FORMAL SPECIFICATION AND VERIFICATION OF XML-

BASED BUSINESS DOMAIN MODELS

Wolfgang Schuetzelhofer

IBM Austria, Tullnertalgasse 74/1, A-1230 Vienna, Austria

Karl M. Goeschka

Vienna University of Technology, Gusshausstrasse 27-29/384, A-1040 Vienna, Austria

Key

words: Semantic meta model, Business domain model, Graph theory, Constraint modeling, XML language

Abstract: The rapidly growing use of XML in the development of business to business (B2B) applications requires

new approaches in building enterprise application infrastructures. In this field the modeling of business

domain semantics, thus focusing on the user’s perception of data, in contrast to physical data representation,

is gathering more and more importance. It is increasingly important to provide a sound mathematical

foundation on modeling business domains, together with a well defined way to map business domain

semantics to XML-structures. In our recent work we propose a semantic meta model, built on set- and

algebra-theory, considered to serve for the formal definition of operations and transformations and to prove

the correctness and completeness of design methods. Based on the mathematical model we propose an XML

language to construct domain models and to formally express business domain semantics. The language not

only allows to express structural schemas and static constraints but also provides to formulate dynamic

business rules, which is considered critical for the quality of a business domain model and which is

therefore centrally focused in our work. In addition we provide an XML syntax to encode domain instances

and we apply standardized XML technologies to formally verify the validity of domain instances with

respect to their specifying domain models. With our paper we contribute to the field of formal software

engineering by proposing a business domain modeling language based on XML and founded on a sound

mathematical model. The expression of dynamic business rules and the application of XML technologies to

formally verify validity of domain instances and of entire domain models are the strength of our approach.

1 INTRODUCTION

The field of research on semantic data models has

grown rapidly over the last years (Schmidt 1975,

Peckham 1988, Gogolla 1991, Schnase 1993, Chen

1999, Trastour 2002) with a continuous change of

focus towards modeling complex business domains.

We contribute to this development with our recent

work by introducing a semantic meta model based

on set- and algebra-theory. It provides a framework

for the specification of complex business domains,

and it serves as a basis for the formal definition of

operations, mappings and transformations and to

prove the correctness and completeness of new and

extended design methods. Algebraic specifications,

by means of algebraic equations (called Σ-

equations), serve to formally define validity of

business domain models as well as of domain

instances. Our special focus is on the seamless

integration of business knowledge in form of static

and dynamic business rules, which highly influences

the expressiveness and quality of a business domain

model.

On the other hand XML, as a standardized data

description language, is gathering more and more

importance in the field of data interchange in B2B

applications. XML-based data exchange between

different systems requires transformations of XML-

structures. These transformations in turn have to be

proved for equivalence and soundness.

In our work we propose a formal method to map

business domain semantics to XML-structures based

on our theoretical model, and we additionally

provide an XML-encoding for domain instances.

This allows to formally verify validity of XML-

based business domain models and of XML-encoded

209

Schuetzelhofer W. and M. Goeschka K. (2004).

FORMAL SPECIFICATION AND VERIFICATION OF XML-BASED BUSINESS DOMAIN MODELS.

In Proceedings of the Sixth International Conference on Enterprise Information Systems, pages 209-216

DOI: 10.5220/0002605302090216

 SciTePress

domain instances and it provides for the formal

proof of equivalence and soundness of

transformations on XML-structures.

The contribution of our recent work to the field

of formal software engineering is

• to provide a sound mathematical foundation in

form of a semantic meta model, which builds a

framework for the specification of complex

business domains,

• to provide a mathematical method which allows

to verify validity of business domain models

and of domain instances,

• to propose a formal method how to apply

domain semantics to XML-structures,

• to outline an approach, which allows to leverage

standardized XML-technologies to verify

validity of XML-based business domain models

as well as of XML-encoded domain instances.

2 A SEMANTIC META MODEL

FOR SPECIFYING BUSINESS

DOMAINS

As core of our work we introduce a semantic meta

model, which allows to formally specify business

domains. Business domains are commonly

expressed by means of their concepts (e.g. person,

car, address, ...) and by means of relationships

between these concepts (e.g. ownership, residence,

...). Directed graphs are considered to serve as the

basis to describe business domain models. Research

in the field of semantic nets (Rada 1990) has

successfully proven that directed graphs are well

suited to express business domain concepts and

relationships between business domain concepts. We

call such graphs domain graphs. We furthermore

introduce types on nodes and links of directed

graphs, so that business domain concepts are

mapped to node-types and so that relationships

between these business domain concepts are mapped

to link-types. Recursive link composition and type

hierarchies are proposed as powerful means of

abstraction. Structural constraints on types, together

with a formalism to describe complex dependencies

between model elements, are used to express

business knowledge in form of business rules. The

consequent separation of structure and content in

combination with the proposed method to define

business rules, enforces the introduction of a three-

layer meta model. We also introduce algebraic

specifications to formally define validity of domain

graphs as well as of domain instances. A number of

simplified examples and graphical views are used to

provide an intuitive approach to the underlying

mathematical theory.

2.1 Typed Directed Graphs –

Foundation of the Meta Model

An extended version of directed graphs serves as the

fundamental basis for our approach. In contrast to a

common definition, where a directed graph (DG)

consists of a set of vertices (nodes) and of a set of

edges, we propose an extended definition by

introducing the concept of links. Links allow to

recursively specify connections between nodes of a

directed graph. Every edge of a DG is represented as

a link and every connected sequence of links forms a

link in turn. This recursive approach serves as a

powerful means of abstraction, which especially

proves profitable when the goal is to model business

domains with the necessity to view and describe

those business domains at different levels of

abstraction.

By additionally defining mappings of nodes to

node-types and of links to link-types, the concept of

typed directed graphs (simply called typed graphs) is

introduced. Two layers, called type-level and

instance-level, provide a clear separation of type and

instance. The graph type GT populates the type-

level:

GT = (NT, LT)

NT... a set of node-types,

LT ... a set of link-types.

The typed graph TG populates the instance-level:

TG = (N, L)

N... a set of typed nodes,

L ... a set of typed links.

Type mappings are defined:

type: N → NT and type: L → LT

Additionally nodes are mapped to node-values, so

that a node of a typed graph can be written as a pair

consisting of a node-value and of a node-type:

n = 〈v

node

, t

node

〉; t

node

∈ NT

Typed links are defined recursively:

= 〈(〈n

, n

〉), t

link

〉; l

∈ L, n

, n

∈ N,

link

∈ LT

... every edge of the graph is represented

(encapsulated) by a link. Such a link is called

direct link (l

l = 〈( l

, l

, ..., l

), t

link

〉; l, l

, l

, ..., l

∈ L;

k ≥ 1 ∧∀ i, 1 ≤ i < k : t(l

) = s(l

i+1

), t

link

∈ LT

... a connected sequence of links is a link in turn

and it is called indirect link (l). s(l) maps a link to its

source node and t(l) maps a link to its target node.

ICEIS 2004 - INFORMATION SYSTEMS ANALYSIS AND SPECIFICATION

210

2.2 Three Layer Meta Model

So far the graph type (GT) simply consists of a set

of node-types and of a set of link-types. Business

domain concepts are mapped to node-types and

relationships between business domain concepts are

mapped to link-types. Hence a graph type models a

business domain and specifies the domain’s

structure. Business rules express structural

constraints on domain instances. Consequently they

are specified as part of the graph type. In particular,

the structural constraints are expressed on link-types

and on node-types. Whereas one possibility is to

specify constraints in form of structured values of

the appropriate node- and link-types, the proposed

approach is to express the structural constraints in

form of distinct nodes and links as part of a directed

graph, moreover, as part of a typed directed graph

which is modeled at the type-level. This means, the

graph type (GT) itself is extended to form a typed

directed graph. The semantic of a specific constraint

is then covered by a link of GT, whereas a value for

a constraint whenever needed (e.g. a range for a

cardinality constraint) is defined by means of a node

of GT.

This approach enforces the introduction of a

third layer which we call meta-type-level. The layer

is introduced, so that nodes and links at the type-

level are instances of meta-types. These meta-types

are defined at the meta-type-level.

More generally stated, nodes and links at the

instance-level are instances of nodes at the type-

level, which in turn are instances of meta-node-

types. The three layers of the resulting meta model

are depicted in Figure 1.

At the meta-type-level

, a set of meta-node-types

and a set of meta-link-types define the model

semantic.

At the type-level

, typed graphs are constructed to

model specific business domains (e.g. the sales

domain).

At the instance-level

, typed graphs are used to

present business domain instances (e.g. a specific

sales transaction).

The entire three-layer model is called Domain

Graph Model (DGM).

At the instance-level

a node of the typed graph

represents either

• an

OBJECT i.e. an instance of a business domain

concept (e.g. a specific person) or

• a

PRIMITIVE-VALUE ( instance of a primitive

data type) (e.g. the integer value 20).

A link

at the instance-level represents a RELATION

between an

OBJECT and/or a PRIMITIVE-VALUE (e.g.

a link of type residence may relate a specific person

to a certain address, or a link of type birthDate may

relate a person to a primitive D

ATE value).

A simple analogy with E-R modeling concepts

can be constructed, so that an

OBJECT corresponds to

an entity-instance, so that a

PRIMITIVE-VALUE

corresponds to an attribute-value and so that a

RELATION corresponds to either a relationship-

instance or to an attribute-name respectively.

At the type-level

a node of the typed graph

represents either

• a business domain

CONCEPT (e.g. Person),

which specifies a type of

OBJECTs or

• a primitive

DATA TYPE (e.g. Integer, Date, ...),

which specifies a type of

PRIMITIVE-VALUEs or

• a

CONCEPT-RELATIONSHIP, a relationship

between business domain concepts (e.g.

residence), which is a link-(

RELATION-) type

• a

CONSTRAINT-VALUE (e.g. a specific range for

a cardinality constraint).

A link

at the type-level covers constraint semantics

(e.g. a distinct super-type relation, a source-node-

type constraint, a cardinality constraint, ...), hence it

is called a

SEMANTIC-RELATION. The graph at the

type-level is called Domain Graph (DoG) because it

is the means to model business domains.

At the meta-type-level

the model semantic is covered

by a set of meta-node-types which represent the

types of possible nodes for the type-level, and by a

set of meta-link-types representing all possible sorts

SEMANTIC-RELATIONs.

2.3 Model Semantic

Figure 2 lists the set of meta-node-types and the set

of meta-link-types. Possible links between nodes at

the type-level with respect to the nodes’ and links’

meta-types are also shown.

Figure 1: Three-layer meta model

meta-type-level

type-level

instance-level

meta-types

types

instances

instance-of

Level

Elements

Covers / Expresses

Model Semantic

Business Domain

Model

Domain Instance

FORMAL SPECIFICATION AND VERIFICATION OF XML-BASED BUSINESS DOMAIN MODELS

211

Meta-Node-Types

bd_concept ... Instances represent business

domain

CONCEPTs (e.g. Person, Address, ...).

p-type ... Instances represent primitive

DATA TYPEs

(e.g. Integer, String, Date, ...).

bd-relat ... Instances describe relationships between

business domain concepts (e.g. residence,

ownership, ...).

range ... Instances serve to specify valid ranges

for cardinality constraints.

condition ... Instances are used to formulate

dynamic business rules.

lt-sequ ... Instances constrain the sequence of

intermediate links of composed

RELATIONs

(indirect links at the instance-level).

Meta-Link-Types

Meta-link-types cover the semantic of structural

constraints. Instances of meta-link-types are

SEMANTIC-RELATIONs at the type-level.

super ... Instances of super relate types to their

super-type.

s-type ... Instances constrain the source-node-type

RELATIONs.

t-type ... Instances constrain the target-node-type

for

RELATIONs.

s-card, t-card ... Instances are used to model

cardinality constraints.

composition ... Instances of composition connect

CONCEPT-RELATIONSHIPs to lt-sequ instances,

thus constraining intermediate link sequences of

composed

RELATIONs.

abstract ... Instances of abstract connect

CONCEPTs

CONCEPT-RELATIONSHIPs to condition nodes

in order to specify abstract types.

if ... Instances represent if-branches of condition

trees.

else ... Instances represent else-branches of

condition trees.

2.4 Static and Dynamic Business

Rules

A major concern of our work is the seamless

integration of business rules. In the proposed

approach such business rules are defined in form of

cardinality constraints which are specified on

CONCEPT-RELATIONSHIPs. We distinguish between

static and dynamic business rules. Dynamic business

rules, in contrast to static ones, depend on the state

of distinct domain instances. As an example one can

think of a sales transaction which, depending on the

age of the customer, allows only certain products to

be added as line-items. In DGM such dynamic

business rules are expressed in form of conditional

cardinality constraints. Figures 3 and 4 provide a

simplified example. Whereas Figure 3 shows a UML

representation, Figure 4 outlines a graphical view of

the appropriate domain graph.

ure 3: D

namic business rule ex

ressed as annotation.

Person

birthDate

Sales-

Transaction

customer

line-item

Item

Product

minAg

spec

[1..1]

[0..n]

[1..1]

An Item of

certain product

can be purchased

by a customer

only if the

customer’s age is

≥ the product’s

minAge

[0..n]

[1..1]

Figure 2 : The model semantic is defined by meta-node-

types and by meta-link-types

d-conce

p-type

bd-relat

range

condition

lt-sequ

Meta-

Node-

Types

Meta-

Link-

Types

Instance-Level

super

s-type

t-type

compo-

sition

s-card

-card

else

abstract

O – OBJECTs

V –

PRIMITIVE-VALUEs

R –

RELATIONs

– CONCEPT-RELATIONSHIPs

CV –

CONSTRAINT-VALUEs

BC – CONCEPTs

PT – primitive

DATA TYPEs

Meta-T

e-Level

Type-Level

ICEIS 2004 - INFORMATION SYSTEMS ANALYSIS AND SPECIFICATION

212

Figure 4 provides a graphical representation of

the set theory based formalism. It is more suitable

and easier to read, especially as the presented model

is based on graph theory. Note, that the

representation in Figure 4 can be unambiguously

transformed into the set theory based formalism.

However, the used notation is not intended to serve

as a graphical modeling language (although

possible). Other graphical notations, such as used

with UML (UML, 2001), are specifically designed

to accomplish this task. Figure 4 demonstrates how a

boolean expression is used to formulate a dynamic

business rule. Path expressions are the means to

select values out of distinct domain instances. These

values serve as arguments for the boolean

expression. Based on the result of evaluating the

boolean expression, the condition tree (encircled in

Figure 4) is traversed (if, else branches). The

traversal results in a specific range node which

specifies the cardinality constraint to be applied.

OCL (OCL, 2002), a constraint language, has been

adapted to the DGM in order to formulate dynamic

business rules.

2.5 Domain Graph Model - Summary

DGM provides a semantic meta-model to formally

specify and verify business domains. The meta-

model consists of three layers, which are called

levels. The topmost layer is named meta-type-level

and defines the model semantic. The medium layer

is called type-level and hosts typed-directed-graphs,

called domain graphs (DoGs), which model distinct

business domains. The bottom layer is named

instance-level, and it is the layer where instances of

specific business domains, again in form of typed-

directed-graphs, are constructed.

At the type-level,

CONCEPTs and CONCEPT-

RELATIONSHIPs describe the basic domain structure,

and constraints in combination with boolean OCL-

expressions are used to formulate static- and

dynamic business rules. At the instance-level,

OBJECTs, (PRIMITIVE-)VALUEs and RELATIONs

compose domain instances, and they are constructed,

so that they satisfy the structural constraints and

business rules defined by their domain graph.

The theory of algebraic specifications is applied

to formally define validity. Algebraic specifications

are based on algebraic signatures, so that a

specification extends a signature with the formal

construction of

-equations. A set of such

equation provides the formal specification of valid

domain graphs and of valid domain instances. Figure

5 outlines the basic building blocks of the DGM.

3 XML-ENCODING OF THE

DOMAIN GRAPH MODEL

Based on the semantic meta model we propose an

XML-language to specify domain graphs (DoGs),

thus modeling business domains. We call this

language XDoG. We also provide an XML-

ure 5: Domain

h Model

(

DGM

)

(bool. xprsn)

:condition

Algebraic Spec of

Domain Graphs

Spec

DoG

sorts: bd-concept, ..

s-type, t-type, ...

opns: vars: eqns:

Terms define Path-Expessions

Σ-Path

:bd-concept . l:bd-relat =

:bd-concept

Model Semantic (Meta-Types)

MS = {MNT, MLT}

MNT = {bd-concept, p-type, bd-relat,

range, condition, lt-sequ}

MLT = {super, s-type, t-type,

s-card, t-card, composition,

abstract, if, else

}

Meta-types are sorts in

Spec

DoG

and T

Σ-Path

instances(bd-concept) ... CONCEPTs

instances(bd-relat) ...

CONCEPT-

RELATI

ONS

HIP

path-

expressions

l:bd-relat

:if

:else

:s-card

[0..0]:

range

[1..1]:

range

[3..n]:range

are

part-

specifies valid

domain-

instances

specifies valid

domain graphs

OBJECTs,

(

PRIMITIVE-)VALUEs,

RELATIONs

boolean-

OCL-expressions

(specify

business rules)

Figure 4 : Business rules expressed as conditional

cardinality constraints

(Date.today –

Sales-Transaction.customer.birthDate

≥

Item.spec.minAge

) :condition

birthDate

:bd-relat

Person

:bd-concept

type-level

:s-card

:if

:else

[1.. 1]:range

:s-type

Sales-Transaction

:bd-concept

Item

:bd-concept

int:p-type

Product

:bd-concept

line-item

:bd-relat

minAge :

d-rela

spec:

d-rela

customer

d-rela

Date

:p-type

:s-type

:t-type

[0.. 0]:range

FORMAL SPECIFICATION AND VERIFICATION OF XML-BASED BUSINESS DOMAIN MODELS

213

encoding for domain instances, so that instances of a

business domain (e.g. specific sales-transactions)

can be encoded in form of XML-structures.

The decision to develop a business domain

modeling language based on XML is motivated by

several reasons. Beside its already leading role in

data interchange in business to business (B2B)

applications, XML is also gathering more and more

importance in the field of semantic data modeling.

Based on the foundation of the XML Information

Set (W3C, 2004) and on a clear and simple syntax,

the extensibility of XML is targeted towards the

development of domain specific languages. Grouped

around a set of stable and consistent standards, a

rapidly growing number of tools and applications are

established. This allows new developments to build

on mature and well tested technologies and to

benefit from a high amount of re-use. This, together

with the widespread use of XML, leads to an ever

growing number of XML-languages arising in the

field of formal software engineering. Recent

developments on Web-Ontologies (W3C, 2001)

specify XML-languages which aim to define the

terms used to describe and represent specific areas

of knowledge. DAML+OIL (DAML + OIL, 2001) is

an example of such languages.

For our work, interoperability, standards

compliance and the possibility to re-use software

tools for practical implementations are the major

motivations to develop an XML-language for

modeling business domains as well as to provide an

XML-encoding for business domain instances.

Rather than providing the complete specification

of the domain modeling language XDoG and of the

XML-encoding for domain instances as part of this

paper, we will focus on how we utilize XML

technologies to model XML-based, valid business

domains and how we apply standardized XML

technologies to verify validity of XML-encoded

domain instances.

Figure 6 depicts how formal modeling languages

in general and the XDoG language in particular are

aligned with the domain graph model (DGM).

Expressions of the XDoG language are used to

encode a domain graph in XML thus modeling a

business domain. The XDoG language itself is

specified by means of an XML-Schema, which is

derived from Spec

DoG

and which restricts the XDoG

language to describe valid domain graphs (Figure 6

(1)). A domain graph is encoded in XDoG and

serves to specify valid domain instances (Figure 6

(2)). Domain instances are XML-encoded in turn.

The encoding follows an instance-encoding-

specification, which basically defines how

OBJECTs,

PRIMITIVE VALUEs and RELATIONs of a domain

instance are represented as XML elements and

attributes respectively (Figure 6 (3)).

Just like an XML-schema provides the structural

constraints for XML-documents which are instances

of that schema, a domain graph or the domain

graph’s XML encoding respectively, constrains

domain instances. With that relationship in mind, it

seems straight forward to derive an XML-schema

from a domain graph, or, even better, to directly

encode a domain graph in form of an XML-schema.

However, the XML-schema-language proves not to

be powerful enough to express all constraints

specified by a domain graph. Especially dynamic

business rules, which play a central role in the DGM

theory, but also the composition property of

composed

RELATIONs cannot be formulated by

means of the XML-schema-language. On one hand

this is the reason why the XDoG language was

developed to provide an appropriate domain graph

encoding. On the other hand it is the reason why an

XML-schema alone is not sufficient to completely

specify domain instances. Nevertheless, the XML-

schema-language is not entirely omitted in the

specification of the domain instance encoding.

Instead, constructs of the XML-schema-language are

provided to specify the static constraints on XML-

encoded domain instances. This ‘static schema’ is

derived from the XML-encoded domain graph. This

is done by providing a set of transformation rules in

form of an XSL-stylesheet, so that a standard XSL-

processor can generate the ‘static schema’ out of the

XML-encoded domain graph (Figure 6 (4)).

In order to perform validation of XML-encoded

domain instances with respect to dynamic business

rules and composed

RELATIONs, a different approach

Figure 6: DGM and XML-encoding

Modeling Language

Specification

XML Modeling Language

Specification

(XDoG Schema

)

Meta-Types

Spec

DoG

derived

DoG

specifies

type-level

instance-level

XDoG - instance

XML

domain instance

XSL

static schema

construction rules

transformation

XSL

(validation

stylesheet)

XSL

validation stylesheet

construction rules

XSD

(static schema)

validity-

statement

encodes

(1)

(2)

instance

encoding

spec

follows

(3)

(4)

(5)

(6)

schema

validation

transformation

Domain Instance

validity-

statement

meta-type-level

transformation

ICEIS 2004 - INFORMATION SYSTEMS ANALYSIS AND SPECIFICATION

214

is required. A set of rules in form of another XSL-

stylesheet serves to generate the ‘XSL-validation-

stylesheet’ (Figure 6 (5)) out of the XML-encoded

domain graph. The ‘XSL-validation-stylesheet’ is

constructed, so that it contains XPath (W3C, 1999)

expressions which properly encode path-expressions

(they are part of boolean OCL expressions) which in

turn specify dynamic business rules. The XPath

expressions serve to select values or value sets out of

domain instances. The ‘XSL-validation-stylesheet’

itself is an XSL-stylesheet. Applied to an XML-

encoded domain instance it generates a statement

about the domain instance’s validity (with respect to

dynamic business rules and composed

RELATIONs).

By performing schema-validation based on the

‘static schema’ and by applying the ‘XSL-

validation-stylesheet’ (Figure 6 (6)), we provide

validation of XML-encoded domain instances,

utilizing standard XML technologies.

4 RELATED WORK

In the field of semantic data modeling a number of

publications can be found, which apply set- and

graph-theory to map domain semantics to structured

hypertext systems and hyperlinked data sets. Our

work, providing a semantic meta model together

with a proposed XML-encoding, is highly related to

this field of research, as the origin of XML can be

found in hypertext systems. Moreover, hypertext

systems may profitably be viewed as semantic nets

(Wang, 1998), which actually provide the basis of

our approach on business domain modeling.

Beside publications on formal models for

hypertext (Lange, 1990) and on constraining

hypertext structures (Chidlovskii, 2000), a lot of

related approaches stresses the need for our work:

Bench-Capon and Dunne (Bench, 1889), in an early

approach use a DAG (directed graph) structure and a

set of constraints to model electronic documents.

Contrasting our approach links are not typed and

only represent the containment relationship,

providing limited possibilities to express domain

semantics. The formal hypertext model described in

Tochtermann and Dittrich (Dittrich, 1995) provides

some formally defined structural concepts, lacking

mechanisms to define more powerful structural and

relational constraints. Wang and Rada (Wang, 1998)

have developed a semantic data model based on the

concept of a semantic net, introducing organizational

and relational link types on a DAG. In contrast to

our work they do not provide an extensible type

system and they also do not provide a mechanism to

formulate dynamic constraints. Abiteboul and Hull

(Abiteboul, 1987) in their well known approach on

formalizing a semantic model recognize the

importance of types which are used to model object

structures (IFO model), but they do not provide link

type hierarchies. E-R modeling, which is very much

influenced by the work of P.P.Chen (Chen, 1976,

Chen, 1999) provides another field of related work.

In contrast to E-R approaches our work is highly

built on graph theory and we centrally focus on the

possibility to formulate dynamic business rules.

H.V.Jagadish et.al. (Jagadish, 2001) provide an

algebraic approach for query and transformation of

XML tree structures. Whereas they propose a sound

mathematical theory, their approach in contrast to

our work applies to tree graphs rather than to

directed graphs. The OMG with its MOF (Meta-

Object-Facility) specification (OMG, 2000),

introduces a four layer meta-data architecture in

contrast to the three layer model we are proposing in

our paper. The Unified Modeling Language (UML)

specifies semantics on the level of Meta-Models

(UML, 2001, Schleicher, 2001), but does not

provide expressing complex business rules as

integral part (although the recent integration of OCL

as part of UML is targeted in that direction). Recent

developments in the field of (Web-) Ontologies

(W3C, 2001), such as DAML+OIL, aim to define

the terms used to describe and represent specific

areas of knowledge. They provide expressing object

constraints, but are limited in specifying dynamic

constraints which express complex element

dependencies (Trastour, 2002).

Our work is mainly build on a theoretical

approach which is inherently complex, especially

concerning the integration of dynamic business

rules. Whereas most of the related work, discussed

in this section, has already successfully proven its

applicability and usefulness in many practical

implementations, applications, providing a proof of

concept for our approach, are currently still under

construction.

5 CONCLUSION AND FUTURE

WORK

In this paper we have presented the theory of a

three-layered semantic meta model for specifying

business domains, which we call domain graph

model (DGM). We have introduced a Domain Graph

(DoG) as a directed graph with typed nodes and

typed links which models business domains at the

type-level of the DGM. We have outlined, how

domain semantics are applied to a DoG and how

static and dynamic business rules, playing a central

role, are seamlessly integrated by specifying types,

structural constraints, and conditions. We have

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215

discussed how construction rules for DoGs are

specified at the meta-type-level, how business

domains are modeled at the type-level and how valid

domain instances are provided at the instance-level.

This leads to a clear separation of structure and

content and is proposed as a flexible way to deliver

semantic data. The concept of type hierarchies as

well as the approach of recursive link composition

were introduced as powerful means of abstraction.

We have based the domain graph model (DGM)

on set- and algebra- theories, providing a sound

mathematical foundation for the formal definition of

operations and transformations and to prove the

correctness and completeness of design methods.

The formal verification of valid domain graphs and

of valid domain instances, by use of algebraic

specifications, satisfies the requirement for

robustness of semantic data. It was outlined, that by

proposing an XML-encoding for domain graphs and

for domain instances we provide an approach to

apply domain semantics to XML-structures. This

allows to utilize DGM theories for interchange of

semantic data in XML-based B2B applications.

We have discussed structural constraints, the

specification of static and dynamic business rules

and different abstraction mechanisms. The definition

of operations, built on the mathematical basis of the

DGM, is considered to specify additional dynamic

aspects as part of future work. Manipulating a

domain instance by inserting, deleting or updating

nodes and links, thereby maintaining consistency

and validity of the domain instance are such

dynamic aspects to be specified. New and extended

design methods, which can be formally specified

and verified, are seen to be another profitable output

of future work based on this paper.

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