FORMAL METHOD FOR AUTOMATIC AND SEMANTIC MAPPING

OF DISTRIBUTED SERVICE-ONTOLOGIES

Nacima Mellal and Richard Dapoiny

LISTIC/ Polytech’Savoie, universit de Savoie, P.B. 80439, 74944, Annecy Cedex

Keywords:

Services, distributed ontologies, automatic and semantic mapping, Information Flow (IF) model.

Abstract:

Many distributed heterogenous systems exchange information between them. Currently, most of them are

described in terms of ontologies. When ontologies are distributed, arises the problem of achieving sematic in-

teroperability. This is undertaken by a process which deﬁnes rules to relate these ontologies, called “Ontology

Mapping” in order to achieve a given goal. This paper describes a methodology for automatic and semantic

mapping of ontologies. Our main interest is focused on ontologies describing services of systems. These

ontologies are called “Service Ontologies”. So, we investigate an approach where the mapping of ontologies

provides full semantic integration between distributed service ontologies using Information Flow model.

1 INTRODUCTION

In the Artiﬁcial Intelligence ﬁeld, exchange of infor-

mation between distributed systems is a challenging

theme. Systems usually need to interoperate, they

also need to understand what they exchange. This in-

troduces the notion of Semantic Interoperability. To

reach this last, information must be expressed in a for-

mal way. Ontologies seem good mean to achieve this.

An ontology is generally seen as an explicit speciﬁ-

cation of a conceptualization (Gruber, 1993), (Fikes,

1996). It should give an explicit deﬁnition of concepts

and relations between them. In order to exchange in-

formation basing on the use of ontologies, this prac-

tice of ﬁnding correspondences between ontologies is

called “Ontology Mapping”. It arises in many appli-

cation scenarios. In (Doan and Halevy, 2004) authors

have focused on the semantic integration work in the

database community. Where, in (Noy and Stucken-

schmidt, 2005) this issue is studied by giving a brief

review of ontology-based approaches to semantic in-

tegration. In (Kalfoglou and Schorlemmer, 2003),

a formalization of the coordination process between

ontologies is described, based on exchange that cap-

tures progressive partial semantic integration, using

the IF model (Barwise and Seligman, 1997). Most

of these works propose semi automatic mappings to

reach the semantic interoperability. Thus, it is neces-

sary to develop automatic techniques for mapping on-

tologies. Our approach shares the idea in (Kalfoglou

and Schorlemmer, 2003), which uses of IF Model

to solve semantics coordination of ontologies in dis-

tributed systems. We propose a methodology allow-

ing automatic mapping between distributed ontolo-

gies. As a crucial topic, information exchange be-

tween ontologies must occur in a semantic and sound

manner. The IF model is mainly based on a theory,

called IF Theory. This latter introduces a consequence

relation ⊢ on a set of types, so that we can retrieve

from a type t

the corresponding type t

by ⊢, t

and

belonging to different sets of types. Precisely, how

the IF model selects two entities A and B, located re-

spectively in two systems. To relate these entities, the

model starts from the type of A, ﬁnds out what type is

related to it in the second system . Then, ﬁnds the cor-

responding entity B thanks to the relation ⊢. Entities

of two systems are linked by an information channel.

As many nowadays distributed systems are based on

the notion of services, we describe systems by a set

of functionalities offered by its components as ser-

vices. Certainly, services may depend on others of the

same system or of different systems. An efﬁcient and

promising way to implement this is through the use

of ontologies. In our approach, concepts of ontolo-

gies are services, relationships between them express

the functional dependencies among them. Our inter-

est is to achieve the semantic interoperability when

services depend to others in a distributed system us-

ing IF model to connect services in order to solve a

high level service.

In this paper, we introduce in section 2 the notion of

Service Ontology, illustrating it by an example. Then,

we describe in section 3 the Ontology Mapping mech-

anism. We conclude by some perspectives.

259

Mellal N. and Dapoiny R. (2007).

FORMAL METHOD FOR AUTOMATIC AND SEMANTIC MAPPING OF DISTRIBUTED SERVICE-ONTOLOGIES.

In Proceedings of the Second International Conference on Software and Data Technologies - PL/DPS/KE/WsMUSE, pages 259-263

DOI: 10.5220/0001329602590263

 SciTePress

2 SERVICE ONTOLOGY

2.1 Case Study

The example will illustrate the different deﬁnitions

proposed in this paper. We consider a distributed

system which employs ticket agents. Each agent is

situated in a sub-system. Agents attempt to achieve

some services for distributing, selling, buying, book-

ing tickets from a range of sources. They may com-

municate and exchange services on the web. We

will treat a case where an agent (Agent

) attempts to

achieve a service of buying a ticket to go from Annecy

(France) to Barcelona (Spain). Once the depart and

the destination are identiﬁed, agent may obtain the

itinerary, but how to do if the agent can not achieve

the service of obtaining the itinerary? We will give

details about this problem in the next sections.

2.2 Service Notion

In (Kitamura et al., 2004), authors denoted a function-

ality of a component as a “verb+noun” style for rep-

resenting the components activities. Following this

approach, we associate with each service some pos-

sible actions in order to fulﬁll the intended service

(Hertzberg and Thiebaux, 1994), (Lifschitz, 1993).

So, we describe each service as a tuple: (Action verb,

{Property, Object}), where the action verb acts on

the object’s property. For each object, corresponds

a type deﬁning its classiﬁcation domain. We denote

a type an “Object Type” and the object itself speci-

ﬁed by an identity is denoted “Object Token”. The

tuple {Property, Object} is called a context, when the

object is an object type, we call the context “Context

Type”, otherwise, “Context Token”.

Deﬁnition 1 “Context Type (respectively, Context

Token)”

A context type ξ

(resp, context token) is a tuple:

de f

≡ (p, {ψ

, ψ

, ...ψ

}). Where p is a property, ψ

, ... ψ

is a set of object types (resp, object tokens).

Following the example, we suppose that the dis-

tributed system is represented by two ticket agents.

Thus, we propose some context types to the agent

Agent

= (Departure, Trip), ξ

= (Destinaton, Trip),

= (Date, Trip), ξ

= (Itinerary,Trip), and

= (Price, Trip).

Context tokens are not limited to:

= (Annecy, Flight − Trip), c

(Barcelona, Flight − Trip), c

= (July − 22 −

2007, Flight − Trip), c

= (Itinerary

, Flight −

Trip), and c

= (200euros, Flight − Trip).

Remark: We propose the same context types and

tokens to Agent

replacing ξ by ξ

′

and c by c

′

The problem of ﬁnding a formal structure to the

notion of service is treated in several researches. In

(Umeda et al., 1996), author suggested a represen-

tation of the form “To do X” for intended services.

Following this principles, we deﬁne a service such

as:

Deﬁnition 2 “Service Type (resp, Service Token)”

A Service type (resp, Service token), denoted by γ

, is

deﬁned as a pair:

de f

≡ (a, {ξ

, ..., ξ

}). Where a, is an action verb, Ξ,

a non-empty set of context types (resp, context tokens)

and {ξ

, ..., ξ

} ⊆ Ξ.

According to our example, there are basically some

primitive service types. Some are given to Agent

= (to

identify, {ξ

}), γ

= (to identify, {ξ

}),

= (to

identify, {ξ

}), γ

= (to obtain, {ξ

})

and γ

= (to

obtain, {ξ

})

Some service tokens for Agent

= (to

identify, {c

}, θ

= (to identify, {c

= (to

identify, {c

}, θ

= (to obtain, {c

}

and θ

= (to

obtain, {c

}

Remark: As a special case, we propose the same ser-

vice types and tokens to Agent

replacing γ by γ

′

and

θ by θ

′

2.3 Service Ontology

An ontology is a description of the concepts and re-

lationships between them. In our context, ontology is

described by:

1. Concepts: We associate service types with ontol-

ogy concepts.

2. Relations: An ontology is related to a Gentzen

system, which is a deduction system expressed by

the ﬁrst order logic. The notion of sequent is cen-

tral in Gentzen system. Given a set S, a sequent of

S is a pair hX,Yi of subsets of S. A binary relation

⊢ between subsets of S is called a consequence

relation on S. The syntax of sequent is X ⊢ Y

Sequents will represent subsets of ontology con-

cepts (service types), ⊢ will express the functional

dependency between these services.

Deﬁnition 3 “Functional Relation ⊢”

Let C be a non empty set of ontology concepts.

The binary relation ⊢ between subsets of C is the

Gentzen consequence relation on C, such that:

The notation X ⊢ Y may be written by x

, x

, .. ⊢

, y

, .., where x

, x

, .. ∈ X and x

, x

, .. ∈ Y. The comma

on the left is interpreted like a conjunction, the comma on

the right like a disjunction

ICSOFT 2007 - International Conference on Software and Data Technologies

260

Two subsets of C: c

and c

are related by ⊢, de-

noted c

⊢ c

, iff the service types of c

inﬂuence

functionally service types belonging to c

The expression c

⊢ c

must be understood that

the only way to achieve services in c

is to have

already achieved services in c

Therefore, we propose the following deﬁnition of a

service ontology:

Deﬁnition 4 “Service Ontology”

A Service Ontology “SO”is a tuple < C, R >, where

C is the set of ontology concepts and R is the set of re-

lations. SO is described by an oriented graph, where,

its nodes represent concepts, and edges linking nodes

represent ⊢.

The deﬁned SO describes a set of concepts, service

types, and the relations between them. This set can

be seen as complex service which is called global

service and its elements (ontology concepts) as sub-

services. We deduce that a global service is associ-

ated with a SO. It is a particular service token. We

detail two global services Θ

related to Agent

and

′

for Agent

. Θ

= (to

buy, {ticket,Flight − Trip})

represented by the service ontology SO

. Θ

′

(to

obtain, {Duration,Flight − Trip}) is represented

by SO

, (see ﬁgure 1). In this section, we described

Figure 1: Service Ontologies of Θ

and Θ

′

that the aim of an ontology of services is to describe

systems. The question which should be asked is how

to map between ontologies if they describe distributed

systems?

3 ONTOLOGY MAPPING

The approach is presented by different steps: Formal

description of services, building service-ontologies,

building the information channel to the given applica-

tion, and identiﬁcation of the logic on the core of the

information channel and its distribution on this chan-

nel. Before developping the ﬁrst and second steps, we

invite the reader to see (N. Mellal, 2006) and (Barwise

and Seligman, 1997) for more details on IF Model.

Table 1: The binary relation |= of IF-C

and IF-C

′

1 0 0

′

0 1 0

′

0 0 0

′

0 0 1

′

0 0 0

′

1 0 0

′

0 1 0

′

0 0 0

′

0 0 1

′

0 0 0

3.1 Building the Information Channel

3.1.1 Identiﬁcation of IF Classiﬁcations

For each global service described by a service ontol-

ogy, we associate an IF classiﬁcation. For the agent

Agent

, we associate the classiﬁcation C

to Θ

and

′

to Θ

′

, see table 1:

3.1.2 Identiﬁcation of IF Theories

IF Theories describe the different constraints on in-

formation ﬂowing in the system. In our context a

constraint on service types is denoted γ

⊢ γ

repre-

sents the fact that γ

depends functionally on γ

. Ac-

cording to our objectives, IF theory speciﬁes service

ontology. We give in the following the IF theories

of agents Agent

and Agent

: For (Agent

), we have

⊢ γ

, γ

⊢ γ

, γ

⊢ γ

and γ

, γ

⊢ γ

, γ

⊢ γ

For (Agent

), we have γ

′

⊢ γ

′

, γ

′

⊢ γ

′

, γ

′

, γ

′

⊢ γ

′

3.1.3 Construction of IF Channel

It is the central aspect in the process of mapping

between service ontologies. In this step, we aim to

achieve Θ

. As assumed in section (2), Agent

cannot

obtain the itinerary from Annecy to Barcelona, so the

service token θ

= (to

obtain, {c

}) is not achievable

locally. Therefore, we will assume a partial align-

ment of context tokens. c

will be connected with

the context tokens candidates where their types are

related by the ⊢, so having the same type as c

. These

candidates (c

′

, ..) are obtained from remote systems.

Let us code that we may ﬁnd service types having the

same context type as the context type of c

or not. It

is formalized by the classiﬁcation A given in the table

2. Type of A is c

and its possible tokens are a and

b. A plays the role of reference to compare types of

distributed classiﬁcations. In our case, we compare

types of C

with those of C

′

. Let us note that in this

application, we get only two cases, but in general

for m context tokens we will get 2

different cases.

Our aim is to relate via infomorphisms the context

token c

appearing as a token in C

with those of

FORMAL METHOD FOR AUTOMATIC AND SEMANTIC MAPPING OF DISTRIBUTED SERVICE-ONTOLOGIES

261

Table 2: A and its ﬂip A

⊥

A :



a 0

b 1

⊥



⊥

a b

0 1

distributed classiﬁcations (C

′

). We note that c

appeared as a type in A, where the context tokens in

the other classiﬁcations are classiﬁed as tokens and

not as types. That is, it is useful to introduce the ﬂip

of the classiﬁcation A, by interchanging rows and

columns. See the table 2. Thus, this gives rise to the

respective infomorphisms ζ

(Agent

)

, ζ

′

(Agent

)

permit to

connect A

⊥

with C

and C

′

. ζ

(Agent

)

: A

⊥

→ C

(Agent

)

and ζ

′

(Agent

)

: A

⊥

→ C

′

(Agent

)

Applying these infomorphisms we ﬁnd:

with C

: ζ

∧

(γ

) = a, ζ

∧

(γ

)=a, ζ

∧

(γ

)=a, ζ

∧

(γ

)=b,

∨

)= c

with C

′

: ζ

′

∧

(γ

′

) = a, ζ

′

∧

(γ

′

) = a, ζ

′

∧

(γ

′

) = b, ζ

′

∨

)

= c

′

The alignment allows the generation of the desired

channel between C

(Agent

)

and C

′

(Agent

)

. A core clas-

siﬁcation C is built with a couple of infomorphisms:

(Agent

)

: C

(Agent

)

⇄ C and g

(Agent

)

: C

′

(Agent

)

⇄ C

. Types of C are the elements of the disjoint union

of types from C

(Agent

)

and C

′

(Agent

)

. Tokens are the

cartesian product of tokens in C

and tokens in C

′

According to our scenario, c

of type γ

is connected

to a token c

of type γ

in the classiﬁcation C

′

(Agent

)

to form the pair (c

, c

) iff ζ

∧

(γ

)=ζ

′

∧

(γ

′

). This con-

dition means that γ

and γ

′

are of the same type in

the classiﬁcation A

⊥

. As a result, we have the pair:

, c

′

). The IF theory on the core is built on the

union of types. The theory expresses how the types

of C

are related logically to the types of C

′

on the

core of the information channel. The IF theory relates

with the types in C

′

. As a result, we have one con-

straint: γ

′

⊢ γ

for the sumC

′

. In this example, we

ﬁnd only one constraint, but it is possible to ﬁnd more

than one and agent will choose the correspondent ser-

vice type, to achieve the global service.

3.2 Identiﬁcation of the Logic on the

Core and the Distributed IF Logic

Given the logic Log(C)=L on the core C, the dis-

tributed logic DLog(C) on the sum of classiﬁcations

(Agent

)

′

(Agent

)

is the inverse image of Log(C)

on this sum. In other words, the inverse im-

age of the IF logic in C is the result of the co-

product of C

(Agent

)

and C

′

(Agent

)

with the mor-

phism [g

(Agent

)

, g

(Agent

)

]

−1

. We obtain sequents like

(γ

′

(Agent

)

, γ

(Agent

)

) relating service types on remote

systems to the local service type γ

. This result de-

scribes the semantic interoperability. According to

the initial constraint on service tokens the sequent

(γ

′

(Agent

)

, γ

(Agent

)

) matches the conditions. There-

fore, the C

has to be mapped semantically to C

′

order to constitute a sound distributed service.

4 CONCLUSION

We have presented in the present paper a formal

method for mapping distributed service ontologies in

a sound and automatic manner, basing on IF model.

In (N. Mellal, 2006), we proposed an algorithm spec-

ifying the process of mapping among multi agent sys-

tems which represent distributed systems. Each agent

is situated in a a system and has its own service on-

tologies. In this work, the IF-based approach tackles

the problem of building these dependencies from dis-

tributed logics. Future work includes implementing

a multi agent system to achieve automatically the se-

mantic mapping of service ontologies.

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