double is derived from the other.
Thus,
"40"^^xsd:double and "40"^^xsd:float
are treated as not equal, and:
eg:JeremyCarroll eg:ageInYears "40"^^xsd:double .
does not
entail
eg:JeremyCarroll eg:ageInYears "40"^^xsd:float .
Similarly:
eg:car eg:engineSizeInLitres "1.3"^^xsd:double .
does not
entail
eg:car eg:engineSizeInLitres "1.3"^^xsd:float .
Similarly, the two types string
and anyURI, are distinct
primitive base datatypes. So that,
despite superficial similarities,
"http://www.example.org/doc"^^xsd:string
is different from
"http://www.example.org/doc"^^xsd:anyURI, and:
eg:doc dc:identifier "http://www.example.org/doc"^^xsd:anyURI .
does not entail
eg:doc dc:identifier "http://www.example.org/doc"^^xsd:string .
The final case where the value spaces of two XML Schema simple
types appear to the same is for
xsd:hexBinary and
xsd:base64Binary. For both the value space is described
as: the set of finite-length sequences of binary octets
. For
instance the binary sequence of two octets (00001111 10110111)
(i.e. the 16-bit integer 4023) can be written in hexadecmial as
0FB7. In base64 encoding
[RFC 2045] this same sequence of two octets is represented as
D7c=.
Despite this, the two types hexBinary
and base64Binary, are distinct
primitive base datatypes. So that,
"0FB7"^^xsd:hexBinary
is different from
"D7c="^^xsd:base64Binary, and:
eg:doc eg:checkSum "0FB7"^^xsd:hexBinary .
does not entail
eg:doc eg:checkSum "D7c="^^xsd:base64Binary .
While some of the non-entailments shown may be counterintuitive,
it is possible to use SPARQL to
query a graph and retrieve literal values that
are similar even if not derived from the same primitive base
type.
For example, related to examples 3H and
3K. Given a graph including the
following three triples:
eg:car eg:engineSizeInLitres "1.3"^^xsd:double .
eg:car eg:engineSizeInLitres "1.3"^^xsd:decimal .
eg:car eg:engineSizeInLitres "1.3"^^xsd:float .
The following
[SPARQL] query will match all three.
SELECT ?size
WHERE { eg:car eg:engineSizeInLitres ?size .
FILTER (?size = 1.3) . }
In the current
[SPARQL] working draft, the mapping from the typed
literal, as a syntactic object, to its corresponding value, is done as
part of the operation of the = operator in the above query, rather
than
as part of say a D-interpretation from [RDF Semantics].
This mapping is specified in
[Functions & Operators], and, being strongly
typed, is not identical with that specified in [RDF Semantics]
A different approach, better embedded in [RDF Semantics], could enable
meaningful mappings among values from different datatypes.
This could give better foundations for operations such as the type
promotion of the XML Path Language 2.0 [XPath 2.0] and the = operator in
SPARQL mentioned in Section 3.5. A quick sketch is that we extend the
RDF D-interpretation to support value approximate maps, as follows:
[Definition:] A value approximate map mapsTo
is a partial mapping from typed literals to typed literals.
An example value approximate mapping is
"1.3"^^xsd:decimal owlx:mapsTo "1.3"^^xsd:float .
[Definition:] Given a datatype map D and a value approximate map mapsTo, the approximate equality aeq is defined as follows:
- aeq(
"s1"^^u1,
"s2"^^u2)=true if
L2S(D(u1))(s1) =
L2S(D(u2))(s2) or if mapsTo("s1"^^u1)="s3"^^u2 and L2S(D(u2))(s3) =
L2S(D(u2))(s2),
- aeq(
"s1"^^u1,
"s2"^^u2)=false otherwise.
Note that, according to the above definition, aeq("s1"^^u1,
"s2"^^u2)=true does not imply that "s1"^^u1 and
"s2"^^u2 are interpreted as the same value (L2S(D(u1))(s1) =
L2S(D(u2))(s2)). The approximate equality is different from equality and is not necessarily symmetric, depending on the corresponding value approxiate map. The unsymmetry is needed to support e.g. type promotions in the XML Path Language 2.0 [XPath 2.0]. Note that notion of value approxiate mappings is very general - it does not disallow having symmetric mappings between two typed literals. In Example 3N, one can also specify a value approximate mapping from "1.3"^^xsd:float to "1.3"^^xsd:decimal to make the mappings between the two typed literals symmetric.
To sum up, applications can specify a value approximate map mapsTo and make use of the approximate equality aeq for their purposes.
The [RDF Semantics]
Recommendation discourages the use of the
xsd:duration datatype (see [XML SCHEMA2]). It says:
[Some] built-in XML Schema datatypes are unsuitable for various
reasons, and SHOULD NOT be used:
xsd:duration does not have a well-defined value space
(this may be corrected in later revisions of XML Schema datatypes,
in which case the revised datatype would be suitable for use in RDF
datatyping);
The underlying difficulty is the impossibility of an unequivocal
answer to the question "How many days in a month?" This has proved
problematic in other applications of XML Schema datatypes. The
XQuery and XSLT Working Groups have a proposed solution. They
derive two new datatypes,
xdt:yearMonthDuration and
xdt:dayTimeDuration from
xsd:duration, sidestepping the unanswerable question.
In
section 10.2 of [Functions & Operators] we
read:
[Definition:] xdt:yearMonthDuration is derived from
xs:duration by restricting its lexical representation
to contain only the year and month components. The value space of
xdt:yearMonthDuration is the set of
xs:integer month values. The year and month components
of xdt:yearMonthDuration correspond to the Gregorian
year and month components defined in section 5.5.3.2 of [ISO 8601], respectively.
and
[Definition:] xdt:dayTimeDuration is derived from
xs:duration by restricting its lexical representation
to contain only the days, hours, minutes and seconds components.
The value space of xdt:dayTimeDuration is the set of
fractional second values. The components of
xdt:dayTimeDuration correspond to the day, hour,
minute and second components defined in Section 5.5.3.2 of [ISO 8601], respectively.
These two new datatypes are suitable for use with RDF and OWL.
(Note that they are not yet recommended, since F&O is still in
Working Draft).
For much data on the Semantic Web
a motivation for providing type information
is to permit the use of the data
by engineering applications, and interoperation
between engineering applications.
Most such data will be marked up using the numeric types
from XML Schema.
Loss in
precision or unexpected changes in values due to automatic type
conversion could be problematic in an engineering environment.
In the engineering domain there are
three important
types of usage for numerics: count, measurement,
and constant.
- count
-
A count is an integer representing essentially the
cardinal number for a set of things classified by some set of tests.
An example would be the count of packages of candy available for
shipment. A count is an exact number. Tests may include
measurements, but a count is not an approximation of a sum of
these measurements nor is it a sum of the approximation of these
measurements. A type such as
xsd:integer
or a type derived from xsd:integer is appropriate for
counts.
- measurement
-
A measurement is an inexact numeric value (usually represented as a
real) produced by some measurement method. This value indicates a
value range which includes the actual value. The actual value is
unknowable, but more precise measurement methods can reduce the
range of uncertainty. The precision or uncertainty is
usually included with the measurement value. Either implicitly
using significant figures or explicitly using a separate property
value such as error range.
Either the
xsd:float or xsd:double
datatypes are appropriate for measurement, but it should be noted
that these do not include a precision or uncertainity, which should
be included as the value of a separate property.
[XML SCHEMA2]
explicitly states for xsd:decimal
that, "Precision is not
reflected in this value space, the number 2.0 is not distinct from
the number 2.00."
- constant
-
A constant is an exact value used in computation. It may or may not
be possible to express exactly as a numeric. A millimeter is exactly
0.001 meters, but Pi is not 3.14159.
Often an
xsd:decimal will be more appropriate than
an xsd:float or xsd:double for expressing
a constant.
As an example of a measurement with an error range
to indicate a weight in the interval (73.0Kg, 73.2Kg).
eg:JeremyCarroll eg:weight _:w .
_:w eg:units "kilogram" .
_:w eg:value "73.1"^^xsd:float .
_:w eg:errorRange "0.1"^^xsd:float .
These different usages suggest
some potential needs and concerns for a type system
underlying this.
-
Because the value spaces for these types
are different, measurements are disjoint from counts and constants.
-
Some means of capturing precision or error/uncertainty is needed
for measurement values.
- Some means is desirable for writing down
constants that cannot be expressed precisely in numeric form.
The first of these issues will generally be reflected
in the use of xsd:integer for counts,
xsd:float and xsd:double for
measurements, and xsd:decimal for constants.
The second issue concerning precision of measurements,
must be addressed at the modelling level by
using objects to state precision or error
properties for measurements. This is not a bad approach,
in any case, since
there are often other properties or metadata associated with a
measurement.
For the third issue, concerning some constants, no
solution is offered.
Evan Wallace is the author of Section 5.
Evan Wallace,
Ashok Malhotra,
Pat Hayes,
Dave Peterson,
Dave Reynolds,
Michael Sperberg-McQueen and Ralph Swick
contributed useful reviews.
- [RDF-SEMANTICS]
- RDF
Semantics, Patrick Hayes, Editor, W3C Recommendation, 10
February 2004, http://www.w3.org/TR/2004/REC-rdf-mt-20040210/ .
Latest version available
at http://www.w3.org/TR/rdf-mt/ .
- [RDF
Primer]
- RDF
Primer, Frank Manola and Eric Miller, Editors, W3C
Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-rdf-primer-20040210/ . Latest version available at
http://www.w3.org/TR/rdf-primer/ .
- [RDF
Concepts]
- Resource
Description Framework (RDF): Concepts and Abstract
Syntax, Graham Klyne and Jeremy J. Carroll, Editors, W3C
Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/ . Latest version available
at http://www.w3.org/TR/rdf-concepts/ .
- [RDF
Syntax]
- RDF/XML
Syntax Specification (Revised), Dave Beckett, Editor,
W3C Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-rdf-syntax-grammar-20040210/ .
Latest
version available at http://www.w3.org/TR/rdf-syntax-grammar/
.
- [N-triples]
- RDF Test
Cases, Jan Grant and Dave Beckett, Editors, W3C
Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-rdf-testcases-20040210/ . Latest version available
at http://www.w3.org/TR/rdf-testcases/ .
- [OWL Abstract Syntax]
- [OWL
Semantics]
- OWL Web
Ontology Language Semantics and Abstract Syntax, Peter
F. Patel-Schneider, Patrick Hayes, and Ian Horrocks, Editors, W3C
Recommendation 10 February 2004,
http://www.w3.org/TR/2004/REC-owl-semantics-20040210/ . Latest version available
at http://www.w3.org/TR/owl-semantics/ .
- [OWL Guide]
- OWL Web
Ontology Language Guide, Michael K. Smith, Chris Welty,
and Deborah L. McGuinness, Editors, W3C Recommendation, 10 February
2004, http://www.w3.org/TR/2004/REC-owl-guide-20040210/ . Latest version available at
http://www.w3.org/TR/owl-guide/ .
- [OWL Test Cases]
-
OWL Web Ontology Language Test Cases
,
Jeremy J. Carroll and Jos De Roo, Editors.
W3C Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-owl-test-20040210/.
Latest version
available at http://www.w3.org/TR/owl-test/.
- [XPointer Framework]
- XPointer Framework
, Paul Grosso, Eve Maler, Jonathan Marsh and Norman
Walsh, Editors, W3C Recommendation, 25 March 2003,
http://www.w3.org/TR/2003/REC-xptr-framework-20030325/ . Latest version available
at http://www.w3.org/TR/xptr-framework/ .
- [XML-SCHEMA1]
- XML Schema
Part 1: Structures, Second Edition, W3C Recommendation,
World Wide Web Consortium, Henry S. Thompson,
David Beech,
Murray Maloney
and Noah Mendelsohn
(editors), 28 October 2004. This version is
http://www.w3.org/TR/2004/REC-xmlschema-1-20041028/. The latest version is
available at http://www.w3.org/TR/xmlschema-1/.
- [XML-SCHEMA2]
- XML Schema
Part 2: Datatypes, Second Edition, W3C Recommendation,
World Wide Web Consortium, Paul V. Biron and Ashok Malhotra
(editors), 28 October 2004. This version is
http://www.w3.org/TR/2004/REC-xmlschema-2-20041028/. The latest version is
available at http://www.w3.org/TR/xmlschema-2/.
- [RFC 2045]
- N. Freed and N. Borenstein. RFC 2045: Multipurpose Internet
Mail Extensions (MIME) Part One: Format of Internet Message
Bodies. 1996. Available at: http://www.ietf.org/rfc/rfc2045.txt
- [RFC
3986]
- T. Berners-Lee, R. Fielding, and L. Masinter. Uniform
Resource Identifiers (URI): Generic Syntax. IETF RFC 3986. See
http://www.ietf.org/rfc/rfc3986.txt.
- [RFC 3066]
- H. Alvestrand, ed. RFC 3066: Tags for the Identification of
Languages 2001. Available at: http://www.ietf.org/rfc/rfc3066.txt
- [ISO 8601]
- ISO (International Organization for Standardization).
Representations of dates and times, 2000-08-03. Available
from: http://www.iso.ch/
- [ISO 11404]
-
ISO (International Organization for Standardization).
Language-independent Datatypes. Available
from: http://www.iso.ch/
- [UNICODE]
- The Unicode Standard, Version 3, The Unicode
Consortium, Addison-Wesley, 2000. ISBN 0-201-61633-5, as updated
from time to time by the publication of new versions. (See http://www.unicode.org/unicode/standard/versions/
for the latest version and additional information on versions of
the standard and of the Unicode Character Database).
- [Functions & Operators]
- XQuery
1.0 and XPath 2.0 Functions and Operators, Ashok
Malhotra, Jim Melton and Norman Walsh (editors), World Wide Web
Consortium Working Draft, work in progress, 15 September 2005. This
version of Functions and Operators is
http://www.w3.org/TR/2005/WD-xpath-functions-20050915/. The
latest version
of Functions and Operators is at
http://www.w3.org/TR/xpath-functions/.
- [XPath 2.0]
- XML Path Language (XPath) 2.0, Anders Berglund, Scott Boag, Don Chamberlin, Mary F. Fernández, Michael Kay, Jonathan Robie and Jérôme Siméon (editors), W3C Candidate Recommendation 3 November 2005. This
version of XML Path Language (XPath) is
http://www.w3.org/TR/2005/CR-xpath20-20051103/. The
latest version
of XML Path Language (XPath) is at
http://www.w3.org/TR/xpath20/.
- [SPARQL]
- SPARQL
Query Language for RDF, Eric Prud'hommeaux and Andy
Seaborne, Editors, W3C Working Draft 21 July 2005,
http://www.w3.org/TR/2005/WD-rdf-sparql-query-20050721/ . Latest version
available at http://www.w3.org/TR/rdf-sparql-query/ .
- [XSCD]
- XML Schema
Component Designators, Mary Holstege and Asir S.
Vedamuthu, Editors, W3C Working Draft, 29 March 2005,
http://www.w3.org/TR/2005/WD-xmlschema-ref-20050329/. Latest version available
at http://www.w3.org/TR/xmlschema-ref/ .
- [Pan 2004]
- Description Logics:
Reasoning Support for the Semantic Web, Jeff Z.Pan, PhD
Thesis, School of Computer Science, The University of Manchester,
2004.
- [PH 2005]
- OWL-Eu: Adding Customised Datatypes into OWL, Jeff Z.Pan and Ian Horrocks. In Proc. of the Second European Semantic Web Conference (ESWC 2005), pages 153-166, 2005. An extended version appears in the Journal of Web Semantic, 4(1). An online version is available at http://www.websemanticsjournal.org/ps/pub/2005-24.
- [N3]
-
Primer: Getting into RDF & Semantic Web using N3
Tim Berners-Lee, Dan Connolly
According to
[RDF Semantics],
(see section 5.1),
RDF allows the use of datatypes defined by any
external type systems, e.g., the XML Schema type system, which
conform to the following specification.
[Definition:] In RDF, a datatype d
is characterised by a value space, V(d), which is a non-empty set,
a lexical space, L(d), which is a non-empty set of Unicode
strings, and a total mapping L2V(d) from the lexical space to the
value space.
This specification allows the use of non-list XML Schema simple
types as datatypes in RDF.
[Definition:]
All literals have a lexical form being a Unicode [UNICODE] string. Typed literals are of
the form "v"^^u, where "v" is a Unicode
string, called the lexical form of the typed literal, and
u is a URI reference of a datatype. Plain literals have a
lexical form and optionally a language tag as defined by
[RFC-3066], normalized to
lowercase.
Boolean is a datatype with value space
{true,false}, lexical space {"true",
"false","1","0"} and lexical-to-value mapping
{"true"→true, "false"→false, "1"→true, "0"→false}.
"true"^^xsd:boolean is a typed literal, while
"true" is a plain literal.
The associations between datatype URI references (e.g.,
xsd:boolean) and datatypes (e.g., boolean) can be provided by
datatype maps defined as follows.
[Definition:] A datatype map D
is a partial mapping from datatype URI references to datatypes.
An RDFS-interpretation w.r.t. a datatype map D can be defined as
follows.
[Definition:] Given a datatype
map D, an RDFS D-interpretation I of a vocabulary V is any
RDFS-interpretation of V∪{u |∃d.D(u)=d} which introduces (i) a
distinguished subset LV of IR, called the set of literal
values, which contains all the plain literals in V, and (ii) a
mapping IL from literals in V into IR, and satisfies the following
extra conditions:
- LV = ICEXT(rdfs:Literal).
- For any plain literal pl∈V, IL(pl) = pl.
- For each pair <u,d> where d = D(u),
- I(u) ∈ ICEXT(rdfs:Datatype),
- there exists d∈IR s.t. I(u) = d,
- ICEXT(d) = V(d) ⊆ LV,
- for
"s"^^u'∈V, I(u') = d, if s∈L(d), then
IL("s"^^u') = L2S(d)(s); otherwise,
IL("s"^^u') ∈ IR \ LV.
- If d ∈ ICEXT(rdfs:Datatype), then <d, I(rdfs:Literal)> ∈
IEXT(rdfs:subClassOf).
OWL Full datatyping follows the RDF Semantics as above;
OWL DL datatyping is specified
in
section 3.1 of the
[OWL Semantics], as follows.
The fundamental difference between RDF datatyping and OWL DL
datatyping is the relationship between datatypes and classes. In
OWL DL, datatypes are not classes, and object and datatype
domains are disjoint with each other.
OWL allows different OWL reasoners to provide different
supported datatypes.
[Definition:] Given a datatype map D, a
datatype URI reference u is called a supported datatype URI
reference w.r.t. D if there exists a datatype d such that
<u,d>∈D (in this case, d is called a supported
datatype w.r.t. D); otherwise, u is called an unsupported
datatype URI reference w.r.t. D.
OWL provides the use of so called enumerated datatypes, which
are built using literals.
[Definition:] Let y1, ...,
yn be literals. An enumerated datatype is of the
form oneOf(y1, ..., yn).
An OWL DL D-interpretation w.r.t. a datatype map D can be
defined as follows.
[Definition:] An OWL DL datatype
interpretation w.r.t. to a datatype map D is a pair (LV,ED),
where the datatype domain LV
(only) contains the value spaces for each datatype in D
and PL
(the value
space for plain literals, i.e., the union of the set of Unicode
strings and the set of pairs of Unicode strings and language tags)
and ED is a datatype interpretation function, which has to satisfy
the following conditions:
- LV = ED(rdfs:Literal).
- For any plain literal pl, ED(pl) = pl ∈ PL.
- For each supported datatype URIref u (let d = D(u)):
- ED(u) = V(d) ⊆ LV,
- if s ∈ L(d), then ED(
"s"^^u) = L2V(d)(s);
otherwise, ED("s"^^u) is not defined.
- For each unsupported datatype URIref u, ED(u) ⊆ LV and
ED(
"s"^^u) ∈ ED(u).
- Each enumerated datatype oneOf(y1, ...,
yn) is interpreted as {ED(y1)}
∪ ...
∪ {ED(yn)}.
Note that here we simplify the presentation by using ED as the
interpretation function for both datatype URI references and
literals, while [OWL Semantics]
uses EC for datatypes URI references and L for literals.
In OWL Full, the disjointness restriction between
object and datatype domains is not required.
[Pan 2004] and [PH 2005] present a scheme of
integrating a large family of decidable Description Logics
(including SHOIN, the underpinning of OWL DL) with unary
datatype groups, so as to support user defined datatypes. A
combined DL is decidable if the unary datatype group is conforming.
A conforming unary datatype group is equipped with a decision
procedure for the satisfiability problem of finite conjunctions
over supported datatypes.
[Definition:] A unary datatype
group G is a triple <D,B,dom>, where D is a datatype map,
B is the set of primitive base datatype URI references in G and dom
is the declared domain function. We call S the set of supported
datatype URI references, i.e., for each u∈S, D(u) is defined; we
require B ⊆ S. The declared domain function dom has the following
properties: for each u ∈ S, if u ∈ B, dom(u) = u; otherwise, dom(u)
= v, where v ∈ B. We assume that there exists a datatype URI
reference rdfsx:DatatypeBottom such that D(rdfsx:DatatypeBottom) is
undefined.
Note that in [Pan 2004] datatype
groups allow arbitrary datatype predicates, while here we consider
only datatypes, which can be regarded as unary datatype
predicates.
G1=(D1,B1,dom1) is a
unary datatype group, where
- D1 = {xsd:integer
→ integer, xsd:string
→ string, xsd:nonNegativeInteger →
≥0, xsdx:integerLessThanN →
<N},
- B1 = {xsd:integer, xsd:string},
- dom1 = {xsd:integer
→ xsd:integer,
xsd:string → xsd:string, xsd:nonNegativeInteger
→ xsd:integer, xsdx:integerLessThanN →
xsd:integer}.
According to D1, we have S1 = {xsd:integer,
xsd:string, xsd:nonNegativeInteger, xsdx:integerGreaterThanN},
hence we have B1 ⊆ S1. Note that the value
space of <N is
V(<N) = {i ∈ V(integer) | i
< L2S(integer)(N)} and by
<N we mean there exists a built-in
datatype <N for each integer
L2S(integer)(N).
In a unary datatype group, datatype expressions can be used to
represent user defined datatypes.
[Definition:] Let G be a unary
datatype group, the set unary datatype expressions for G,
abbreviated Dexp(G), is inductively defined as follows:
- let u be a datatype URI reference, u ∈ DPexp(G);
- let u be a datatype URI reference, its (relativised) negation
not(u) ∈ DPexp(G);
- let y1, ..., yn be literals, the
enumerated datatype oneOf(y1, ..., yn) ∈
DPexp(G);
- for any p,q ∈ DPexp(G), their conjunction and(p,q) ∈
DPexp(G);
- for any p,q ∈ DPexp(G), their disjunction or(p,q) ∈
DPexp(G).
The XML Schema user defined datatype humanAge defined in
[Example 1A] can be represented by the
following unary datatype expression:
and(xsd:nonNegativeInteger,
xsdx:integerLessThan150).
[Definition:] A datatype
interpretation of a unary datatype group G = (D,B,dom) is a
pair (LV,ED), where the datatype domain LV is a non-empty set and
ED is a datatype interpretation function that has to satisfies the
following conditions:
- ED(rdfs:Literal)=LV and ED(rdfsx:DatatypeBottom)} = ∅.
- For each plain literal pl, ED(pl) = pl ∈ PL and PL ⊆ LV.
- For any two primitive
base datatype URI references u1 and u2,
ED(u1) ∩ ED(u2) = ∅.
- For each supported datatype URI reference u ∈ S (let d = D(u)):
- ED(u) = V(d) ⊆ V(D(dom(u))) ⊆ LV, L(D(u)) ⊆ L(D(dom(u)) and
L2S(D(u)) ⊆ L2S(D(dom(u)),
- if s ∈ L(d), then ED(
"s"^^u) = L2V(d)(s);
otherwise, ED("s"^^u) is not defined.
- For each unsupported datatype URI reference u ∉ S, ED(u) ⊆ LV
and
"s"^^u ∈ ED(u).
The datatype interpretation function ED can be extended to provide
semantics to unary datatype expressions as follows:
- Relativised negations: if u ∈ S \ D, ED(not(u)) = ED(dom(U)) \
ED(u); otherwise, ED(not(u)) = LV \ ED(u).
- Enumerated datatypes: ED(oneOf(y1, ...,
yn)) = {ED(y1)}
∪ ... ∪
{ED(yn)}.
- Conjunctions: ED(and(p,q)) = ED(p) ∩ ED(q).
- Disjunctions: ED(or(p,q)) = ED(p) ∪ ED(q).
[PH 2005] shows that we can combine
any decidable DL (including SHOIN, the underpinning of OWL DL)
that provides the conjunction and bottom constructors with a
conforming unary datatype group and the combined DL is still
decidable.
C.1 Typos etc.
'Semanitcs' in introduction.
Updated syntax for XML Schema Component Designators.
Deleted broken link from description of
[ISO 11404]. Added reference to ISO homepage instead.
C.2 Discussion removal
The earlier draft was a discussion document.
This note is not intended as such, so some issues,
particularly to do with the interactions between various
standards, recommendations, RFCs etc. has been removed.
Removed
DAML+OIL solution.
Removed
true values solution.
Removed
XPath eq solution.
Moved OWL syntax example from DAML+OIL section to the end of
id section.
In the
XML Schema Component Designator section:
- Discussion of relationship between XSCD, XPointer
and RFC 3023 has been removed.
- Discussion about the exact semantics of an
XSCD fragment has been removed.
Deleted words "(less contentious)" and "Moreover, "
from id solution.
Changed
XML Schema Component Designator section, to indicate that
XSCD is a good practice. In particular, see last paragraph.
Changed
discussion subsection on user defined datatypes
to suggest that both the (remaining) solutions are appropriate,
and have no discussion. Changed title to Suggested Practice.
Discussion of
harder examples cut down
substantially, since these are all trivially
non-entailments with the agreed semantics.
Removed EDITORS' OPINION notes.
Deleted all uses of the word "derivation" in section 1.3 since it has
caused confusion. Added links to the XML Schema document for union, list and restriction,
to make it clear that the intended concept is "derivation"
as defined by that document.
Added brief discussion
of target namespace after example 2A
providing further examples example 2B and
example 2C.
Scoped this document to not
address "XML Schema [...] assembled from multiple schema
documents".
Added reference [XML SCHEMA1].
In the
XML Schema Component Designator section: added more extended discussion of target namespace issue;
and
added example XSCD for schema with target namespace.
Added text showing how the
@id solution does
comply with the secondary resource concept from RFC 3986,
when read in conjunction with RDF Concepts, XPointer and XML Schema.
C.4 Restructuring of section 3
Reordered subsections in section 3,
deleting
old
3.5,
3.6 and 3.7, and ordering the
remaining subsections as follows:
3.1,
3.4,
3.2, 3.3. Followed by renumbering.
Text discussing examples has changed, and the change tracking
is not detailed.
Moved definition of
primitive base datatype
from the examples
subsection to the
formal analysis subsection.
Deleted references to the examples
from the new section 3.2 (was
3.4)
Added example
SPARQL query, to show how
to use = in SPARQL to compare across the type hierarchy.
Added an updated discussion of mapsTo.
C.5 Other changes
Added
further acknowledgements.
Updated reference to RFC 2396 to be to RFC 3986
Updated
Table of Contents
Removed unused
references.
Updated versions of
W3C WD's in references.
