NEW EXTENDED AND QUANTIFIED CONSTRAINTS IN XML
SCHEMA
A. Duffoux
Groupe esaip - 18 rue du 8 mai 1945 49180 Saint Barthelemy d’Anjou, France
LERIA - 2 Boulevard Lavoisier 49045 Angers cedex 01
B. Duval, S. Loiseau
LERIA - 2 Boulevard Lavoisier 49045 Angers cedex 01, France
Keywords:
XML Schema, Quantified constraint, Conditional constraint, Validation.
Abstract:
In this paper, we present a new model to represent complex constraints in XML schema. Due to its flexibility
and its capacity to describe all kinds of data, XML has become a widely used exchange format during the
last years. Hence, such data have been integrated in several information systems. However these systems
need strengthness and coherence that XML in its primary form can not provide. We thus propose to extend
classical XML schema in order to integrate a quantification of constraints and to allow conditional constraints
on several elements. Thanks to this extension, XML applications can have a richer and stronger framework.
To illustrate the use of this new model, we present a case study concerning XML curriculum vitae treatment.
1 INTRODUCTION
eXtensible Markup Language format (Bray et al.,
2004) has become the new data exchange standard.
The success met by XML is due to its flexibility and
its capacity to describe all kinds of data. Indeed, XML
documents convey not only the data but also their de-
scription. This description is made thanks to the con-
cept of XML schema
1
which is used as a grammar
to validate the data description. This grammar can be
specifically adapted to each application description. It
defines the attended structure of processed documents
and can specify some simple constraints on the data
embedded in them. These simple constraints are es-
sentially based on the document structure - presence
or absence of elements
2
, cardinality, imbrication. Un-
fortunately, most of the current schema formalisms
are not powerful enough to deal efficiently with more
complex constraints like constraints concerning sev-
eral elements at any level of the document hierarchy.
We thus need to develop specific methods to deal with
1
In this paper, we differenciate XML schema which is a
generical term and W3C XML Schema which is the specific
W3C definition
2
In the rest of this paper, we will use element indiffer-
ently for elements and attributes
such constraints and validate the data description.
A lot of studies have been lead in order to add
complex constraints to XML schemas. We can clas-
sify them according to two different approaches :
one that we call ”integrated” (Thompson et al., 2001;
Clark and Murata, 2001) and the second that we call
”composed” (Jacinto et al., 2003; Jelliffe, 2001). The
integrated solutions are the more used. They essen-
tially specify simple structure constraints. Some of
them (Thompson et al., 2001) also express some con-
tent constraints - enumeration, domain range check-
ing, pattern matching. Their advantages are that they
need only one specification document - the schema
- and only one validation. However, they are essen-
tially based on structure definition and take a little
into account the content. The composed solutions are
more complete. They allow to express a wide set of
rich content constraints on XML documents, using
for example aggregation functions. These constraints
are expressed in XML compatible languages and use
existing XML technologies such XPath (Clark and
DeRose, 1999) or XSL (Berglund, 2006). Their draw-
back is that they can not affect the validation result.
Furthermore, they need at least two specification doc-
uments, one for the schema and another one for the
description of constraints, which implies at least two
261
Duffoux A., Duval B. and Loiseau S. (2009).
NEW EXTENDED AND QUANTIFIED CONSTRAINTS IN XML SCHEMA.
In Proceedings of the International Conference on Agents and Artificial Intelligence, pages 261-266
DOI: 10.5220/0001662202610266
Copyright
c
 SciTePress

validation steps. Moreover, the constraint definition
is totally disconnected from the type definition.
In this paper, we present eqCXSD, for extended
quantified Constraints in XML Schema Definition, a
more complete solution capable to express quanti-
fied and conditional constraints on any element or
set of elements. We extend a classical ”integrated”
XML solution, W3C XML schema format (Thomp-
son et al., 2001), with constraint quantification and
conditional content constraints. The constraint quan-
tification is made thanks to a quantifier added to the
element concerned by the constraint. It expresses how
much occurences of the element is concerned by the
constraint. The proposed extension is made in the
same Schema to keep the coherence between the ele-
ment structure definition and its constraints.
We first present the expressiveness of XML
schemas. Second, we present extended constraints
on XML elements. Third, we introduce our new ex-
tended formalism. Fourth, we present the XML trans-
lation in W3C XML Schema of our new formalism.
2 XML SCHEMAS AND THEIR
EXPRESSIVENESS
An XML document can been seen as an unranked or-
dered and labelled tree composed of simple or com-
plex elements. The general structure of the doc-
ument and its elements definition are given in its
schema. This schema essentially describes structural
constraints on XML documents. There are several
schemas formalisms, the most known and used are
W3C XML Schema (Thompson et al., 2001) and Re-
lax NG (Clark and Murata, 2001). Each of them
have different constraint mechanisms and expressive-
ness. A detailed description and comparison of these
schema languages can be found in (Murata et al.,
2005; Lee and Chu, 2000). In (Mani and Lee, 2002),
the authors have proposed a new formalism, called
XSchema, which matches with XML Schemas.
Definition 1 (Mani and Lee, 2002). An XSchema is
a 6-tuple X = (E,A,M,P,r,Σ) where :
• E is a finite set of element names,
• A is a function from an element name e ∈ E to
a set of attribute names a,
• M is a function from an element name e ∈ E to
its element type definition α where α is
α ::= ε | τ | α + α | α,α | α
∗
| α
?
| α
+
where ε denotes the empty element, τ is an
atomic data type (e.g., String, Integer, ...), ”+”
the union, ”,” the concatenation, α
∗
for the
Kleene star, α
?
for (α + ε) and α
+
for (α , α
∗
),
• P is a function from an attribute name a to its
attribute definition β = (τ,n,d, f ) where n is ei-
ther nullable or not nullable, d is a finite set of
valid domain values of a (that can be ε) and f a
default value of a (that can be ε),
• r ⊆ E is a finite set of root elements,
• Σ is a finite set of integrity constraints. These
constraints concern ID and IDREF elements
and represent XML keys and foreign keys.
To illustrate the notions presented in this article,
we use a case study concerning the selection of can-
didates in a Master program. These candidates are
represented by their XML Curriculum Vitae. The fol-
lowing example shows a XSchema corresponding to a
part of our case study. We represent the candidate ex-
perience with its scholar experiences, its professional
experiences and its competencies.
Example 1 : G
1
= (E, A, M, P, r,Σ) is a XSchema.
• E ={Experience, Diploma, Degree, Year,
Mark, Field, Professional, Competence, Type}
• M = {Experience 7−→ (Diploma+, Profes-
sional*, Competence*);
Diploma 7−→ (Degree, Year, Mark, Field);
Degree 7−→ String; Year 7−→ Integer;
Mark 7−→ float; Field 7−→ String;
Professional, Competence 7−→ (Type, Field);
Type 7−→ String}
• r ={Experience}
• A,P, Σ =
/
0
G1 defines the expected structure of a CV. E is
the set of all the element names. Their definition
are expressed in M. A complex type definition is
composed of subelements, like Experience which is
composed by at least one Diploma and several or no
Pro f essional and Competence. A simple type defini-
tion is an atomic data type, like Mark which is a float.
Experience is the root element (r). For the sake of
simplicity, this example contains no attribute.
XSchema can express integrity constraints and
simple constraints of different kinds that are listed in
the taxonomy of figure 1.
Figure 1: A classification of XML simple constraints
In addition to these constraints, W3C XML
Schema manages content constraints as Enumeration,
Domain range checking and Pattern matching. In
this language, a constraint is applied to a simple type
ICAART 2009 - International Conference on Agents and Artificial Intelligence
262

element (leaf) and if this element has multiple oc-
curences, the constraint will concern each occurence.
The definition of W3C XML Schema based on
XSchema is given in Definition 2. For a complete
formal definition, please refer to (Brown et al., 2001).
Definition 2. W3C XML Schema extends XSchema
considering :
• (E,A,P,r,Σ) as in a XSchema.
• M is a function from an element name e ∈ E to
its element type definition α where α is
α ::= ε | ϕ | α + α | α,α
where ε denotes the empty element, ϕ a 4-tuple
(τ,d,o
i
,o
s
) where τ is an atomic data type (e.g.,
String, Integer, ...), d is a finite set of valid do-
main values of e (that can be ε), o
i
and o
s
are
respectively the minimum and maximum cardi-
nality of the element α, ”+” the union and ”,”
the concatenation,
3 EXTENDED CONSTRAINTS
We extend the classical expression of constraints with
respect to three aspects. The first one is the use of a
quantifier to define the application scope of the con-
straint. The second one is the expression of con-
straints on elements of complex type. The third one is
the management of conditional constraints expressed
by implication rules.
3.1 Quantification
Classical constraints in W3C XML Schema are im-
plicitly universally quantified, i.e. the constraint con-
cerns each occurence of the concerned element. Our
formalism, eqCXSD, offers the possibility to use an-
other quantifier, the existential quantifier. An existen-
tially quantified constraint will be satisfied if at least
one occurence of the concerned element satisfies it.
For example, the constraint ”∀ Mark, Mark > 15”,
which is equivalent to ”Mark > 15” in W3C XML
Schema, means that each occurence of the element
Mark in the document must have a value superior to
15. The constraint ”∃ Mark, Mark > 15” means that
one occurence of the element Mark in the document
must be superior to 15.
3.2 Constraints on Complex Type
Elements
The introduction of the existantial quantifier offers the
possibility to deal with more complex situations that
can be correctly expressed only if a constraint is ap-
plied to an internal node defining a complex element.
This is illustrated by the following example. The con-
straint ”There exists one diploma the degree of which
is a Bachelor and the field of which is in Computer
Science” does not have the same meaning as ”There
exists a diploma.degree which is a Bachelor and there
exists a diploma.field in Computer Science”. The
first constraint concerns the same diploma, which
must satisfy two requirements: its degree is a Bach-
elor AND its field is ”Computer Science”. The sec-
ond expression does not necessary concern the same
Diploma. It will be verified if the document con-
tains one diploma with a Bachelor degree and another
diploma in the field of ”Computer Science”. The first
requirement can be expressed by a constraint which
is exitentially quantified and where the quantification
concerns the complex type element Diploma. Con-
sequently, our eqCXSD formalism allows to express
constraints on every level of the tree. The semantic of
the constraint will be then dependent of the quantifier
previously defined and the node level on which we
want to express the constraint. The section 4 will give
the precise syntax for these quantified constraints.
3.3 Conditional Content Constraints
Conditional content constraints express relations, i.e.
implication rules, between the contents of different
elements. The figure 2 shows the different types of
constraint that we can encounter.
Figure 2: A classification of XML complex constraints
A conditional constraint can be a conditional enu-
meration, domain range checking or pattern match-
ing where the enumeration, domain range checking
or pattern matching depends on the value of an el-
ement. For example, ”If the diploma title is ”profes-
sional bachelor”, the mark has to be greater than 15.”
is a conditional domain range checking.
4 EQCXSD: EXTENDED AND
QUANTIFIED CONSTRAINTS
IN XML SCHEMA DEFINITION
This section presents the formalism eqCXSD that we
propose to deal with extended constraints. It is based
on XSchema and manages quantified and conditional
constraints.
NEW EXTENDED AND QUANTIFIED CONSTRAINTS IN XML SCHEMA
263

Definition 3. The extended model EX
t
is a 6-tuple
EX
t
= (E
t
,A
t
,M
t
,P
t
,r
t
,Σ
t
) where
• E
t
,A
t
,P
t
,r
t
are defined as in XSchema defini-
tion presented in definition 1.
• M
t
is defined as W3C XML Schema definition
presented in definition 2.
• Σ
t
is a finite set Σ of integrity constraints for
XML model and a finite set Σ
cc
of extended
constraints. Σ
t
≡ Σ ∪ Σ
cc
.
To define which kind of expression can be found
in Σ
cc
, we give the definitions of a quantified XML
formula and an extended quantified constraint.
Definition 4. A XML formula is defined by the fol-
lowing rules:
- f ormula ::= atom, atom
∗
- atom ::= element relation value
- relation ::= = | ≡ | 6= | < | > | ≤ | ≥
- element ∈ E
t
- value is a value of an atomic data type
The formula below is a conjunction of two atoms
concerning two elements of a CV document.
Mark>12, Field≡”Computer Science”
As explained in section 3, a formula can be quan-
tified in order to precise which element is concerned
and how its occurences are concerned.
Definition 5. A quantification is a couple composed
by a quantifier φ ::= ∀ | ∃ and an element e ∈ E
t
.
Definition 6. A quantified formula is a quantification
followed by a XML formula. The XML formula
will be surrounded by square brackets, this brack-
ets define the scope of the quantification.
As XML documents are hierarchically organised,
if an element e of complex type is concerned by a
quantification, the formula in its scope can contain
any element of the subtree attached to e.
For example, the following quantified formula
means that ”there exists a diploma whose mark is
strictly superior to 12 and whose field is equivalent
to ”Computer Science””.
∃ Diploma [Mark>12, Field≡”Computer Science”]
In order to express the desired constraints, we also
need to define quantified implications.
Definition 7. A quantified implication has the form:
φX
k
[H =⇒ B] where
• φX
k
is the quantification of the implication
• H is a XML formula
• B is an atom
We can give now the definition of an extended
constraint.
Definition 8. An extended quantified constraint C ∈
Σ
cc
can be:
• a quantified implication φX
k
[H =⇒ B]
• an expression φX
k1
[H
1
] ∧ ... ∧ φX
kn
[H
n
] =⇒
φX
k
[B] where
– n can be equal to 0.
– φX
ki
is the quantification of the formula H
i
– H
i
is a formula
– B is an atom
For each extended constraint, we have a set of
Head expressions (H
i
), which can be ε, and a Body
expression (B). Head and Body expressions can be
respectively considered as conditions and conclusion.
A head expression is an XML formula. Each head
and the body can have their specific quantification. In
case of a quantified implication, the implication is un-
der the scope of a sole quantifier.
For example, the following extended constraint
means that if there is no diploma whose field is equiv-
alent to Computer Science, there must exist a compe-
tence in Computer science.
∀ Diploma[Field 6= ”Computer Science”] =⇒
∃ Competence[Field=”Computer Science”]
This other constraint means that ”If the diploma
title is a professional bachelor, the mark for this
diploma must be superior to 15.”
∀ Diploma [Title = ”BachelorP” =⇒ Mark> 15]
5 XML TRANSLATION OF
EQCXSD
This section presents how our formalism can be ex-
pressed in XML representation. As eqCXSD is based
on W3C XML Schema, we have translated eqCXSD
in W3C XML Schema Definition.
As explained in the previous section, a constraint
is composed of XML formulas that are themselves
composed of atoms, and a atom contains only one el-
ement. To integrate our formalism into schema, we
have chosen to split a constraint representation into
atomic parts. Each atomic part concerns a single el-
ement and will be expressed inside this element def-
inition. Likewise a quantification concerns a single
element and will be expressed in the same way, inside
the definition of the quantified element. To integrate
this decomposition, eqCXSD extends the classical el-
ement type definition of W3C with additional infor-
mation concerning the constraints. Moreover, to link
these different parts of a constraint representation, a
constraint is represented by a unique identifier.
For example, considering the XML formula
”there exists a long term contract professional expe-
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264

rience in Computer science”, this formula is com-
posed by 2 atoms. We then decompose the formula
on each element concerned by each atom. We join to
the definition of ”Professional.Type” the atom type ≡
”Long term contract” and to the definition of ”Profes-
sional.Field” the atom field ≡ ”Computer Science”.
In order to garantee the coherence of the formula, we
assign a unique identifiant to the formula. Further-
more, we join the existential quantifier, any, to the
definition of the concerned element, ”Professional”.
To summarize, we redefine classical XML ele-
ment definitions wrt quantification of the formula and
the atom definition as defined in definition 4 plus the
information concerning the place ot this atom in the
constraint (head or body). For each case, we propose
a new XML Schema definition of ”element”.
5.1 Quantification Representation
Definition 9. The new definition of a quantification
is the classical W3C XML Schema element def-
inition extended by a 3-tuple (ID
cc
, ID
f
, Op)
where
• ID
cc
is the global identifiant of the constraint
• ID
f
is the identifiant of the formula
• Op is the logical operator : ”all” for ∀ and
”any” for ∃.
The classical definition of element given in the
W3C XML Schema specification is extended with a
sub element called quantification. An element can
be part of several or no quantification, depending
on the different constraints expressed in the model.
The quantification is an empty element with three at-
tributes : IDcc, IDf and Operator, which can have two
values : ”all” or ”any”. The corresponding new XML
Schema is given in table 1 and an example of use is
given in table 2. We will then use this element def-
inition in our schemas instead of W3C definition. In
order to avoid any confusion between W3C element
and our element, we will use a specific namespace for
our extended schema (”exsdc”).
5.2 Atom Representation
Definition 10. The new definition of an atom element
is the classical W3C XML Schema element defi-
nition extended by a 5-tuple (ID
cc
, ID
f
, place,
relation, value) where
- ID
cc
is the global identifiant of the constraint
- ID
f
is the identifiant of the formula
- place is the place in the constraint : ”head”, for
condition, or ”body”, for conclusion
- relation and value correspond to the elements
definition of the XML formula given in Def 4.
Table 1: Definition of the new element ”quantification”.
<xsd:complexType name="elementquantification">
<xsd:complexContent>
<xsd:extension base="xsd:element">
<xsd:sequence>
<xsd:element name="quantification" minOccurs="0"
maxOccurs="unbounded">
<xsd:complexType>
<xsd:simpleContent>
<xsd:extension base="xsd:empty">
<xsd:attribute name="IDcc" type="xsd:int"/ >
<xsd:attribute name="IDf" type="xsd:int"/ >
<xsd:attribute name="operator" use="required">
<xsd:simpleType>
<xsd:restriction base="xsd:string">
<xsd:enumeration value="all"/ >
<xsd:enumeration value="any"/ >
< /xsd:restriction>
< /...>
< /xsd:complexType>
Table 2: Example of definition of a quantification : The
quantification of the formula 1 of the constraint 1 is ∀
Diploma.
<exsdc:element name="diploma" type="diplomaType">
<exsdc:quantification IDcc="1"
IDf="1" operator="all"/ >
< /exsdc:element>
As for the element quantification, we extend the
classical definition of element with a sub element
atom. An element can be implied in several or
no atom, depending on the different constraints ex-
pressed in the model. The atom is an empty ele-
ment with five attributes : IDcc, ID f , place which
can only have two values : ”head” - in case of con-
dition - or ”body” - in case of conclusion -, relation
which represents the comparison operator and value
which is the information with which the element will
be compared. These five information are defined as
additional attributes of the W3C element. The corre-
sponding new XML Schema is given in table 3 and an
example of use is given in table 4.
6 CONCLUSIONS AND FUTURE
WORKS
In this paper, we have proposed a new formalism of
integrated XML Schema capable to manage quanti-
fied and conditional constraints on XML documents.
This extended XML Schema is based on a classical
schema definition. Our contribution is on three folds.
NEW EXTENDED AND QUANTIFIED CONSTRAINTS IN XML SCHEMA
265

Table 3: Definition of the new element ”Atom”.
<xsd:complexType name="elementAtom">
<xsd:complexContent>
<xsd:extension base="xsd:element">
<xsd:sequence>
<xsd:element name="atom" minOccurs="0"
maxOccurs="unbounded">
<xsd:complexType>
<xsd:simpleContent>
<xsd:extension base="xsd:empty">
<xsd:attribute name="IDcc" type="xsd:int"/ >
<xsd:attribute name="IDf" type="xsd:int"/ >
<xsd:attribute name="place">
<xsd:simpleType>
<xsd:restriction base="xsd:string">
<xsd:enumeration value="head"/ >
<xsd:enumeration value="body"/ >
< /xsd:restriction>
< /xsd:simpleType>
< /xsd:attribute>
<xsd:attribute name="relation">
<xsd:simpleType>
<xsd:restriction base="xsd:string">
<xsd:enumeration value="="/ >
...
< /...>
<xsd:attribute name="value" type="xsd:any"/ >
< /xsd:extension>
< /...>
< /xsd:complexType>
Table 4: Example of definition of an atom : An atom of
the formula 1 of the constraint 1 is a condition (head) and
concerns the element ”field”. It can be binded to the quan-
tification defined previously. It means ”∀ Diploma[field 6=
”Computer Science”...]”
<exsdc:element name="field" type="xsd:string">
<exsdc:atom IDcc="1" IDf="1" place="head"
relation="6=" value="Computer Science"/ >
< /exsdc:element>
Firstly, we have added a quantifier to constraint
parts. This quantifier can be universal or existen-
tial. On the one hand, the universal quantifier means
that each occurence of the element concerned by a
constraint has to verify this constraint. On the other
hand, the existential quantifier means that only one
occurence of the element concerned by the constraint
needs to verify the constraint. W3C XML Schema,
which is the current richest integrated solution, only
manages implicitly universal quantifier.
Secondly, we express constraints at any level of
the XML Schema hierarchy. Constraints can be ex-
pressed not only on leaves, as made in W3C WML
Schema, but also on any node of the XML tree, even
on complex type elements. We then enrich the classi-
cal definition of the element which will be concerned
by the constraint. Thus, the element concerned by
the constraint added with the quantifier defined previ-
ously are what we call the quantification of the con-
straint. They precise the scope of the constraint and
then give a richer framework.
Thirdly, we have defined a new type of constraints,
the conditional content constraints. Such constraints
are implication rules between several elements, they
express relations between the contents of these el-
ements. This type of constraint does not exist in
integrated approach. To have a richer semantic of
constraints, these constraints are composed of quan-
tified subconstraints that we have called quantified
formulas. Hence, this formalism is more expressive
than other integrated approaches and allows to ex-
press more complex constraints.
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