METHOD FOR APPROXIMATION TO ONTOLOGY REUSE

PROBLEM

Eleni Tsalapati, Giorgos Stamou and Giorgos Koletsos

School of Electrical and Computer Engineering, National Technical University of Athens

GR-15773 Zographou, Athens, Greece

Keywords:

Ontology Reuse, Module, Locality.

Abstract:

We describe a methodology that approximates the safety condition in the integration of ontologies. Intuitively,

the safety condition ensures that, after the reuse, the external ontology remains intact. It was recently proved

that it is a problem of high complexity to examine whether this condition holds. In order to approximate the

problem, we suggest a method by which the ontology designer that reuses concepts from an ontology network

will be informed about the degree in which the safety is violated and according to this information she can

choose the appropriate ontologies to reuse concepts from.

1 INTRODUCTION

Today, one can ﬁnd in the Web a vast number of

ontologies on the same domain in different levels

of granularity or in different domains, available for

reuse. The research conducted on the problem of

ontology reuse process, regardless of the approach

method, has revealed some very crucial obstacles. It

is essential that the ontology integration should be

carried out in such a way that the consequences of

the axioms of the external ontology are not changed

when its elements are reused in the ontology under

development. It is proved (Lutz et al., 2007) that to

question whether this condition holds, even in lan-

guages of very low expressivity, is practically unde-

cidable (2EXPTIME-complete).

In this paper, we assume that the ontology de-

signer wishes to generalise (e.g., add new supercon-

cepts) some of the concepts of the ontology under

development by importing concepts from an external

one. At the same time though, we do not prevent the

developer from reﬁning (e.g., add new subconcepts)

some concepts, as well. However, the simultaneous

generalization and reﬁnement from the same external

ontology may introduce new knowledge to this ontol-

ogy. For instance, if the ontology developer reuses

in his ontology P the concepts X, Y from the ontol-

ogy Q to create the following axioms: A v Q : X and

Q : Y v B, and the axiom B v A is already present

in P, then the axiom Q : Y v Q : X is implied, which

may not hold in Q. In the same way, non anticipated

changes may also occur in the ontology P.

We have developed a tool that provides the on-

tology developer with an estimation of the changes

caused not only in the external ontology, but also in

the ontology under development. Being aware of the

effects of the integration of the two ontologies, the

user is enabled to choose ﬁrstly, whether he will reﬁne

a concept or not, and secondly, the most appropriate

external ontology to choose concepts from, based on

the criterion “to cause the least possible damage”.

2 PRELIMINARIES

We consider ontologies to be a set of axioms in a

descriptions logic language L. Description Logic is

the language that underlies the modern ontology lan-

guages, like OWL DL. The signature of an ontology

O is the set of atomic concepts (C), atomic roles (R)

and individuals (I) that occur in O. An ontology based

on S HOIQ language contains also nominals.

The notions of logical entailment, S-

interpretation, restriction of an S-interpretation

and satisﬁability follow the deﬁnitions of the D.

L. Handbook (Baader et al., 2003). We omit their

description in this paper due to limited space. An

expansion of an S

-interpretation I

to S is an

S-interpretation I such that I |

= I

(Grau et al.,

2007b). In bottom expansion, atomic concepts and

roles, not in S are interpreted as Bottom (⊥), whereas

416

Tsalapati E., Stamou G. and Koletsos G. (2009).

A METHOD FOR APPROXIMATION TO ONTOLOGY REUSE PROBLEM.

In Proceedings of the International Conference on Knowledge Engineering and Ontology Development, pages 416-419

DOI: 10.5220/0002296304160419

 SciTePress

in top expansion, they are interpreted as Top (>).

The reuse of an external ontology can lead to un-

desirable side effects, such as the entailment of new

axioms or even inconsistencies involving the reused

vocabulary. However, a safe ontology for a signature

S, enables the implementation of the ontology reuse

process without any fallacies:

Deﬁnition 2.1. (Safety for a Signature, (Grau et al.,

2007b)). Let L be an ontology language, and let P

be an ontology and S a signature over L. We say that

P is safe for S w.r.t. L , if for every ontology Q over

L with Sig(P) ∩ Sig(Q) ⊆ S, we have that P ∪ Q is a

conservative extension of Q w.r.t. L.

The conservative extension property ensures that the

additional axioms of the ontology under development

will not add any new consequences over the vocabu-

lary of the reused ontology.

Following, we describe the syntactic deﬁnitions

>-locality and ⊥-locality concepts (Jim

enez-Ruiz

et al., 2008), as they are heavily used in our method.

Deﬁnition 2.2. (Syntactic ⊥-Locality and >-Locality for

SHIQ). Let S be a signature. An axiom a is ⊥-local w.r.t. S

(>-local w.r.t S) if a ∈ Ax(S), as deﬁned in (a) ((b)), where

C and R denote arbitrary concepts and roles. An ontology

⊥

-local (

-local) w.r.t. S if

⊥

-local (

-local) w.r.t.

S for all a ∈ O.

(a) ⊥ − Locality. Let A

⊥

, R

⊥

6∈ S, C

⊥

∈ Bot(S), C

(i)

∈

Top(S), n ∈ N \{0}:

Bot(S) ::= A

⊥

|⊥ | (¬C

)| (C uC

⊥

)| (C

⊥

uC) |(∃R

⊥

.C) |(∃R.C

⊥

)|(≥ nR

⊥

.C) |(≥ nR.C

⊥

)

Top(S) ::= > |(¬C

⊥

)| (C

)| ≥ 0R.C

Ax(S) ::= C

v C |C v C

⊥

v R |Trans(R

⊥

)

(b) > − Locality. Let A

, R

6∈ S, C

⊥

∈ Bot(S), C

(i)

∈

Top(S), n ∈ N \ {0}:

Bot(S) ::= (¬C

)| ⊥ |(C uC

⊥

)| (C

⊥

uC) |(∃R.C

⊥

)| (≥ nR.C

⊥

)

Top(S) ::= A

|> | (¬C

⊥

)|(C

)

|(∃R

)|(≥ nR

)| ≥ 0R.C

Ax(S) ::= C

v C |C v C

⊥

|R v R

|Trans(R

)

If an ontology P is ⊥-local or >-local w.r.t. a signa-

ture S, then P is safe for S (Grau et al., 2007a). The

simultaneous reﬁnement and generalization of an on-

tology from the same external one, may compromise

safety (Jim

enez-Ruiz et al., 2008). Particularly, when

the signature S is to be reﬁned (generalized), the on-

tology P must be ⊥-local (>-local) w.r.t. S. Conse-

quently, in the case of reﬁnement of the signature S

(and thus generalization of P) the set of non-⊥-local

axioms contains the axioms that threaten the safety.

3 METHOD FOR PARTIAL

ONTOLOGY REUSE

The goal of this method is to enable the ontology de-

veloper to reﬁne and generalise several concepts from

the same external ontology by providing him with an

estimation of the non-safety degree resulted from this

ontology reuse. Particularly, we are interested in pro-

viding the user not only with the affected part of the

external ontology Q, but also with the non anticipated

changes (new axioms over the language of P) caused

in the ontology under development.

According to the previous paragraph the set of the

non-⊥-local axioms w.r.t. Sig(Q) equals to a super-

set of the axioms that threaten the safety of the inte-

gration. To clarify this, we demonstrate the follow-

ing example, in which two ontologies developed for

the BOEMIE Project (www.boemie.org), the Athletic

Event Ontology, aeo, and the Geographic Information

Ontology, gio are used.

Example 3.1. Supposing that SportsPOI is concept of

aeo ontology and aeo reuses concepts from gio, then

the following is a non-⊥-local axiom wrt Sig(gio):

gio:Stadium v SportsPOI (1)

If the following axioms also exist in aeo ontology :

gio:Stadium v ∃isLocatedIn.Cityu

uSportsPOI u ∃hasArea.TrackArea

(2)

∃isLocatedIn.City u SportsPOI v

gio:ManMadeFeature

(3)

Then following new axiom of gio is implied:

gio:Stadium v gio:ManMadeFeature (4)

Apart from the fact that this axiom might introduce an

inconsistency in gio, it also adds a new deﬁnition on

the concept Stadium, that did not initially exist. We

call the axiom (1) as directly affected axiom.

The set of directly affected axioms is the remain-

ing set of non-⊥-local axioms after the abstraction of

the axioms already included in gio:

Deﬁnition 3.2. Let L be an ontology language and P and

Q be ontologies over L. If ontology P reuses concepts from

ontology Q, then the set A of the directly affected axioms of

P for Q is:

A = {a ∈ P|a : non − ⊥ − localAxiom w.r.t.Sig(Q)∧

∧a 6∈ Q}

In Example 3.1 the deﬁnition of the concept Stadium

of gio ontology, is changed. To approximate the sub-

set of the reused entities affected by this integration it

sufﬁces to ﬁnd the subsumed concepts of the set of di-

rectly affected axioms. For instance, in Example 3.1,

the Stadium concept is a directly affected entity. At

A METHOD FOR APPROXIMATION TO ONTOLOGY REUSE PROBLEM

417

present this theory concerns only simple axioms (ax-

ioms of the form A v C, where A is atomic concept).

The set of directly affected entities of an axiom a by

an ontology P is symbolized as DAE(a,P). The set of

directly affected entities of an ontology Q by an on-

tology P is symbolized as DAE(Q,P) and represents

the set of affected entities of each axiom of Q.

The modiﬁcation of the Stadium concept deﬁni-

tion also affects all the concepts that are related di-

rectly or indirectly to Stadium in gio. To make this

more clear we demonstrate the following example:

Example 3.3. Suppose that gio contains the following

axioms:

IndoorStadium v Stadium (5)

OutdoorStadium v Stadium (6)

then the concepts IndoorStadium and OutdoorStadium

are also altered. The modiﬁcation of these deﬁnitions

is propagated to other concepts related to them. For

instance, the deﬁnition of IndoorAthleticCenter con-

cept is also affected:

IndoorAthleticCenter v

∃contains.IndoorStadium

(7)

Thus, to ﬁnd the total set of the affected concepts is

sufﬁces to ﬁnd all the subconcepts, directly and in-

directly related to an affected entity. To achieve this

we calculate, the set of >-local axioms of ontology Q

w.r.t. S

= Sig(Q) \ S, where S is the set of affected

entities of Q by ontology P. Intuitively, in this way,

all affected entities become equivalent to the top con-

cept and thus, the set of >-local axioms includes the

subsumption axioms that their right hand side concept

is affected. If an axiom is found to be >-local then it

is added to the set of affected axioms and its directly

affected entities are abstracted from S

, thus the next

checked axiom is tested w.r.t. >-locality for the new

. More formally, the set of affected axioms is de-

ﬁned as:

Deﬁnition 3.4. Let P and Q be ontologies, such that

P reuses concepts from Q. Then the set of affected

axioms of Q by ontology P is deﬁned as:

AA(Q,P) = {a ∈ Q|a : > − local w.r.t.(Sig(Q)\

(DAE(Q,P) ∪ DAE(Q,AA(Q, P))))}

Similarly, if P is the ontology under development and

the ontology P before the reuse of the external

ontology, the set of affected axioms of the ontology

is AA(P

,P). To calculate the rate of affected ax-

ioms of an ontology Q from an ontology P, r(Q, P),

it sufﬁces to divide the number of axioms of the set

AA(Q,P) to the total number of axioms of Q (i.e.

r(Q, P) = | AA(Q,P) | / | Q |).

Having the rates r(Q,P) and r(P

,P), we can cal-

culate the total cost of the reuse process in relation to

two weights w

and w

, that determine how important

is the particular change to each ontology:

Deﬁnition 3.5. (Total Cost) Let P and Q be two on-

tologies, S the set of entities of Q reused by P and

, w

> 0 the weights. The total cost of the ontology

reuse procedure is:

TotalCost =

· r(Q,P) + w

· r(P

,P)

+ w

Following, we demonstrate the algorithm that com-

putes the affected axioms of ontology Q from P.

Algorithm 1: AA(Q,DAE(Q,P)).

Input:

DAE(Q,P):set of Directly Affected Entities of Q from P

Q: external ontology

Output:

: Affected Axioms

S ← (Sig(Q) \ DAE(Q,P)), Q

←

0, Q

← Q

2: while

(¬

empty

)){

3: forall

a ∈ {a|a ∈ Q

∧ a : OW LSubClassAxiom} {

4: if

(> − locality −test(a,S)){

= Q

∪ {a}

S = S \ {LHS(a)}

= Q \ Q

}

8: else

= Q

\ {a}}

}}

10: return

For the locality-test we used the method provided by

PRoSE (http://krono.act.uji.es/people/Ernesto/safety-

ontology-reuse/proSE-current-version). The LHS

function returns the left hand side of a subclass ax-

iom.

Proposition 3.6. For every input P and Q, the Algo-

rithm 1 computes the affected axioms of the partici-

pating ontologies.

Proof (Sketch). The algorithm terminates as in every

iteration of the while loop the size of Q

decreases.

Initially, all the >-local axiom are transferred from

to Q

, and then the rest axioms, which are non->-

local, are removed from Q

. Note, that the syntactic

locality test has polynomial complexity.

The output AA(Q, DAE(Q,P) is the set of affected

axioms of Q from P, as every axiom that is nei-

ther in Q

nor in Q

is non->-local wrt Sig(Q) \

(DAE(Q,P)∪DAE(Q,AA(Q,P))), since, as indicated

in line:8, it remains in the set Q \ (Q

∪ Q

). ¤

In order to evaluate this algorithm, we tested it

with the ontologies aeo and gio:

Example 3.7. After the ontology reuse, aeo contains

2473 axioms and gio 607. The current form of aeo

KEOD 2009 - International Conference on Knowledge Engineering and Ontology Development

418

ontology, has generalized only some of its concepts by

reusing external concepts from gio ontology. Thus, gio

ontology is not threatened by aeo. For the purpose of

this example, we added the following axioms to aeo:

Table 1: Experimental results.

Axiom Thr. Ax. % Time

g:GeographicObject v HLC 33.4 7.06

g:Polygon v HLC 0 6.87

g:Surface v HLC 0.4 9.51

g:Building v ∃hasPart. MLC 2.6 7.79

The ﬁrst column of the table demonstrates the ax-

ioms added, the second the percentage of gio ontology

threatened by the corresponding axiom and the third

the time (seconds) required to return the results.

The GeographicObject concept of gio ontology is

relatively high in the hierarchy and thus the potential

modiﬁcation of its deﬁnition will affect a large part of

gio ontology. On the other hand, Polygon concept is

on the bottom of the ontology and thus does not affect

any part of gio ontology. Consequently, the user is al-

lowed to reﬁne this concept, although other concepts

of gio have been generalized, without any change on

the information provided by gio. The Surface concept

affects the following axioms:

Polygon v Surface (8)

MultiSurface v ∃hasGeometryObject. Surface (9)

MultiPolygon v MultiSurface (10)

which were traced by our method (0,4% of the whole

ontology). The modiﬁcation of the Building concept

threatens 16 other subconcepts of this concept.

4 RELATED WORK

Two basic directions deﬁne the research areas devel-

oped in the ﬁeld of knowledge reuse. The ﬁrst direc-

tion is concentrated on the safe ontology reuse. The

second direction is focused on the development of ap-

propriate formalisms that enable the ontology reuse

via conceptualized interpretations (Bao et al., 2007).

The research based on the ﬁrst direction has lead

to the exploitation of the notion of module and the

development of tools like PRoSE, which enables the

safe ontology reuse but under very strict constraints

(the user is allowed only to generalise or to reﬁne the

concepts of the target ontology). Another interesting

approach is suggested by (Suntisrivaraporn, 2008),

where a new kind of module is introduced, but it con-

cerns only E L+ ontologies.

5 CONCLUSIONS - FURTHER

RESEARCH

In this study we described a method by which we can

approximate the ontology reuse problem. After the

integration of two ontologies, the ontology designer

is informed about the extent of the loss of information

that will occur in order to maintain the safety state. In

this way, the designer can choose the appropriate on-

tology to reuse concepts from, based on the criterion

of causing the least loss of information.

For further research, we are interested in adjusting

the method in order to deal with more complex ax-

ioms than the simple axioms. We are also interested

in examining the condition of safety, in case the set of

reﬁned entities belongs to a disjoint module from the

set of generalised entities. Finally, another direction

followed by our research could be to investigate the

ontology reuse problem in the case of interaction of

more than two ontologies.

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