This paper presents a new ontology mapping method between a source ontology and a target one considered as a reference. Both ontologies are composed of triplets of the form (object, characteristic, value). Values describing the objects of the reference ontology are hierarchically organized using the a kind of relation. The proposed method considers the ontology mapping problem as a rule application problem in the Conceptual Graph model. First, a vocabulary common to both ontologies is defined using mapping between values and characteristics. Each value of the source ontology is associated with a fuzzy set of values of the reference ontology. Then, the source ontology is translated into a fuzzy conceptual graph base and the reference ontology into a conceptual graph rule base. Finally, rules are applied into the fact base in order to find correspondences between objects of both ontologies. This method is implemented and applied to the mapping of ontologies in risk assessment in food products, and experimental results are presented.
Introduction
Information systems which are characterized by the presence of multiple and
independent knowledge representation are concerned by the problem of the
interoperability among them. Mappings play a key role to treat that problem and
may be used for different purposes (schema or ontology integration, ontology
engineering, ...). Ontology matching is defined as a process that takes two
ontologies as input and returns a mapping which identifies corresponding concepts
in the two ontologies by taking into account their descriptions and constraints in
terms of names, properties and semantic relations. The problem on the ontology
matching problem has been widely investigated in the literature (see [
In the framework of Conceptual Graphs (CG), previous works [
The aim of the proposed mapping method is to establish correspondences between objects of two ontologies. The mapping problem adressed in this paper is not a symmetric problem since one of the two ontologies is considered as a reference. So we propose a new ontology mapping method in which the reference ontology is considered as a rule base and the source ontology as a fact base. The ontology mapping problem then becomes a rule application problem. Nevertheless, in order to apply rules into a fact base, both rules and facts must be defined with the same vocabulary. So, our mapping method can be divided into three main steps. The first step (section 2) consists in defining a vocabulary common to the source and the reference ontologies. The second step (section 3) concerns the translation of the source ontology into a fact base and of the reference ontology into a rule base. The third step (section 4) deals with the application of the rules into the fact base in order to find correspondences between objects of both ontologies. Finally, experimental results are presented in section 5. 2
Definition of a common vocabulary
We have chosen the Conceptual Graph (CG) model as formalized in [
In order to compare objects of S with objects of R, we would like to use
the projection operation on CGs. But the objects of S are not defined with the
same vocabulary as the objects of R. Since the ontology R is a reference one,
we propose to express each object of S in terms of characteristics and values of
R. For that, we define a mapping between values and characteristics of S and
R. We only briefly recall this mapping which has already been presented in [
First, each value v of S is associated with a set of values {w1, . . . , wn} of R,
weighted by their lexical closeness to the value v using the Dice coefficient. Such
a set of values is represented by a fuzzy set [
Example 1 Let pollock raw be a value of S. Let pollock, Alaska pollock be values of R. μpollockraw={ 0.66/pollock + 0.5/Alaska pollock }.
The lexical mapping between values is used to identify correspondences between characteristics of S and R. The result of the mapping between values and characteristics of S with values and characteristics of R is defined below.
Definition 1 We call linked values of the source ontology S, denoted LVS , the set of values of S such that each of them is associated with a set of values of the reference ontology R with a given relevance score, represented by a discrete fuzzy set. We call linked characteristics of S, denoted LCS , the set of characteristics of S such that each of them is associated with one characteristic of R.
Thanks to this mapping, we can now present the terminological knowledge common to S and R. The concept type set is composed of the object names of S and R, the set of characteristics of R, the hierarchized set of values of R and the concept type NumVal. The relation type set is composed of the relation types HasForCharac, HasForValue, IsAnnotatedBy and HasForScore. The set of individual markers contains values of the reference domain of the real numbers IR. 3
Translation of the ontologies into fact and rule bases Since the vocabulary common to the source ontology S and the reference ontology R has been defined, we can now deal with the second step of our mapping method i.e. to translate S into a CG fact base and R into a CG rule base. 3.1
Translation of the source ontology into a fuzzy CG base
Each object of S is represented by a CG using the terminological knowledge
described above: each of its characteristics and each of its associated values are
represented by means of their corresponding characteristic and values in R. Since
each value of the object in S is associated with a fuzzy set of values in R1, the CG
contains fuzzy values. We have proposed in [
Definition 2 Let f be the fuzzy value function which associates each value of LVS with its corresponding values in the reference ontology R and their relevance score. Let g be the value function which associates each characteristic of LCS with its corresponding characteristic in R. Let CT = { Charac1T , . . ., CharacpT } be the set of characteristics of R. Let N ameY be the name of an object Y of the source ontology S. Let CT = { g(Charac1Y ), . . ., g(CharacYm) } ∈ CT , m ≤ p,
Y be the set of characteristics associated with Y in R, where CharaciY ∈ LCS , i ∈ [1, m]. Let CT′ = { CharaclT , . . ., CharackT }, p − m ≤ l ≤ k ≤ p, be the set of characteristics of R such that CT′ = CT \ CYT . Let Value1, . . ., Valuem be the values associated with the characteristics of Y and belonging to LVS . Then each object Y of S can be represented by the CG GYT of Figure 1. 1 This fuzzy set of values has a semantic of similarity and represents the ordered list of the most similar values of R associated with a value of S. " # %$ " # %$ ... Example 2 Let fresh fish be an object of S. Its associated list of couples (characteristic : value) is: (presentation: whole) and (which fish ?: pollock raw). Figure 2 presents the CG GfTf associated with fresh fish, where g(presentation)= ‘origin of main ingredient’ and g(which fish?)= ‘physical state, shape’. Each object of R is represented by means of a CG rule which allows objects of S to be annotated with objects of R according to the correspondences between their characteristics and associated values.
Definition 3 Let CT = { Charac1T , . . ., CharacpT } be the set of characteristics of the reference ontology R. Let N ameX be the name of an object X of R. Let CX = { Charac1X , . . ., CharacnX }, n ≤ p, be the set of characteristics associated
T with X . Let CT′ = { CharaclT , . . ., CharackT }, p − n ≤ l ≤ k ≤ p, be the set of characteristics of R such that CT′ = CT \ CXT . Let Value1, . . ., Valuen be the values associated with the characteristics of X . Then, each object X of R can be represented by the CG rule RX of Figure 3 where the marker *scoreproj is the adequation degree between the hypothesis of RX and a CG into which there exists a δ-projection (see Definition 4). Rcr
Example 3 Let cod, raw be an object of R. Its associated list of couples (characteristic : value) is: (origin of main ingredient: cod or codfish), (physical state, shape: whole, shape solid) and (preservation method: preserved by refrigeration). Figure 4 presents the CG rule associated with the object cod, raw of R.
Using CG rules for fuzzy matching of objects
Objects of the ontologies S and R are now represented by comparable CGs using the same vocabulary. The objects of S are represented by fuzzy CGs and the objects of R by CG rules. The next and last step of our mapping method consists in applying the CG rules into the fuzzy CGs in order to find correspondences between objects of S and objects of R. These rules application allows the objects of S to be enriched with annotations that are sets of similar objects of R.
The rule application requires to compare a crisp CG which represents the
hypothesis of a rule with a fuzzy CG which represents an object of S and may
contain fuzzy values. This comparison is made using the δ-projection which is
an extension of the projection operation defined in [
Definition 4 A δ-projection from a crisp CG G into a fuzzy CG G′ is a triple (g, h, δ), g (resp. h) being a mapping from the set of concept (resp. relation) vertices of G into the set of concept (resp. relation) vertices of G′ such that: (i) the edges and their numbering are preserved; (ii) the labels of the relation vertices may be restricted; (iii) ∀ crisp concept vertex ci ∈ G, i ∈ [1, . . . , n], labelled ti : mi, ci is mapped with its image g(ci) ∈ G′ labelled ti : m , with an ′ ′ i adequation degree δi = μclos(t′i)(ti), μclos(t′i) being the membership function of the fuzzy type closure of t′i. The adequation degree of G by G′ is δ = mini=1,...,nδi.
We can now identify the correspondences between objects of S and R. Each
rule associated with each object of R is β-applied into the fuzzy CGs representing
the objects of S, β being a threshold allowing the end-user to avoid too bad
correspondences between objects. The β-application is an extension of the rule
application defined in [
Definition 5 There exists a β-application from a rule GH ⇒ GC into a CG G if there exists a δ-projection from GH into G such that δ ≥ β.
Example 4 Let us consider the object fresh fish of S described in Example 2 and represented by the CG GTff of Figure 2. Let us consider the object cod, raw of R described in Example 3 and represented by the rule Rcr of Figure 4. There exists a 0.5-projection from the hypothesis of Rcr into GTff . So, Rcr can be 0.4-applied into GTff . The resulting CG R[GTff ] is described in Figure 5.
Thus, at the end of this mapping process, each object Y of the source ontology S is associated with a set of candidate objects (see Definition 6) of the reference ontology R, weighted by their adequation degrees to the object Y . Definition 6 An object X of the reference ontology R is a candidate for an object Y of the source ontology S with the adequation degree δ if the generic concept vertex of type N ameY is linked by the relation vertex IsAnnotatedBy to the generic concept vertex of type N ameX which is linked by the relation vertex HasF orScore to the individual concept vertex (N umV al: δ).
Example 5 According to Example 4, the object cod, raw of R is a candidate for the object fresh fish of S with the adequation degree 0.5. 5
Experimentation We have developed methods to estimate the exposure of a given population of consumers to chemical contaminants using two databases: the first one, called CONTA, considered as the reference ontology R, gives the degree of chemical contamination for 472 food products; the second one, called CONSO, considered as the source ontology S, stores household purchases of 2595 food products.
We have realised an expert manual mapping: 398 food products from the CONSO ontology (i.e. 84.32% from 472) have been associated with 2041 food products from the CONTA ontology (i.e. 78.65% from 2595) by 3258 mappings. Only 118 mappings (i.e. 3.82% from 3258) associate one food product from the CONSO ontology with exactly one food product from the CONTA ontology.
Table 1 gives precision (the percent of the found correct mappings to the found mappings) and recall (the percent of the found correct mappings to the correct mappings found manually) for different correspondences. Mapping of food product names, without mapping of characteristics, permits to retrieve half of the manual matches but has a very bad precision (8.8%). Mapping of characteristics enhances the recall till around 77%. We have also evaluated the influence of the taxonomy defined on the values of R: for the mapping of 6 (resp. 20) characteristics, 6.96% (resp. 8.38%) of 74.40% (77.04%) are obtained.
#nb charac #f ound #correct p × 100 r × 100 In this paper we present an ontology mapping method between a source ontology and a reference one. Both ontologies are composed of triplets of the form (object, characteristic, value). Values describing the objects of the reference ontology are hierarchically organized using the a kind of relation. First, all the objects of the source ontology S are represented into a fuzzy CG base, denoted KBS T . Then, all the objects of the reference ontology R are represented as a set of CG rules, denoted RulesR. Finally, the rules from RulesR are applied into KBS T . This application produces an annotation for objects from S that encodes correspondences with objects from R and the associated adequation degrees. We have shown in this paper that, thanks to our fuzzy extension of the CG model, it is possible to represent and manipulate lexical mapping results combined with semantic properties. This method has been implemented and applied to the mapping of ontologies in risk assessment in food products. Our experimentation shows that the method has a rather good recall but a poor precision.
A first perspective to enhance our method is to study other comparaison
techniques between characteristics and values such as semantic techniques or
contextual matching techniques. An other perspective is to apply, in post-treatement,
semantic constraints on the generated mappings between objects. Finally, we
want to compare our results with the one obtained using other ontology
alignement methods thanks to ontology alignment comparison systems ([