a hybrid method for integrating multiple ontologies

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A HYBRID METHOD FORINTEGRATING MULTIPLEONTOLOGIESTrong Hai Duong a , Ngoc Thanh Nguyen b & Geun SikJo aa School of Computer and Information Engineering,Inha University , Koreab Institute of Computer Science, WroclawUniversityof Technology , PolandPublished online: 06 Feb 2009.

To cite this article: Trong Hai Duong , Ngoc Thanh Nguyen & Geun Sik Jo (2009) AHYBRID METHOD FOR INTEGRATING MULTIPLE ONTOLOGIES, Cybernetics and Systems:An International Journal, 40:2, 123-145, DOI: 10.1080/01969720802634055

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A HYBRID METHOD FOR INTEGRATING MULTIPLE

ONTOLOGIES

TRONG HAI DUONG1, NGOC THANH NGUYEN2,and GEUN SIK JO1

1School of Computer and Information Engineering,Inha University, Korea2Institute of Computer Science, Wroclaw Universityof Technology, Poland

While there has been a variety of research focusing on ontology

integration based on simple techniques (e.g., element- or structure-

level techniques), the hybrid approaches combining the simple tech-

niques have not been explored. In this paper we describe a hybrid

method to integrate multiple ontologies in several levels, such as

the element level, internal structure, and relational structure. A sem-

antic supporting environment (SSE) combining special domains

(e.g., WordNet) and text corpus are defined in the proposed

approach. An enriched ontology model (EOM) has been proposed

to reduce the initial complexity of the process of ontology inte-

gration. Subsequently, the semantic network called OnConceptSNet

is provided. The relations between the concepts in the OnConceptSNet

are derived from the SSE. An enhanced algorithm (EA) has been

proposed to enhance OnConceptSNet.

INTRODUCTION

Ontology has become a ‘‘buzz word’’ in semantic Web and semantic data

processing, and its importance is being recognized in a multiplicity of

Address correspondence to Trong Hai Duong, Intelligent E-commerce Systems Lab,

School of Computer and Information Engineering, Inha University, Korea.

Cybernetics and Systems: An International Journal, 40: 123–145

Copyright Q 2009 Taylor & Francis Group, LLC

ISSN: 0196-9722 print=1087-6553 online

DOI: 10.1080/01969720802634055

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research fields and application areas, such as knowledge engineering,

database design, and integration, information retrieval and extraction,

standard search (e.g., Yahoo and Lycos), e-commerce (e.g., Amazon

and eBay), configuration (e.g., Dell and PC-Order), and government

intelligence (e.g., DARPA’s High Performance Knowledge Base [HPKB]

program). The ontologies play a central role in facilitating data exchange

between the several sources.

In general, the problem of ontology integration can be formulated as

follows: for given ontologies O1,. . .,On one should determine an ontology O

which could replace them (Gangemi et al. 1998; Pinto and Martins 2001).

Ontology integration is then a complex task. Because the ontologies have

various characteristics and forms, such as languages and domains, struc-

tures of ontologies may differ from each other. Therefore, the authors of

Lee et al. (2006) have suggested an ontology-based architecture that

provides a solid basis for existing studies about ontology integration task.

Pinto and Martins (2001) identified the activities which should be

performed in the ontology integration process. Recently, there has been

an increased interest in creating various tools serving ontology

integration: PROMPT (Noy and Musen 2003) is a semiautomatic and

interactive tool suitable for performing ontology mapping, alignment,

versioning, and merging, based on the Frame paradigm. Noy and Musen

have developed ANCHORPROMPT (2001) for ontology mapping and

PROMPTDIFF (2002) for ontology merging. The limitation of

PROMPT is that two ontologies taking part in the mapping (and

merging) process must be different versions of the same ontology.

MAFRA (Maedche et al. 2002) is an ontology mapping frame-work

using semantic bridge ontology (SBO). In MAFRA, similarity between

two concepts is calculated mainly using lexical analysis via WordNet,

domain glossaries, bilingual dictionaries, and corpuses. There is no

explicit deterministic heuristics other than lexical heuristics (or

synonyms) in the semantic bridge construction. ONION (Mitra and

Wiederhold 2002) is a heuristic-based ontology composition system to

resolve the terminological heterogeneity using two matching approaches:

linguistic matching via WordNet and instance-based matching via data-

bases. Chimaera (McGuinness et al. 2000) is an ontology merging and

diagnosis tool developed by the Stanford University Knowledge Systems

Laboratory (KSL). Owing to this tool, two semantically identical terms

from different ontologies are coalesced so that they are referred to by

the same name in the resulting ontology. Next, chimaera identifies the

124 T. H. DUONG ET AL.

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terms that should be related with each other by subsumption, disjoint-

ness, or instance relationships and provides the support for introducing

those relationships. GLUE (Doan et al. 2001; Doan et al. 2002) is a

system that employs a multistrategy machine learning technique with

jointing probability distribution. First, GLUE identifies the similarities

of instances. Second, it compares the relations, based on the similarity

results of instances. GLUE uses two kinds of base learners: a name

learner and a number of content learners.

The purpose of the above mapping tools is not to create a new

ontology from multiple ontologies. In this paper, we propose a new

method to integrate multiple ontologies. Our main contributions consist

of the following elements:

. Enriched Ontology Model (EOM) has been proposed to improve

the semantic concepts in ontologies from which the complexity is

reduced initially, by a direct matching between the same types of con-

cept, instead of matching blindly or exhaustively among all concepts.

. Semantic Supporting Environment (SSE) has been defined. It not only

provides the semantic relations between the concepts in which the rela-

tions are acquired from the knowledge of combining the special

domain (e.g., WordNet) and the text corpus discovery, but it also

enhances the ability of special domain, such as supplementing new

relations of concepts to the special domain. Moreover, the techniques

of similarity analysis used in SSE are combined with instance-based

similarity, lexical-based, schema-based, and taxonomy-based.

. A semantic network called OnConceptSNet has been also provided. It

allows two concepts owing many relations in the progress of ontology

integration. The OnConceptSNet provides a rich semantic environment

in order that the relations between concepts can enhance themselves.

. An Enhanced Algorithm (EA) has been proposed in which OnCon-

ceptSNet is initiated by the static rules and the knowledge included

in SSE, then enhanced by the meta-rules, and finally, reduced by the

dynamic rules. The final OnConceptSNet will be the one that represents

the candidate ontologies.

BASIC NOTIONS

We assume a real world (A,V) where A is the finite set of attributes and V

is the domain of A. Also, V can be explained as a set of the values of the

INTEGRATING MULTIPLE ONTOLOGIES 125

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attribute, and V ¼ Uc2AVa (Va is the domain of attribute a). In this

paper, we accept the following assumptions:

Definition 1. (ontology). An ontology is a quintuplet:

O ¼ ðC;R; I ;R;ZÞ

where,

. C: set of concepts (the classes)

. I: set of instances of the concepts

. R: set of binary relations between the concepts from C, or between the con-

cepts from C and values defined in a standard or user-defined data type

. Z: set of axioms, which can be interpreted as integrity constraints or rela-

tionships between instances and concepts; it means that Z is a set of restric-

tions or conditions (necessary and sufficient) to define the concepts in C

. hC;Ri: is the taxonomic structure of the concepts from C, where R is the

collection of subsumption relationship (v) between any two concepts from

C; for two concepts c1 and c2 2 C; c2 v c1, if and only if any instances that

are the members of concept c2 are also the members of concept c1, and not

vice versa

The R is known as the set of properties. For every p 2 R, there is a spe-

cific domain D and range R such that p : D ! R, where D � C, and if

R � C, then p is called object property; else, if R is a set of standard

of user-defined data types, then p called data type property. We assume

that concepts c and c0 correspond to the domain and range of property p,

respectively, where p is also known as the attribute of the concept c, with

two given instances i and i0 that belong to the corresponding concepts c

and c0, respectively. We denote iRpi0 as the relation from instance i to i0

via the property (attribute) p. If p is an inversely functional property, the

relation from instance i0 to i via the property p is denoted as i0R�pi.

Definition 2. (concept). A concept of an ðA;V Þ-based ontology is defined

as a quadruple:

concept ¼ ðc; zc;Ac;V cÞ

where c is the unique identifier for the instances of the concept. The Ac � A is

a set of attributes describing the concept and V c � V is the attributes’

domain: V c ¼ [a2Ac Va. The zc � Z is a set of restrictions or conditions


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(necessary & sufficient) to define concept c. The zc can be presented as a

constraint function zc: Ac ! Z, such that zcðaÞ 2 Z for all a 2 Ac.

Pair ðAc;V cÞ is called the possible world of concept c, and Ac is

called the structure of concept c. It should be noticed that within

ontology there may be two or more concepts with the same structure.

If this situation takes place, the constraint function zc 2 Z will be useful

to express the relationship between them. For example, two concepts

RedWine and WhiteWine are the same structure {hasMaker, hasColor},

but zRedWine (hasColor)¼ {9 hascolor ¼ red} and zWhiteWineðhasColorÞ ¼f9 hascolor ¼ white}.

Definition 3. (instance). An instance of a concept c is described by the

attributes from set Ac with the values from set V c. Thus, the instance of a

concept c is defined as a pair:

instance ¼ ðidc; vcÞ

where idc is the unique identifier of the instance in world (Ac;V c), and vc is

the value of the instance, which is a tuple of type Ac, and constraint function

zc is satisfied. The value vc can be presented as a function: vc : Ac ! V c, such

that vcðaÞ 2 V c for all a 2 Ac.

Value vc is also called the description of the instance within concept

c. A concept may be interpreted as a set of all instances described by its

structure. By InsðO; cÞ we denote the set of instances belonging to con-

cept c in ontology O, and we have I ¼ Uc2CInsðO; cÞ.

Definition 4. (key identity). Key identity (KI) of a concept is an attribute

from set Ac that provides a unique value to each individual of the concept in

the real world (A,V). Formally, if ki is a KI of concept c, it satisfies the

following conditions:

. ki 2 Ac

. x 2 InsðO; cÞ j 8y; z 2 V � xRkiy ^ xRkiz ! y ¼ z

. x 2 InsðO; cÞ j 8y; z 2 V � yR�kix ^ zR�kix ! y ¼ z

The first two conditions mean than the KI of a concept must neces-

sarily provide the same KI value for the same instance of the concept.

The third condition means that it must be sufficient to recognize two

instances that actually exist and with the same KI value as the same

instance. All the above conditions imply that KI of a concept should


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be globally identifiable for instances inside the real world ðA;V Þ. The KI

is also known as such rigid property (Guarino and Welty 2000) that is

essential to all its instances.

Example 1. We consider the concept person owing the hasFingerprint,

which is KI. We say that the instance Jean has hasFingerprint of

000155BDC and the instance Peggy has hasFingerprint of 000155BDC.

Because hasFingerprint is a KI, we can deduce that Jean and Peggy must

be the same instance. It is necessary to note that because hasFingerprint

is a KI, there always exists the inverse relation isFingerprintOf. If two

instances, 000155BDC and 000155BEF, are isFingerprintOf of the

instance Jean, 000155BDC and 000155BEF must be the same instance.

However, it should be noted that if 000155BDC and 000155BEF were

explicitly stated to be two different instances, the above statements

would lead to an inconsistency.

Definition 5. (local identity). Local identity (LI) of a concept is an attri-

bute from set Ac that provides a unique value to each individual of the con-

cept in the possible world ðAc;V cÞ. Formally, if li is an LI of concept c, it

satisfies the following conditions:

. li 2 Ac

. x 2 InsðO; cÞ j 8y; z 2 V c � xRliy ^ xRliz ! y ¼ z

. x 2 InsðO; cÞ j 8y; z 2 V c � yR�lix ^ zR�lix ! y ¼ z

The difference between a KI and a LI is that a LI of a concept can be

only locally identifiable for instances inside the possible world ðAc;V cÞ.

ENRICHED ONTOLOGY INTEGRATION

There are two possible relationships within the semantic matching corre-

spondence between concepts. They are the subsumption relationship ðvÞand equality ð()Þ. Most previous mapping tools try to find the matching

among all concepts in different ontologies, therefore the complexity

increases rapidly in mapping between large ontologies or in integrating

multiple ontologies. Consequently, a novel possibility of the enriched

ontology model defined in this paper is that it can flatten the iterations

of a matching process and therefore reduce the complexity. This is its

advantage over other existing mapping methods.


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A Classification of Concepts

Definition 6. (defined concept). Defined concept (DC) is a concept that

has at least one KI. Formally, if c is a DC, its constraint function zc satisfies

the following conditions:

. 9a 2 Ac; zcðaÞ is the necessary and sufficient condition

. the attribute a is a KI

Example 2. We refer to Example 1 in which the concept person is an

example of the DC. The DC is also known as a rigid sort (Guarino and

Welty 2000) that supplies a principle of identity for its individuals.

Definition 7. (partition concept). Partition concept (PC) is a part of a

DC. Formally, if c is a PC, it satisfies the following conditions:

. 9a 2 Ac; 8x 2 vc : xðaÞ is a constant value

. the concept c is a defined concept satisfying zcðaÞ

Example 3. We consider two concepts, maleperson and femaleperson,

with the same structure {hasgender}. The maleperson is defined as the

concept person that satisfies zmalepersonðhasgenderÞ ¼ f9 hasgender ¼maleg. The femaleperson is defined as the concept person that satisfies

zfemalepersonðhasgenderÞ ¼ f9 hasgender ¼ femaleg. Thus, the concepts

maleperson and femaleperson are the PC.

Definition 8. (inherited concept). Inherited concept (IC) is a subconcept of

either defined concept or partition concept, or another inherited concept. It

has at least one LI. Formally, if c is an IC, then its constraint function zc

satisfies the following conditions:

. 9a 2 Ac; zcðaÞ is the necessary and sufficient condition

. the attribute a is a LI

Example 4. If we say that two concepts student with its LI hasIdstudent

and employee with its hasIdemployee are subconcepts of the concept

person, we can infer that the student and employee must be IC.

Definition 9. (primitive concept). Primitive concept (PvC) is a concept that

has neither KI nor LI. Formally, if a concept is a PvC, then its constraint

function zc hasn’t any set of necessary and sufficient conditions.


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Example 5. We consider the undergraduatestudent, masterstudent, and

doctoralstudent as defined through the concept student. But because we

do not have any set of necessary or sufficient conditions, we can infer

that these concepts must be the PvC. It is important to notice that the

concepts will never be placed as subconcepts of a PvC.

Proposition 1. (concept classification). For given an ontology O belonging

to real world (A,V), we denote four different sets of DCs, PCs, Ics, and PvCs

to be CDC ;CPC ;CIC, and CPvC, respectively.

1. CDC [ CPC [ CIC [ CPvC ¼ C

2. CDC \ CPC \ CIC \ CPvC ¼ /3. the levels of concepts increase in the order of PvC, IC, PC, and DC,

respectively.

Proposition 2. (axiom). For two given concepts: ðc1; z1;Ac1 ;V c1Þ belong-

ing to ontology O1, and ðc2; z2;Ac2 ;V c2Þ belonging to ontology O2:

1. the necessary condition for c1 to be equivalent with c2 is that c1 and c2 are

of the same type

2. for any two concepts c1 2 C1 and c2 2 C2 is in the CPvC then c1 can not

be placed as a subconcept of c2

3. for any two concepts c1 2 C1 and c2 2 C2; c1 is subsumption of c2, if and

only if c1’s level is higher than c2’s

Enriched Ontology Model

The EOM is a process to enrich the semantic of concepts in ontologies in

which the concepts are classified to four different types of concept, such

as the above proposition. We define an EOM as follows:

Definition 10. (enriched ontology model). Enriched ontology model

(EOM) is a quintuplet:

OE ¼ ðO;CDC;CPC;CIC;CPvC;<Þ

and, where O is an ontology. The sets of concepts DC, PC, IC, and PvC

correspond to CDC, CPC, CIC, and CPvC, which satisfy < being a set of


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ontological axioms and constraint as follows:

< ¼

ðcs1Þ for any c 2 CDC ;9 a 2 Ac and a is a KI ;

ðcs2Þ for any c 2 CPC ; 9a 2 Ac; 8n 2 lnsð0; cÞ; nðaÞ is constant

and 9c0 2 DC; c ¼ aPc0;

ðcs3Þ for any c 2 CIC ; 9c0 2 CDC [ CPC [ CIC ; c v c0;

9 a 2 Ac and a is a LI ;

ðcs4Þ for any c 2 CpvC ; 8a 2 Ac and zcðaÞ 6¼ D&;

ðax1Þ for any c 2 CDC [ CIC ; if n 2 lnsðc; 0Þ then n satisfies

zc and vice versa;

ðax2Þ for any c 2 CpvC ; if n 2 lnsðc; 0Þ then n satisfies zc

and it is not vice versa;

ðax3Þ for any n 2 lnsðc2; 0Þ; if n satisfies zc1then c2 v c1

and vice versa;

ðax4Þ for any c1 2 CPVC ; and 8c2 2 C then c2 v= c1;

ðax5Þ for any c1; c2 2 CPC and c3 2 CDC ; if c1 v c3

and c2 v c3 then c1 ffl c2;

8>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

Here, D is the necessary condition, & is the sufficient condition,ffl is the dis-

joint relationship, and c ¼ aPc0 means that concept c is defined by the inter-

section between the concept c0 and the attribute a.

Figure 1 illustrates our proposed method for heuristic matching.

According to the above proposition, there are only direct matching equal-

ities between the concepts asserted in the same classification types and the

matching subsumption from the low level of concepts to the higher level of

concepts in classifications, instead of matching to all concepts by travers-

ing taxonomies completely. Moreover, while calculating similarity between

concepts, most of the existing mapping methods often compare all proper-

ties belonging to each concept and its name=label. However, our metho-

dology does not require that. Instead of comparing blindly or exhaustively

among all properties belonging to each concept, we focus on some proper-

ties that identify the concept. For example, while computing the similarity

between two concepts in the DC type, we only compare their key identity

property. It is called key identity-based as show in Figure 1.

Our approach depends on analyzing the internal structure of

concepts, so we refer to it as an internal structure-based or EOM-based

matching (similarity).


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SEMANTIC SUPPORTING ENVIRONMENT

Similarity Between Two Words

There have been lots of previous works focusing on finding similarity

between words based on the WordNet-based. However, we can dis-

tinguish two basic approaches: (1) the similarity measures are based

on the path’s lengths between concepts such as Lch (Leacock and

Chodorow 1998), Wup (Wu and Palmer 1994). Most of these similarity

measures are subject to an is-a hierarchy in which the concepts occur.

But is-a relations in WordNet do not cross part of speech boundaries,

so these WordNet-based similarity measures are limited to making judg-

ments between noun pairs (e.g., cat and dog) and verb pairs (e.g., run and

walk). While being included by WordNet, the adjectives and adverbs are

not organized into is-a hierarchies. (2) The similarity measures are based

on information content, which is a corpus-based measure of the speci-

ficity a concept. These measures include Res (Resnik 1995), Lin (Lin

1998), and Jcn (Jiang and Conrath 1997). Intrinsic to the calculation

of information content is the use of tagged corpora; the intuition is that

the more often a concept appears in a corpus, the less specific it is, so the

methods depend on tagged corpora. Such a strategy is not without an

unpleasant consequence; two well known and somewhat discouraging

problems are inherent to them. Manually tagging corpora is a wearisome

Figure 1. Heuristic matching.


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and highly time consuming burden. It is very difficult to obtain a

statistically valid and reliable corpus that truly reflects the word usage;

many relatively common words may not appear even in very large cor-

pora. This problem is usually referred to as the sparse data problem.

Therefore, we have proposed a new method (Duong et al. 2008b)

based on the WordNet to measure the similarity, which has advantages

over the above methods. Moreover, the similarity is across part of

speak. WordNet is limited by its database and lack of relations

between the concepts existing in it. For this reason, our method seeks

to acquire a relation between the entities from the text corpus. We

also combine WordNet-based and text corpus to provide the relations

between the concepts, which is called semantic supporting environ-

ment (SSE).

Combining Text Corpus and WordNet-Based

Similarity Between Two Concepts. Most instances of a concept

involve the set of hyponyms of the concept. For example, when the

concept country has instances such as Vietnam, Korea, Poland, it is

considered as the hypernym of Vietnam, Korea, and Poland. For this

reason, a method to compute the similarity between two concepts via

their instances has been proposed as follows:

Lc ¼ fl1; l2; . . . ; lng, is the name=label of the instances of concept c.

Ai ¼ fa1; a2; . . . ; akg is the set of the tokens resulting from two pro-

cesses: the processing of demarcating and the possibility of classifying

sections of string li 2 Lc, and the processing of determining the lemma

for each word of the tokens. For example, parsing the name Hands

Free Kits into tokens{hands, free, kits} by recognizing the punctuation

and determining the part of speech of each word in the tokens to the final

one {hand, free, kit}.

Gj ¼ fg1; g2; . . . ; gkg is the set of more general words of aj 2 Ai;

j ¼ 1::k.

The words of Gj are generated from the WordNet’s relations and

Text corpus discovery (Duong et al. 2008a).

H ¼[ni¼1

ðG0iÞ


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where G0i � Gi and if gj 2 G0i , gj exist at least 12

n sets Gi; i ¼ 1; 2; . . . ; n

M ¼[ni¼1

ðA0iÞ

where A0i � Ai and if ak 2 A0i , there exists at least gj 2 Gi and gj is more

general word of ak .

We define the similarity between two structures of two concepts as

follows:

Ac is the representation of the structure of the concept c. Ac ¼fp1; p2; . . . png, where pi; i ¼ 1; 2; . . . ; n are the properties of the concept:

simðAc;Ac0 Þ ¼P

p2Ac ðmaxðsimp02AC0 ðp; p0ÞÞÞsizeðAc0 Þ

The similarity between two concepts c1 and c0 is defined as follows:

simðc;c0Þ¼ asimðl1; l2ÞþbsimðAc;Ac0 Þþ cmaxðsimðHc;Hc0 Þþ simðMc;Mc0 ÞÞwhere 0� a;b;c� 1;aþbþ c¼ 1 and simðl1; l2Þ is the similarity between

two labels of concepts c, and c0

Combining Acquisition Algorithm. The representation of the OnCon-

ceptSNet is built or extended as the initial step by acquiring the knowl-

edge from WordNet-Based and Text corpus discovery. We suppose

that the relation R(c1, c2) will exist between the two concepts c1 and c2

that come from the OnConceptSNet. In comparing a result R(c1, c2) to

the WordNet-based, three possibilities are available:

1. Both concepts c1 and c2 are in WordNet, and their relation R(c1, c2) is

already in the database of WordNet; it is suggested to update the

OnConceptSNet.

2. Both concepts c1 and c2 are in WordNet and their relation R(c1, c2) is

not; it is suggested to update the OnConceptSNet and the WordNet.

3. The concepts c1 and c2 are not present; these concepts and the corres-

ponding R(c1, c2) relation are suggested to add the Knowledge-base of Assist-

ant WordNet and to update OnConceptSNet (just the relation R(c1, c2)).

Here, we sketch the collaborative acquisition algorithm which combines

WordNet-based and Text corpus to discover new relations between the

entities of ontologies for ontology integration tasks as follows (see Figure 2):

. Knowledge of assistance WordNet is a Concept Net based on the ontology

with its relations: is kind of, is equivalent of. It receives messages from the


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Feedback component, then updates the relations between the entities of

ontologies if the relation are not existent in WordNet-based.

. Mining from text Corpus is the procedure that is mentioned in Duong

et al. (2008a). It discovers new relations between the entities of ontol-

ogies through Text corpus.

. Ontology integration task, which will be presented in the next section,

receives the relation R(c1,c2) and updates OnConceptSNet.

. Feedback is a cache of new relations and mark (mark is used to identify

new relations that should be updated in knowledge of assistance

WordNet or WordNet-based).

ONTOLOGY INTEGRATION STRATEGIES

The OnConceptSNet

In this section we present a semantic network of ontologies concept called

OnConceptSNet, which serves to integrate multiple ontologies and rec-

oncile semantic conflicts between the ontologies. The OnConceptSNet

builds or extends the concept representations by acquiring knowledge

from WordNet-Base, Text corpus, and Meta-rules. The knowledge may

Figure 2. Combined acquisition algorithm.


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change the old network by adding or deleting nodes and arcs or by

modifying the numerical values of arcs (relations) or the relation between

nodes (called weights) associated with the arcs.

An OnConceptSNet is a directed loop graph with the quadruple:

G ¼ ðC�;R�;N ;M Þ

where:

. C� is a set of nodes representing concepts that come from 01; . . . ; 0n

. R� is a set of arcs representing the relations between concepts:

semantic equivalent (,), more general (v), disjoint (?), overlap (�);

each arc is associated with a numerical value which is weight (w) of

a corresponding relation

. N is an adjacency matrix of G, written N(G), n-by-n matrix in which n is

the number of nodes in G; entry is the number of arcs in G with end-

points ðvi; vjÞ=vi ¼ vj and entry is used to distinguish vi and its corre-

sponding ontology

. M is the incidence matrix of G, written M(G), n-by-m matrix in which

m is the number of edges (relations) in G; if vi is the starting point of ej ,

entry mij is equal�1; if vi is the second point of ej , entry mij is equal

w (w> 0), which is the weight of the arc ej, and mij is equals 0 in the

other case

. If vertex v is a starting point of edge e, then v and e are incident values

. The degree of vertex v, written d(v) is the number of incident values

of edges

. Local matrix of vertex vi, written LðviÞ, is M(G), limited by left columnPv2ðv0�viÞ dðvÞ þ 1 and right column

Pv2ðv0�viÞ dðvÞ þ dðviÞ, where vi is a

vertex at row i of matrix M(G)

Example 5. We consider the OnConceptSNet as an instance of Figure 3.

Let’s have a look at matrix G(N) from which we can get to know that the

concepts a and d are in ontology 1, and the concepts b and c are in

ontology 2, because N(a, a)¼N(d, d)¼ 1 and N(b, b)¼N(c, c)¼ 2. More-

over, the number of edges with end points (b, c) is 3, because N(b, c)¼ 3.

According to the G(M), we can distinguish the relationship between the

nodes and its corresponding weight. For instance, b is more general than

a and its weight is 0.5. Furthermore, the searching space of concepts is

reduced by focusing in the local matrix of the concepts. The gray window

of matrix M(G) is the local matrix of concept c.


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Example of Meta-Rules for Generating New

Probability Distributions

In the process of determining the relation of candidate ontologies’

concepts, two concepts can have many relations. Each relation has its

own weight. For instance, the best relation between the concepts may

be incorrect if depending only on the weight for determination. Because

the relation of two concepts should be considered in many different

aspects, this relation depends not only on the similar terms or similar

structures themselves, but also on the relationships’ interaction with

neighbor concepts. Therefore, in this section, we discuss on how to

generate the new probability distributions, depending upon the existing

ones that might be able to change and enhance the old network of

OnConceptSNet.

We use the following notation conventions through the rest of this

section:

. The concepts from O0 have the notation with a prime (0), and

conversely, the concepts from O have the notation without prime (0)

. Lower-case q with or without a subscript denotes a property

Figure 3. An example of OnConceptSNet.


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. qðc1; c2Þ indicates that q is the relation between c1 and c2, where c1 is

q’s domain and c2 is q’s range

. Pðc1 r c2; xÞ indicates that the probability of the match ðc1 r c2Þ is x,

where r is the match between c1 and c2, and r is either subsumption

or equivalent

. The max and d are the expert-provided constant less than 1

The equality meta-rules are as follows:

1. Pðc1 , c01; xÞ ^ ðx > maxÞ ^ Pðc2 r1 c1; y1Þ ^ Pðc02 r2 c01; y2Þ:^ ðyi > max; i , 1::2Þ ! Pðc2 r1 c01; y1Þ ^ Pðc02 r2 c1; y2Þ:

2. ðc1 , c01; xÞ ^ ðx > maxÞ ^ Pðc1 r1 c2; y1Þ ^ Pðc01 r2 c02; y2Þ^ ðyi > max; i ¼ 1::2Þ ! Pðc01 r1 c2; y1Þ ^ Pðc1 r2 c02; y2Þ:

3. Pðc1 , c01; xÞ ^ ðx > maxÞ ^ Pðc1 r c2; y1Þ ^ Pðc01 r c02; y2Þ^ ðyi > max; i ¼ 1::2Þ ^ ðr 6¼ ?Þ ! Pðc2 , c02; aÞ;

where a ¼ minð1;minð1; x0 þ dÞÞ, x0 is the previous probability of the

match ðc2 , c02Þ.

4. Pðc1 , c01; xÞ ^ ðx > maxÞ ^ Pðc2 r c1; y1Þ ^ Pðc02 r c01; y2Þ^ ðyi > max; i ¼ 1::2Þ ^ ðr 6¼¼Þ ! Pðc2 � c02; aÞ:

where a ¼ minð1; x0 þ dÞ, x0 is the previous probability of the match

ðc2 � c02Þ.

5. Pðc1 , c01; xÞ ^ Pðc2 r c1; y1Þ ^ Pðc02 r c01; y2Þ ^ ðr 6¼ ?Þ^ Pðc2 , c02; y3Þ ^ ðyi > max; i ¼ 1::3Þ ! Pðc1 , c01; aÞ;

where a ¼ minð1; x þ dÞ.

6. Pðc1 , c01; xÞ ^ Pðq , q0; 1Þ ^ qðc1; c2Þ ^ q0ðc01; c02Þ! Pðc2 , c02;minð1; x þ dÞÞ:

7. qðc1; c2Þ ^ q0ðc01; c02Þ ^ Pðc1 , c01; y1Þ ^ Pðc2 , c02; y2Þ^ ðyi > max; i ¼ 1::2Þ ! Pðq, q0;minð1;minðy1; y2Þ þ dÞÞ:

Here, we present three main steps of the enhanced algorithm to build

OnConceptSNet.

1. Initial step: combining the static rules in our work (Duong et al.

2008b) with EOM-based to find out the relations between the nodes.


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2. Enhanced step: using the meta-rules 1 and 2 to enhance initially

OnConceptSNet, after that the meta-rules 3, 4, and 5 to enhance the

neighbor matching by analyzing the subsumption relationships

between the concepts such as generalization, specialization, and

siblings. Finally, the meta-rules 6 and 7 are used to enhance

OnConceptSNet by analyzing the relation of the OnConceptSNet and

the properties (relations) between concepts. This step repeats until

all edges are applied the meta-rules.

3. Reduced step: we use rules, which are not presented here, to

determine the best representing among the relations between the

same two nodes of OnConceptSNet. Then, the OnConceptSNet is

reduced by dynamic rules in Duong et al. (2008b). An ontology is

represented by the final OnConceptSNet, which best replaces the

candidate ontologies.

Note that the above-mentioned meta-rules are just some examples of

equality meta-rules. Other meta-rules such as the subsumption, overlap,

and disjoint are not presented here. Moreover, because these meta-rules

enhance relations between the concepts of OnConceptSNet by analyzing

the relation structure between the concepts, this approach is called

relation structure-based similarity.

MULTIPLE ONTOLOGIES INTEGRATION PROGRESS

Figure 4 below illustrates the ontology integration progress where

most of the components are already presented in the previous sections.

Therefore, in this section, we just discuss how to recognize the identity

of concepts, where it is the clue to classify concepts in the EOM.

Here we show some methods to recognize identities. We assume that

all candidate ontologies are transformed to ontologies OWL. First, we col-

lect all the necessary and sufficient properties of the concept. Second, we

represent an identity as the property of the concept and distinguish it from

other properties by the characteristic of a one-to-one functional between

its domain and range and by implement two different methods as follows:

1. As we know, the identities can be written in OWL by using owl:

DatatypeProperty with three restrictions: owl:FunctionalProperty,

owl:InverseFunctionalProperty, and owl:cardinality¼ 1. Here, we use

the following heuristic to distinguish a DC: if a concept is one of


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top-most taxonomy in a given ontology and it contains at least one

identity, it must be a DC.

2. We consider the concept of ontology as the possible domain and the

other candidate ontologies in which the concept occurs as global

domain. After that, we check the characteristic of one-to-one func-

tional between its domains (possible domain, global domain) and

range to recognize the KIs and LIs. We also use the following heuris-

tic to distinguish a KI and a LI: if a property has the characteristic of

one-to-one functional between its global domain and range, it is a KI.

If a property has the characteristic of one-to-one functional between

its possible domain and range, it is an LI.

EXPERIMENTS

In this section, we will discuss three aspects as follows: the first aspect

concerns the similarity analysis techniques with existing mapping

Figure 4. Ontology integration processing.


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methods; the second aspect compares the complexity of our method and

CLUE’s Content-based matching; the last aspect refers to the evaluation

of experimental results.

In Table 1, we compare the techniques for similarity analysis of

existing mapping tools with our composed approach in novel internal

structure-based and relation structure-based. It should be noted that

the taxonomy-based similarity is the similarity between two concepts

and is determined by analyzing the subsumption relationships between

them such as generalization, specialization, and siblings. However, the

relation structure-based similarity relation is not only based on analyzing

structural relationships between the concepts in the taxonomy, but also

on their properties.

Here, we present the comparative complexity between our methods

and CLUE’s content-based matching. Suppose that Nc, Np, and Ni are

the maximum numbers of nodes, properties (attributes), and instances.

Let us assume that the complexity of comparing two attribute values

between two instances is O(1). Then, the complexity of calculating

the similarity between two instances will be O(Np). The complexity

for the similarity determination between two nodes is O(Np2�Ni).

Finally, the matching between two ontologies will cost

O(log Nc�Np2�Ni). In order to compare GLUE with our matching

method, let us substitute N for every parameter; the cost of GLUE will

become O(N3� log N), whereas our matching method costs O(N2�log N), because the method does not require comparing all properties

belonging to each class. Figure 5 illustrates the complexity difference

between our methods of matching and GLUE’s content-based matching

in a line-chart style. The chart states that the complexity is difference

especially showing by the number of properties, assuming that the

number of concepts and instances are equal in each case. Whenever

Table 1. Comparative techniques of similarity analysis

Matching

methods

Instance-

based

Lexical-

based

Schema-

based

Taxonomy-

based

Internal

structure

Relation

structure

PROMPT Y Y Y Y N N

MAFRA Y Y Y Y N N

ONION Y Y Y Y N N

GLUE Y Y Y Y N N

HYBRID Y Y Y Y Y Y


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the number of properties belonging to concepts increases, the com-

plexity difference increases proportionally.

We collected a large number of ontologies from the Internet and

composed the ontologies corresponding to them. Each sample includes

at least three ontologies. Ntotal is the total number of pairs of matching

concepts between the candidate ontologies by experts, Ncorrect and

Nincorrect correspond to the number of correct pairs of matching

concepts and the number of incorrect pairs of matching concepts found

out by our system.

Precision is used to evaluate the ratio of incorrectly extracted

relationships:

Precision ¼ Ncorrect

Ncorrect þNincorrect

Recall is used to evaluate the ratio of correct matching found out by the

system:

Recall ¼ Ncorrect

Ntotal

Figure 5. The different complexity between EOM-based and Content-based.

Figure 6. The evaluation of experimental results.


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Figure 6 illustrates some comparative experimental results between

EOM-based matching and combining EOM-based and content-based

matching.

CONCLUSION

According to our studies of ontology integration, the methods of mul-

tiple ontologies integration have not been explored yet. The hybrid

method that is presented in this paper is a smart approach for multiple

ontologies integration in which the OnConceptSNet is a semantic network

serving to reconcile multiple ontologies. The relations between concepts

of the OnConceptSNet are derived from a semantic support environment

SSE combining special domain and text corpus. The OnConceptSNet is

enhanced by the meta-rules. EOM-based matching is a heuristic, whose

advantage is based on the initial reduction of the complexity using a

direct matching between the same types of concepts. In future work,

we will deal with exploring the EOM-based matching, which enables

classifying concepts more correctly.

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a hybrid method for integrating multiple ontologies

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