Z-BASED FORMALIZATION OF KITS OF CHANGES

TO MAINTAIN ONTOLOGY CONSISTENCY

Najla Sassi, Wassim Jaziri and Faiez Gargouri

Higher Institute of Informatics and Multimedia, Sfax University, Tunisia

Keywords: Changing Environment, Ontology, Coherence, Kits of Change, Z language.

Abstract: In changing environments, supporting ontology’s evolution is essential to integrate changes and to manage

ontology versions. It is also important to guarantee the consistency of ontology when changes occur. In this

paper, we present an ontology evolution approach based on kits of changes. These kits are based on changes

operators and additional changes which correct inconsistencies caused by the changes operators. A

formalization of the kits of changes is also proposed based on the Z language.

1 INTRODUCTION

Ontology is an explicit representation of knowledge

related to a domain of study and a particular context.

The application of changes in its conceptual entities

is a modification of a subset of knowledge

represented by the ontology. The application of

changes requires defining the mechanisms

specifying how knowledge can be changed and how

to maintain the consistency of knowledge after each

change.

Ontology evolution is the process of adaptation of

ontology to evolution changes and the consistent

management of these changes to guarantee the

consistency of ontology when changes occur (Klein

et al., 2001) (Noy et al., 2004). It encompasses the

set of activities, both technical and managerial,

which ensures that ontology continues to meet

organizational objectives and users needs in an

efficient and effective way (Stojanovic, 2004).

The adaptation of ontology to evolution changes

is a complex process from which several problems

must be managed: identification of evolution

changes, analysis of effects of changes, management

of the ontology consistency, storage of ontology

versions, etc. We are especially interested in this

paper at defining kits of changes to update, in a

coherent way, the ontology to new evolution

requirements.

This paper is organized as follows: Section 2

presents the evolution approach based on kits of

changes. In section 3, we specify the kits of changes

using pre-conditions, post-conditions, potential

inconsistencies and additional changes. Section 4

defines a formalization of the ontology structure

based on the ontology meta-model. The formal

specification of kits of changes using Z language is

presented in section 5 before concluding in section

2 KITS OF CHANGES

In changing contexts, the management of changes

and the maintaining of the ontology consistency

require analyzing and identifying effects of changes

on all ontology elements as well as defining

additional operations to correct inconsistencies.

In our approach, we express the requirements of

ontology evolution using types of changes. Indeed,

the evolution of ontology is the update of one or

more ontological entities. To allow updating an

ontological entity, we define primitive and

composite operators called types of changes able to

evolve ontology. These types of changes extend

these proposed in the literature (Klein et al., 2002)

(Stojanovic, 2004) to express all evolution

possibilities on the ontological entities: concepts,

relationships, properties and axioms (Sassi et al.,

2008).

However, types of changes ensure only the

modification of ontology. They not guarantee that

ontology remains coherent after modifications. The

definition of types of changes must be associated

with adequate mechanisms to ensure the consistency

388

Sassi N., Jaziri W. and Gargouri F. (2009).

Z-BASED FORMALIZATION OF KITS OF CHANGES TO MAINTAIN ONTOLOGY CONSISTENCY.

In Proceedings of the International Conference on Knowledge Engineering and Ontology Development, pages 388-391

 SciTePress

of ontology and its conformity after evolution. This

task is essential in an ontology evolution process

since it conditions the validation and the adoption of

the new version of ontology. In this work, we

develop anticipatory solutions managing the

inconsistencies upstream of their appearance to

avoid them. We propose a preventive approach to

anticipate inconsistencies due to each type of change

and to propose additional changes allowing

correcting these inconsistencies. These additional

changes are automatically applied by the system in

combination with the type of change.

Additional changes depend on the type of change.

To define additional changes, we identify the types

of change likely to generate inconsistencies, analyze

these inconsistencies and define additional changes

able to correct them. A kit is composed of the type

of change and the additional changes.

3 SPECIFICATION OF KITS

OF CHANGES

The kits of changes allow updating ontology while

preserving its consistency. We define for each kit of

changes: the type of change, the pre-conditions,

post-conditions, potential inconsistencies and

additional changes.

 Pre-conditions: must be checked and controlled

by the system before applying a type of change.

 Inconsistencies: potential problems can be

generated due to a type of change.

 Additional changes: to be attached to each type

of change to correct the inconsistencies that may

be generated.

 Applicative post-conditions: define what must be

true after applying the type of change,

independently of the ontology coherence.

 Coherence post-conditions: define what must be

true if the ontology is coherent.

Each type of change represents with additional

changes, a "coherent kit of change". We define as

many kits of changes as types of changes identified

in the taxonomy of the types of changes (Sassi and

al, 2007).

In addition, we define rules of consistency which

ontology must verify to be considered as consistent.

Definition: a type of change preserves the

consistency of ontology if it preserves the rules of

consistency.

In an evolution process, the application of types of

changes should have as consequence an ontology

which is in conformity with the whole of coherence

rules.

- Examples of rules of consistency:

 Define for each domain the key concepts which

should not be removed from the ontology: Rule

(1).

 Ontology should not have isolated concepts:

Rule (2).

 A concept must comprise at least a property:

Rule (3).

 Ontology should not contain semantically

contradictory information: Rule (4).

 The semantics of information should not be

reversed between ontology versions: Rule (5).

 An ontological entity must conserve all

elements of definition: Rule (6).

 Ontology should not contain redundancies of

data: Rule (7).

Some rules of consistency, such as Rule (1), are

taken into account in the pre-conditions. For

example, to remove a concept, it should not be a

key concept.

4 FORMALIZATION

OF THE ONTOLOGY

STRUCTURE

Formalizing the changes semantics requires a

definition of the ontology model as well as its

change operations. Formalization is based on:

 Formal methods: based on mathematics, can be

used in any step of the cycle of life of ontology

in order to make precise a development process.

 A language of formal specifications: used for an

abstract representation of ontology.

In this work, we use the Z language and Z-eves tool

to formally specify the ontology structure and the

kits of changes.

Ontology is represented as a schema. It is defined as

the set of concepts and relationships between them.

Ontology 

C:  Concept

RAS:  Association

RA:  Aggregation

RC:  Composition

Z-BASED FORMALIZATION OF KITS OF CHANGES TO MAINTAIN ONTOLOGY CONSISTENCY

389

RH:  Hierarchy

RS:  Semantic_Relationship

R:  Relationship

A:  Axiom

AR:  Association_Axiom

AC:  Concept_Axiom

key_C:  Key_Concept

key_Sem:  Key_Semantic_Relationship

L:  Partial_Link



A concept is an ontology element, characterized

with a noun and a set of properties.

Concept

name: WORD

P:  Property_C



P  



A relationship is characterized with a noun and

its related concepts.

Relationship

name: WORD

c1: Concept

c2: Concept



We distinguish conceptual relationships

(association, aggregation, composition, hierarchy)

and semantic relationships. An association has a

noun, a set of related concepts, cardinalities and a set

of properties.

Association

Relationship

P:  Property_R

CL:  Concept

AC:  Cardinality_Axiom



To take into account the n-ary associations

(n>2), we define the notion of Partial_Link which

allows extending an existing association with a link

to another concept.

Partial_Link 

concept: Concept

rel: Association

AC: Cardinality_Axiom



5 FORMAL SPECIFICATION

OF KITS OF CHANGES

We present in this section a formal specification of

some kits of changes.

1. Add_Concept:Syntax: Add_Concept (cnew)

Z statement:

cname?: WORD

c?: Concept

pname?: WORD

rname?: WORD

cnew!: Concept

rnew!: Relationship

pnew!: Property_C

Pre-conditions: c: C cname?  c . name

Potential inconsistencies:

Rule (2) ; Rule (3)

Applicative post-conditions: C' = C  cnew!

Coherence post-conditions:

R' = R  rnew!;

cnew! . P = cnew! . P  pnew!

Additional changes:

Add_Relationship (cnew, c, rname)

Add_Concept_Property (c, pname)

2. Rename_Concept:

Syntax: Rename_Concept (c, cnameNew)

Z statement:

c?: Concept

cname?: WORD

Pre-conditions: c?  C ; x: C  x . name  cname?

Applicative post-conditions: c?. name = cname?

Coherence post-conditions: Ø

Additional changes: Ø

3. Remove_Concept:Syntax: Remove_Concept

(c)

Z statement:

c?: Concept

Pre-conditions:

c?  C

Potential inconsistencies:

Rule (6)

Applicative post-conditions: C' = C \ c?

Coherence post-conditions:

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c? . P = 

r: R | r . C1 = c?  r . C2 = c?  R' = R \ {r}

r: RC | r . C1 = c?  C' = C \ {r. C2}

a: AC | a .C1 = c?  a .C2 = c?  AC' =AC

\{a}

Additional changes:

Remove_Concept_Property (c, p)

Remove_Relationship (r, c1, c2)

Remove_Concept_Axiom (c1, c2, a)

Remove_Concept (co)

4. Remove_Association:

Syntax: Remove_Association (r, c1, c2)

Z statement:

r?: Association

Pre-conditions: r?  RAS

Potential inconsistencies:

Rule (2) ; Rule (6)

Applicative post-conditions: RAS' = RAS \ {r?}

Coherence post-conditions:

r? . P = 

c: C   r: R  r . C1 = c  r . C2 = c

a: AR | a . R1 = r?  a . R2 = r?  AR' = AR \ {a}

r? . AC = 

Additional changes:

Remove_Association_Property (r, p)

Remove_Cardinality_Axiom (r, c1, c2).

Remove_Association_Axiom (r, r1, a)

Remove_Concept (c)

Add_Relationship (c, c

, rname)

5. Remove_Concept_Axiom:

Syntax: Remove_Concept_Axiom (c1, c2, exp)

Z statement:

a?: Concept_Axiom

Pre-conditions: a?  AC

Applicative post-conditions: AC' = AC \ {a?}

Coherence post-conditions: Ø

Additional changes: Ø

6 CONCLUSIONS

This paper presented kits of changes to allow

updating ontology while maintaining its consistency.

An evolution kit is a sequence of a type change and

additional changes. The type of change allows

updating ontology but does not ensure its coherence.

The application of a type of change may produce

inconsistencies in ontological entities. To correct

them, additional changes are automatically done in

combination with the type of changes.

However, other kits of changes can be defined to

facilitate the expression of evolution requirements,

such as add ontology. Add ontology relates to the

problem of ontology merging and require mapping

algorithms to compare ontological entities. We will

consider this problem in future works.

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Noy N., Klein, M., 2004, Ontology evolution: Not the

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Sassi, N., Jaziri, W., Gargouri, F., 2008, Formalisation of

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