Latest editors' draft (CVS copy): http://www.w3.org/2001/sw/BestPractices/XSCH/xsch-sw/
Copyright ©2004 W3C® (MIT, ERCIM, Keio), All Rights Reserved. W3C liability, trademark and document use rules apply.
The RDF and OWL Recommendations use the simple types from XML
Schema. This document discusses three questions left unanswered by
these Recommendations: What 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?
This is an editors' draft for discussion by the SWBPD WG and other interested parties. The remainder of this status section is fictitious.
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 intended to be a part of a future W3C Working Group Note from the Semantic Web Best Practices and Deployment Working Group, part of the W3C Semantic Web Activity.
This document is intended for public discussion: it poses two
questions to do with the use of XML Schema simple types within the
Semantic Web, and sketches multiple answers. None of these
suggestions have any recorded consensus around them. After public
feedback, possibly including additional answers to these questions,
the WG, in co-ordination with other W3C WGs hopes to agree on a
single answer to each of the two questions. This will then form the
basis of a second publication indicating a suggested best
practice
.
In addition, we update the Semantic Web community concerning on-going progress about the duration datatype.
We particularly seek feedback reporting on implementation experience on these issues.
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.
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]. Key ideas of RDF datatyping and OWL datatyping are summarized in Section 1. Related Datatype Formalisms.
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].
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:
@@@todo
Some questions about XML Schema datatypes in the Semantic Web are not directly answered by the published W3C Recommendations. This document considers three of them:
xsd:duration, which are reported
in [RDF Semantics].Before we go into details of these problems, we briefly summarize related datatype formalisms.
[XML SCHEMA2] defines facilities for defining simple types to be used in XML Schema as well as other XML specifications.
[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 by derivation from primitive or existing derived datatypes by the following three means:
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>
According to [RDF Semantics], 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 an non-empty set, a lexical space, L(d), which is an 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:
"s"^^u'∈V, I(u') = d, if s∈L(d), then
IL("s"^^u') = L2S(d)(s); otherwise,
IL("s"^^u') ∈ IR \ LV.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 = PL∪∪for each
supported datatype URIref u w.r.t. DD(u) (PL is 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:
"s"^^u) = L2V(d)(s);
otherwise, ED("s"^^u) is not defined."s"^^u) ∈ ED(u).∪ ...
∪ {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.
As far as OWL Full is concern, the disjointness restriction about object and datatype domains is not required.
[Pan 2004] presents 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
→ integer, xsd:string
→ string, xsd:nonNegativeInteger →
≥0, xsdx:integerLessThanN →
<N},→ 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 of G unary datatype expressions, abbreviated Dexp(G), is inductively defined as follows:
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).
@@@ todo formatting, e.g. above should be centered and ???
[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:
"s"^^u) = L2V(d)(s);
otherwise, ED("s"^^u) is not defined."s"^^u ∈ ED(u).The datatype interpretation function ED can be extended to provide semantics to unary datatype expressions as follows:
∪ ... ∪
{ED(yn)}.The reader is referred to [Pan 2004] for more details about conforming unary datatype groups and how to combine them with Description Logics.
[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 an 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.
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?
OWL was explicitly derived from the earlier [DAML+OIL] ontology language. This did include support for user defined simple XML Schema types, as seen in the definition of Senior in the example file ontology (http://www.daml.org/2001/03/daml+oil-ex). The solution is most clearly articulated by [Patel-Schneider]:
OWL can use XML Schema non-list simple types defined at the top level of an XML Schema document and given a name, by using the URI reference constructed from the URI of the document and the local name of the simple type.
Thus with the example, the URI reference
http://example.org/simpleTypes#adultAge identifies the
datatype.
This is a non-standard approach to fragIDs, and not in conformance with [RFC 2396], which says:
The semantics of a fragment identifier is a property of the data resulting from a retrieval action, regardless of the type of URI used in the reference. Therefore, the format and interpretation of fragment identifiers is dependent on the media type [RFC2046] of the retrieval result. [...]
A fragment identifier is only meaningful when a URI reference is intended for retrieval and the result of that retrieval is a document for which the identified fragment is consistently defined.
and [RFC 3023] which says:
As of today, no established specifications define identifiers for XML media types. However, a working draft published by W3C, namely "XML Pointer Language (XPointer)", attempts to define fragment identifiers for text/xml and application/xml.
In turn, the [XPointer Framework]
says
of fragments like #adultAge
A shorthand pointer, formerly known as a barename, consists of an NCName alone. It identifies at most one element in the resource's information set; specifically, the first one (if any) in document order that has a matching NCName as an identifier. The identifiers of an element are determined as follows:
If an element information item has an attribute information item among its [attributes] that is a schema-determined ID, then it is identified by the value of that attribute information item's [schema normalized value] property;
If an element information item has an element information item among its [children] that is a schema-determined ID, then it is identified by the value of that element information item's [schema normalized value] property;
If an element information item has an attribute information item among its [attributes] that is a DTD-determined ID, then it is identified by the value of that attribute information item's [normalized value] property.
An element information item may also be identified by an externally-determined ID value.
In short, the XML fragment #adultAge should
identify the XML element with id="adultAge" rather
than the datatype with name="adultAge".
While the [XPointer Framework] is a W3C Recommendation, it is not fully standard since it is not yet endorsed by an IETF RFC updating [RFC 3023]. So while the approach defined in the XPointer Framework for such fragments consisting of barenames does have widespread support, discussion continues. Some other aspects of the XPointer Framework are more contentious within the IETF community.
@@todo simple N3 example
Following XML Schema Component Designators [XSCD] the same example would have URI reference
http://example.org/simpleTypes#xscd(/type(adultAge)).
This approach 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.
This is still at WD stage and has a dependency on the [XPointer Framework] W3C Recommendation, but whose relationship with [RFC 3023] is not yet fully secured.
The resulting URI references cannot be used with the qname abbreviation used in [N3] and [RDF/A], because they end in a ")" which is not an NCNameChar.
[XSCD] refers to such URI references as being:
The canonical schema component designator for this simple type definition
i.e. referring to the definition rather than to the type defined.
@@todo simple N3 example
id AttributeIn section 2.2, we saw that the
RFCs and recommendations concerning fragment IDs in XML schema
document were suggestive (but not definitive) in using those
fragment IDs which match the NCName construction as identifying
elements with the corresponding @id attribute.
An alternative to the Daml+OIL solution is, instead of using the
@name attribute, use the @id attribute.
This involves modifying the schema defining the datatype, our
example would be:
<xsd:schema ...>
<xsd:simpleType id="adultAge" name="adultAge">
<xsd:restriction base="integer">
<xsd:minInclusive value="18">
</xsd:restriction>
</xsd:simpleType>
...
</xsd:schema>
Then we would use the URI reference
http://example.org/simpleTypes#adultAge. as
before.
This depends on the (less contentious) shorthand pointer part of the [XPointer Framework].
Our example RDF is as before:
@@@todo N3
The DAML+OIL solution is non-standard, and suffers from problems such as the non-uniqueness of names within some XML Schema.
The other two solutions are conformant with XPointer, but this is not fully endorsed by the IETF who control the XML mimetype (RFC 3023), which RFC 2396 defers to concerning fragment ID semantics.
The XSCD solution is still at WD stage.
Both the XSCD and the id solutions have the problem that the proposed URI references designate a syntactic thing, rather than the datatype itself. This could be seen as a property of the relevant definitions (XSCD and XPointer) being concerned about representations of resources rather than resources themselves. The URIref potentially can be seen as denoting (in the sense of RDF Semantics) the datatype, and represented by the XML element describing the datatype.
A position combining aspects of all three solutions might be to use id where possible, and once XSCD goes to Rec to also use that, particularly for XML Schema that are not under the control of the RDF or OWL author.
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 are 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.
We give some examples, both ones for which the RDF and OWL Semantics are clear, and ones for which the semantics is not clear.
Each example is presented in two ways:
A key term we will use is primitive base datatype in a type system. A recursive definition is:
In other words, the primitive base datatype of a type system is found by walking up the derivation 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_1C, xsd:integer is a primitive base datatype in the unary datatype group G1.
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:
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:
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:stringsanctions 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:
When the two typed literals being compared have different
primitive base datatypes, the situation is more difficult. The
number one for instance can be a float, a double, or a decimal. Are
these all the same? Is a URI (an xsd:anyURI) a string?
Is a binary blob the same whether it is hex encoded or base64
encoded?
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 Jeremy was forty, is
"40"^^xsd:integer the same as
"40"^^xsd:float, does:
eg:JeremyCarroll eg:ageInYears "40"^^xsd:integer .
entail
eg:JeremyCarroll eg:ageInYears "40"^^xsd:float .
Floats and doubles are defined with value spaces which are not
dense, but heavily influenced by the binary system. Typical decimal
numbers, such as 1.3, do not map neatly into that value space, so
that "1.3"^^xsd:float takes the value that is as close
to 1.3 as possible within the float value space. This is an
approximation. So strictly, as numbers,
"1.3"^^xsd:float is not the same as
"1.3"^^xsd:decimal, but perhaps that is too severe and
unhelpful for application developers. Does:
eg:car eg:engineSizeInLitres "1.3"^^xsd:decimal .
entail
eg:car eg:engineSizeInLitres "1.3"^^xsd:float .
Every value that can be represented as a float can also be
represented as a double, but as with float and decimal, the two
types are derived one from the other. Thus, it can be argued that
"40"^^xsd:double and "40"^^xsd:float are
different, they typically will be implemented differently in a
computer. Thus we can also ask, does:
eg:JeremyCarroll eg:ageInYears "40"^^xsd:double .
entail
eg:JeremyCarroll eg:ageInYears "40"^^xsd:float .
The engine size example is also confusing.
"1.3"^^xsd:float has the value
10905190×2-23, (i.e. approx 1.2999999523) whereas,
"1.3"^^xsd:double has the value
5854679515581644×2-52, (i.e. approx
1.299999999999999822). So we can again ask whether these two typed
literals should be treated as the same value or not. This is only a
rounding error. Does:
eg:car eg:engineSizeInLitres "1.3"^^xsd:double .
entail
eg:car eg:engineSizeInLitres "1.3"^^xsd:float .
It is not entirely clear what the intended values of the
anyURI datatype are.
[RFC 2396] says: A Uniform Resource Identifier (URI) is a
compact string of characters for identifying an abstract or
physical resource.
, so we may choose to think of an
anyURI as essentially the same as the equivalent
xsd:string, or maybe not. Thus we can ask whether
"http://www.example.org/doc"^^xsd:string is the same
or different from
"http://www.example.org/doc"^^xsd:anyURI. Does:
eg:doc dc:identifier "http://www.example.org/doc"^^xsd:anyURI .
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 are 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=. So we can ask whether "0FB7"^^xsd:hexBinary is the
same as "D7c="^^xsd:base64Binary. As an
entailment:
eg:doc eg:checkSum "0FB7"^^xsd:hexBinary .
entail
eg:doc eg:checkSum "D7c="^^xsd:base64Binary .
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 reflexive, symmetric and transitive.
In terms of the
[RDF Semantics] the equivalence classes of ~ can
be constructed from the interpretation function IL, in the
following way:
~ = { X | X = IL-1( lv ) for each lv ∈
LV}
Each X is one of the equivalence classes.
In terms of OWL DL Semantics [OWL Semantics], this can be constructed in terms of the interpretation function ED as:
~ = { X | X = ED-1( lv ) for each lv ∈
LV}
For implementors, the simplest solution is to agree that all primitive XML Schema Datatypes have disjoint value spaces. Thus all the harder examples (examples G through to M) are non-entailments, and the pair of typed literal values being considered are different, since they have different primitive base datatypes. This approach is also easy to understand.
The easier examples (3A through to 3F) are all entailments,
since in each of these, either the primitive base datatype are the
same for both the values being considered, or we are using the
special rule from
[RDF Semantics] that plain literals without language
identifiers can be identified with the equivalent
xsd:string.
In a unary datatype group, value spaces of primitive base datatypes are required to be disjoint with each other.
eqLike RDF and OWL, [XSLT
2.0] and
[XQuery 1.0] require the ability to compare values of typed
literals. The basic operation they use is the [XPath
2.0]
eq operator. Given two literals, this operator
does one of:
eq compares numeric values with different primitive
datatypes. e.g. 0 as a float and 0 as a decimal compare true under
eq.
Most pairs of primitive types are incomparable under
eq, and with the strong typing in [XPath
2.0] such comparisons are errors.
eq is stronger than the primitive-equality
discussed
above, in that whenever two values derived from the same
primitive base datatype are the same according to that primitive
base datatype, then they also compare as eq.
eq is designed to take implementation
considerations into account. xsd:decimal has
implementation variability:
[XML SCHEMA2] specifies:
Note: All �minimally conforming� processors �must� support decimal numbers with a minimum of 18 decimal digits (i.e., with a �totalDigits� of 18). However, �minimally conforming� processors �may� set an application-defined limit on the maximum number of decimal digits they are prepared to support, in which case that application-defined maximum number �must� be clearly documented.
As a result of this, we may expect different implementations to make different comparisons in some corner cases, due to rounding and precision issues.
Further [XML SCHEMA2] leaves implementations freedom with the equality function they use for floats and doubles, specifying:
Note: "Equality" in this Recommendation is defined to be "identity" (i.e., values that are identical in the �value space� are equal and vice versa). Identity must be used for the few operations that are defined in this Recommendation. Applications using any of the datatypes defined in this Recommendation may use different definitions of equality for computational purposes; [IEEE 754-1985]-based computation systems are examples. Nothing in this Recommendation should be construed as requiring that such applications use identity as their equality relationship when computing.
These considerations lead to aspects of the definition of
eq that are surprising to purists. For example,
eq is non-transitive:
"3.2"^^xsd:decimal eq "3.2"^^xsd:float "3.2"^^xsd:float eq "3.20000000000000000001"^^xsd:decimal
but not
"3.2"^^xsd:decimal eq "3.20000000000000000001"^^xsd:decimal
Infinity, which can be represented in both the
xsd:float and xsd:double datatypes is
treated specially, and eq is not even reflexive, i.e.
it is not the case that:
"INF"^^xsd:float eq "INF"^^xsd:float
eq in RDF
and OWLUsing eq as the basis for typed literal value
semantics in RDF and OWL would, from an implementation point of
view, amount to using eq at all points where a
comparison between two literals is needed. Since there are many
different approaches to implementing RDF and OWL semantics such a
procedural definition is somewhat unsatisfactory. If this approach
is pursused the next version of this document will characterize the
resulting implementation variability.
From the point of view of the ontologist or knowledge engineer, this will make clear that for interoperability it is necessary to avoid certain corner cases where rounding errors etc. could give surprising results.
A possible first sketch of a formal expression of the potential variability is as follows. While processing a set S of RDF graphs, over a vocabulary V, then the implementation may use any equivalence relation ~ over the typed literals in V that satisfies the following:
A second possibility might be to require implementations to use an equivalence relation formed as the transitive, symmetric, reflexive closure of eq over the typed literals in the vocabulary V.
Both of the above approaches may give surprises since in the corner cases extending the vocabulary V, by for instance including further graphs, may cause typed literals that were considered different to be considered the same.
A third possibility might be to formally capture the difference
between eq and equality by specifying the approximation mapping
mapsTo between different datatypes. Therefore,
eq("s1"^^u1,
"s2"^^u2) returns:
u1))(s1) =
L2S(D(u2))(s2) or
mapsTo(D(u1),D(u2))(
"s1"^^u1) =
L2S(D(u2))(s2),u1))(s1) ≠
L2S(D(u2))(s2) and
mapsTo(D(u1),D(u2))(
"s1"^^u1) ≠
L2S(D(u2))(s2),u1),D(u2))
is undefined.eqValues of the xsd:string type do not compare
eq to any other primtive type. Thus the
xsd:anyURI example
3L is a non-entailment.
@@@ todo datetime stuff - I think they are all incomparable should check.
hexBinary and base64Binary do not compare under eq,
so that example
3M is also a non-entailment.
Numeric comparisons are provided with detailed casting rules to allow for rounding errors etc., as for 1.3 in example 3H and example 3K. These rules also deal with 40 in example 3G and example 3J. Thus all four of these entailments hold.
As a special case, INF^^xsd:float is not
eq to itself, it is wholly unclear as to why, and what
impact that has.
Following
[CARROLL 2002], it is possible to take a literal reading of
[XML Schema Datatypes]. Under this, the numeric types all have
exact values, and no allowance is made for rounding. The binary
encoding types have the same value space, and can be compared.
anyURI is essentially a string restricted by the
grammar of
[RFC 2396].
With such a literal reading, the harder example entailments hold except for those that involve rounding. i.e. Example 3H and example 3K are non-entailments because despite appearances three different numbers are being considered in these two entailments (1.3, 1.2999999523..., 1.299999999999999822...).
In short, this approach suggests some modifications of the XML Schema datatypes derivation tree.
The XPath 2.0 eq position is a compromise between
the two theoretically sound positions and may well be the best
solution on an 80/20 rule. It is also likely to have best
compatibility with XML technologies based on XPath 2.0, and
[SPARQL], which uses functions and operators from
[F&O]. However, it is problematic that eq is
not an equivalence relation because of the corner cases.
Implementor feedback is needed as to how significant this problem
is.
A summary table showing the examples and how they are treated by the three possible approaches is as follows:
| Example | Literal 1 | Literal 2 | Primitive | eq |
True |
|---|---|---|---|---|---|
| 3A | "15"^^xsd:byte |
"15"^^xsd:decimal |
true | true | true |
| 3B | "15"^^xsd:nonNegativeInteger |
"15"^^xsd:byte |
true | true | true |
| 3C | "en-US"^^xsd:language |
"en-US"^^xsd:string |
true | true | true |
| 3D | "en-US"^^xsd:language |
"en-us"^^xsd:language |
false | false | false |
| 3E | "en-US"^^xsd:string |
"en-US" |
true | true | true |
| 3F | "en-US"^^xsd:language |
"en-US" |
true | true | true |
| 3G | "40"^^xsd:integer |
"40"^^xsd:float |
false | true | true |
| 3H | "1.3"^^xsd:decimal |
"1.3"^^xsd:float |
false | true | false |
| 3J | "40"^^xsd:double |
"40"^^xsd:float |
false | true | true |
| 3K | "1.3"^^xsd:double |
"1.3"^^xsd:float |
false | true | false |
| 3L | "http://www.example.org/doc" |
"http://www.example.org/doc" |
false | true | true |
| 3M | "0FB7"^^xsd:hexBinary |
"D7c="^^xsd:base64Binary |
false | true | true |
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:durationdoes 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 [F&O] we
read:
[Definition]
xdt:yearMonthDurationis derived fromxs:durationby restricting its lexical representation to contain only the year and month components. The value space ofxdt:yearMonthDurationis the set ofxs:integermonth values. The year and month components ofxdt:yearMonthDurationcorrespond to the Gregorian year and month components defined in section 5.5.3.2 of [ISO 8601], respectively.
and
[Definition]
xdt:dayTimeDurationis derived fromxs:durationby restricting its lexical representation to contain only the days, hours, minutes and seconds components. The value space ofxdt:dayTimeDurationis the set of fractional second values. The components ofxdt:dayTimeDurationcorrespond 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).
@@@todo reorganize: recs, rfcs and standards first, then wds, then other