Semantic Web Technologies phần 4 docx

Ontology Repositories: The ontology repositories are used to storeontology statements, provided by external ontology applications.The current version of the PION implements a reasoner ba

5.7 SYNTACTIC RELEVANCE-BASED SELECTION

FUNCTIONS

As we have pointed out in Section 5.4, the definition of the selectionfunction should be independent of the general procedure of the incon-sistency processing (i.e., strategy) Further research will focus on a formaldevelopment of selection functions However, we would like to point outthat there exist several alternatives which can be used for an inconsis-tency reasoner

Chopra et al (2000) propose syntactic relevance to measure therelationship between two formulas in belief sets, so that the relevancecan be used to guide the belief revision based on Schaerf and Cadoli’smethod of approximate reasoning We will exploit their relevancemeasure as selection function and illustrate them on two examples.Definition 9(Direct Relevance and k-Relevance (Chopra et al 2000)).Given a formula set , two atoms p, q are directly relevant, denoted by R(p, q, )

if there is a formula a 2  such that p, q appear in a A pair of atoms p and q arek-relevant with respect to  if there exist p1,p2,   , pk 2 L such that:

 p, p1are directly relevant;

 pi, pi+1are directly relevant, i ¼ 1,   , k 1;

 pk, q are directly relevant

The notions of relevance are based on propositional logics However,ontology languages are usually written in some subset of first order logic

It would not be too difficult to extend the ideas of relevance to those order logic-based languages by considering an atomic formula in first-order logic as a primitive proposition in propositional logic

first-Given a formula f, we use I(f), C(f), R(f) to denote the sets ofindividual names, concept names, and relation names that appear inthe formula f, respectively

Definition 10 (Direct Relevance) Two formula f and c are directlyrelevant if there is a common name which appears both in formula f andformula c, that is I(f) \ I(c) 6¼ Ø _ C (f) \ C(c) 6¼ Ø _ R(f) \ R(c) 6¼ Ø.Definition 11(Direct Relevance to a Set) A formula f is relevant to a set

of formula  if there exists a formula c 2  such that f and c are directlyrelevant

We can similarly specialize the notion of k-relevance

Definition 12 (k-Relevance) Two formulas f, f’ are k-relevant withrespect to a formula set  if there exist formulas c0,  ck 2  such that fand c0, c0and c1,   , and ck and f’ are directly relevant

Definition 13(k-Relevance to a set) A formula f is k-relevant to a formulaset  if there exists formula c 2  such that f and c are k-relevant with respect

the query formula f as a starting point for the selection based onsyntactic relevance Namely, we define:

s(, f, 0) ¼ Ø

Then the selection function selects the formulas c 2  which are directlyrelevant to f as a working set (i.e., k ¼ 1) to see whether or not they aresufficient to give an answer to the query Namely, we define:

s(, f, 1) ¼ {c 2  j f and c are directly relevant}

If the reasoning process can obtain an answer to the query, it stops.otherwise the selection function increases the relevance degree by 1,thereby adding more formulas that are relevant to the current workingset Namely, we have:

s(, f, k) ¼ {c 2  j c is directly relevant to s(, f, k – 1)},

for k > 1 This leads to a ‘fan out’ behavior of the selection function: thefirst selection is the set of all formulae that are directly relevant to thequery; then all formulae are selected that are directly relevant to that set,etc This intuition is formalized in the following:

Proposition 3 The syntactic relevance-based selection function s is tonically increasing

mono-Proposition 4

s(, f, k) ¼ {fjf is (k-1)-relevant to }

The syntactic relevance-based selection functions defined above usuallygrows up to an inconsistent set rapidly That may lead to too manyundetermined answers In order to improve it, we require that theselection function returns a consistent subset 00at the step k when s(,

f, k) is inconsistent such that s(, f, k 1)  00 s(, f, k) It is actually

a kind of backtracking strategy which is used to reduce the number ofundetermined answers to improve the linear extension strategy We callthe procedure an over-determined processing (ODP) of the selectionfunction Note that the over-determined processing does not need toexhaust the powerset of the set s(, f, k) s(, f, k 1) because of thefact that if a consistent set S cannot prove or disprove a query, then norcan any subset of S Therefore, one approach of ODP is to return just amaximally consistent subset Let n be jj and k be n – jSj, that is thecardinality difference between the ontology  and its maximal consistentsubset S (note that k is usually very small), and let C be the complexity ofthe consistency checking The complexity of the over-determined proces-sing is polynomial to the complexity of the consistency checking (Huang

et al., 2005)

Note that ODP introduces a degree of non-determinism: selectingdifferent maximal consistent subsets of s(, f, k) may yield differentanswers to the query  j f The simplest example of this is  = {f, :f}.

5.8 PROTOTYPE OF PION

5.8.1 Implementation

We are implementing the prototype of PION by using SWI-Prolog.5PION implements an inconsistency reasoner based on a linear extensionstrategy and the syntactic relevance-based selection function as discussed

in Sections 5.6 and 5.7 PION is powered by XDIG, an extended DIGDescription Logic interface for Prolog (Huang and Visser, 2004) PIONsupports the TELL requests in DIG data format and in OWL, and theASK requests in DIG data format A prototype of PION is available fordownload at the website: http://wasp.cs.vu.nl/sekt/pion

The architecture of a PION is designed as an extension of the XDIGframework, and is shown in Figure 5.3 A PION consists of the followingcomponents:

 DIG Server: The standard XDIG server acts as PION’s XDIG server,which deals with requests from other ontology applications It not onlysupports standard DIG requests, like ‘tell’ and ‘ask,’ but also providesadditional reasoning facilities, like the identification of the reasoner orchange of the selected selection functions

 Main Control Component: The main control component performs themain processing, like query analysis, query pre-processing, and theextension strategy, by calling the selection function and interactingwith the ontology repositories

5 http://www.swi-prolog.org

Figure 5.3 Architecture of PION

 Selection Functions: The selection function component is an enhancedcomponent to XDIG, it defines the selection functions that may be used

in the reasoning process

 DIG Client: PION’s DIG client is the standard DIG client, which callsexternal description Logic reasoners that support the DIG interface toobtain the standard Description Logic reasoning capabilities

 Ontology Repositories: The ontology repositories are used to storeontology statements, provided by external ontology applications.The current version of the PION implements a reasoner based on a linearextension strategy and a k-relevance selection function as discussed inSections 5.2 and 5.5 A screenshot of the PION testbed, is shown in Figure5.4

5.8.2 Experiments and Evaluation

We have tested the prototype of PION by applying it on several exampleontologies These example ontologies are the bird example, the brainexample, the Married-Woman example, and the MadCow Ontology,which are discussed in Section 5.3 We compare PION’s answers withtheir intuitive answers which is supposed by a human to see to whatextend PION can provide intended answers

For a query, there might exist the following difference between ananswer by PION and its intuitive answer

 Intended Answer: PION’s answer is the same as the intuitive answer

 Counter-Intuitive Answer: PION’s answer is opposite to the intuitiveanswer Namely, the intuitive answer is ‘accepted’ whereas PION’sanswer is ‘rejected,’ or vice versa

 Cautious Answer: The intuitive answer is ‘accepted’ or ‘rejected,’ butPION’s answer is ‘undetermined.’

 Reckless Answer: PION’s answer is ‘accepted’ or ‘rejected’ whereas theintuitive answer is ‘undetermined.’ We call it a reckless answerbecause under this situation PION returns just one of the possibleanswers without seeking other possibly opposite answers, which maylead to ‘undetermined.’

For each concept C in those ontologies, we create an instance ‘the_C’ onthem We make both a positive instance query and a negative instancequery of the instance ‘the_C’ for some concepts D in the ontologies, like aquery is ‘the_C a D?’ PION test results are shown in Figure 5.5 Of thefour test examples, PION can return at least 85.7 % intended answers Ofthe 396 queries, PION returns 24 cautious answers or reckless answers,and 2 counter-intuitive answers However, we would like to point outthat the high rate of the intended answers includes many ‘undetermined’answers One interesting (and we believe realistic) property of the Mad

Figure

Cows ontology is that many concepts which are intuitively disjoint (such

as cows and sheep) are not actually declared as being disjoint (keep inmind that OWL has an open world semantics, and does not make theunique name assumption) As a result, many queries such as ‘is the_cow

a sheep’ are indeed undetermined on the basis of the ontology, and PIONcorrectly reports them as undetermined The average time cost of thetested queries is about 5 seconds even on a low-end PC (with 550 mHzCPU, 256 MB memory under Windows 2000)

The counter-intuitive results occur in the MadCows Example PIONreturns the ‘accepted’ answer to the query ‘is the_mad_cow a vege-tarian?’ This counter-intuitive answer results from the weakness ofthe syntactic relevance-based selection function because it always pre-fers a shorter relevance path when a conflict occurs In the mad cowexample, the path ‘mad cow – cow – vegetarian’ is shorter than the path

‘mad cow –.eat brain – eat bodypart – sheep are animals – eat animal –NOT vegetarian.’ Therefore, the syntactic relevance-based selectionfunction finds a consistent subtheory by simply ignoring the fact

‘sheep are animals.’ The problem results from the unbalanced tion between Cow and MadCow, in which Cow is directly specified as avegetarian whereas there is no direct statement ‘a MadCow is not avegetarian.’

specifica-There are several alternative approaches to solve this kind of problems.One is to introduce the locality requirement Namely, the selectionfunction starts with a certain subtheory which must always be selected.For example, the statement ‘sheep are animals’ can be considered to be aknowledge statement which cannot be ignored Another approach is toadd a shortcut path, like the path ‘mad cow – eat animal – NOTvegetarian’ to achieve the relevance balance between the concepts

‘vegetarian’ and NOT vegetarian,’ as shown in the second mad cowexample of PION testbed The latter approach can be achieved auto-matically by accommodation of the semantic relevance from the userqueries The hypothesis is that both concepts appear in a query morefrequently, when they are semantically more relevant Therefore, from asemantic point of view, we can add a relevance shortcut path betweenstrongly relevant concepts

Example Queries IA CA RA CIA IA Rate(%) ICR Rate(%)

MarriedWoman 50 48 0 2 0 96 100

IA, intended answers; CA, cautious answers; RA, reckless answers; CIA,

counter-intuitive answers; IA Rate, intended answers (%); ICR rate, IA+CA+RA (%).

Figure 5.5 PION test results

5.8.3 Future Experiments

As noted in many surveys of current Semantic Web work, most SemanticWeb applications to date (including those included in this volume) userather lightweight ontologies These lightweight ontologies are oftenexpressed in RDF Schema, which means that by definition they willnot contain any inconsistencies However, closer inspection by Schlobach(2005a) revealed that such lightweight ontologies contain many implicitassumptions (such as disjointness of siblings in the class hierarchy) thathave not been modeled explicitly because of the limitations of thelightweight representation language Schlobach’s (2005a) study revealsthat after making such implicit disjointness assumptions explicit (aprocess called semantic clarification), many of the ontologies do revealinternal inconsistencies In future experiments, we intend to determine towhich extent it is still possible to locally reason in such semanticallyclarified inconsistent ontologies using the heuristics described in thischapter

5.9 DISCUSSION AND CONCLUSIONS

In this chapter, we have presented a framework for reasoning withinconsistent ontologies We have introduced the formal definitions ofthe selection functions, and investigated the strategies of inconsistencyreasoning processing based on a linear extension strategy

One of the novelties of our approach is that the selection functionsdepend on individual queries Our approach differs from the traditionalone in paraconsistent reasoning, nonmonotonic reasoning, and beliefrevision, in which a pre-defined preference ordering for all of the queries

is required This makes our approach more flexible, and less inefficient toobtain intended results The selection functions can be viewed as onescreating query-specific preference orderings

We have implemented and presented a prototype of PION In thischapter, we have provided the evaluation report of the prototype byapplying it to the several inconsistent ontology examples The tests showthat our approach can obtain intuitive results in most cases for reasoningwith inconsistent ontologies Considering the fact that standard reason-ers always result in either meaningless answers or incoherence errorsfor queries on inconsistent ontologies, we can claim that PION can domuch better because it can provide a lot of intuitive, thus meaningfulanswers This is a surprising result given the simplicity of our selectionfunction

We are also working on a framework for inconsistent ontologydiagnosis and repair by defining a number of new nonstandard reason-ing services to explain inconsistencies through pinpointing (Schlobachand Huang, 2005) An informed bottom-up approach to calculate

minimally inconsistent sets by the support of an external DescriptionLogic reasoner has been proposed in Schlobach and Huang (2005) Thatapproach has been prototypically implemented as the DION (Debugger

of Inconsistent Ontologies) DION uses the relevance relation which hasbeen used in PION as its heuristic information to guide the selectingprocedure for finding minimally inconsistent sets That justifies to someextent that the notion of ‘concept relevance’ is useful for inconsistentontology processing

In future work, we are going to test PION with more large-scaleontology examples We are also going to investigate different approachesfor selection functions (e.g., semantic-relevance based) and differentextension strategies as alternatives to the linear extension strategy incombination with different selection functions, and test their perfor-mance

Belnap N 1977 A useful four-valued logic In Modern Uses of Multiple-ValuedLogic, Reidel, Dordrecht, pp 8–37

Benferhat S, Garcia L 2002 Handling locally stratified inconsistent knowledgebases, Studio Logica, 77–104

Beziau J-Y 2000 What is paraconsistent logic In Frontiers of Paraconsistent Logic.Research Studies Press: Baldock, pp 95–111

Budanitsky A, Hirst G 2001 Semantic distance in wordnet: An experimental,application-oriented evaluation of five measures In Workshop on WordNetand Other Lexical Resources, Pittsburgh, PA

Chopra S, Parikh R, Wassermann R 2000 Approximate belief ninary report Journal of IGPL

revision-prelimi-Flouris G, Plexousakis D Antoniou G 2005 On applying the agm theory to dlsand owl In International Semantic Web Conference, LNCS, Springer verlag.Friedrich G, Shchekotykhin K 2005 A general diagnosis method for ontologies InInternational Semantic Web Conference, LNCS, Springer Verlag

Hameed A, Preece A Sleeman D 2003 Ontology reconciliation In Handbook onOntologies in Information Systems Springer Verlag, pp 231–250

Huang Z, van Harmelen F, ten Teije A 2005 Reasoning with inconsistentontologies In Proceedings of the International Joint Conference on ArtificialIntelligence - IJCAI’05, pp 454-459

Huang Z, Visser C 2004 Extended DIG description logic interface support forPROLOG, Deliverable D3.4.1.2, SEKT

Lang J, Marquis P 2001 Removing inconsistencies in assumption-based the-oriesthrough knowledge-gathering actions Studio, Logica, 179–214.

Levesque HJ (1989) A Knowledge-level account of abduction In Proceedings ofIJCAI’89, pp 1061–1067

Marquis P, Porquet N 2003 Resource-bounded paraconsistent inference Annals

of Mathematics and Artificial Intelligence, 349–384

McGuinness D, van Harmelen F 2004 Owl web ontology language, dation, W3C http://www.w3.org/TR/owl-features/

Recommen-Reiter R 1987 A theory of diagnosis from first principles Artificial IntelligenceJournal 32:57–96

Schaerf M, Cadoli M 1995 Tractable reasoning via approximation ArtificialIntelligence, 249–310

Schlobach S 2005a Debugging and semantic clarification by pinpointing InProceedings of the European Semantic Web Symposium, Vol 3532 of LNCS,Springer Verlag, pp 226–240

Schlobach S 2005b Diagnosing terminologies In Proceedings of the TwentiethNational Conference on Artificial Intelligence, AAAI’05, AAAI, pp 670–675.Schlobach S, Cornet R 2003 Non-standard reasoning services for the debugging

of description logic terminologies In Proceedings of IJCAI 2003’

Schlobach S, Huang Z 2005 Inconsistent ontology diagnosis: Framework andprototype, Project Report D3.6.1, SEKT

ontolo-Ontology mediation enables reuse of data across applications on theSemantic Web and, in general, cooperation between different organiza-tions In the context of semantic knowledge management, ontologymediation is especially important to enable sharing of data betweenheterogeneous knowledge bases and to allow applications to reuse data

Semantic Web Technologies: Trends and Research in Ontology-based Systems

John Davies, Rudi Studer, Paul Warren # 2006 John Wiley & Sons, Ltd

from different knowledge bases Another important application area forontology mediation is Semantic Web Services In general, it cannot beassumed that the requester and the provider of a service use the sameterminology in their communication and thus mediation is required

in order to enable communication between heterogeneous businesspartners

We distinguish two principled kinds of ontology mediation: ontologymapping and ontology merging With ontology mapping, the correspon-dences between two ontologies are stored separately from the ontologiesand thus are not part of the ontologies themselves The correspondencescan be used for, for example, querying heterogeneous knowledge basesusing a common interface or transforming data between different repre-sentations The (semi-)automated discovery of such correspondences iscalled ontology alignment

When performing ontology merging, a new ontology is created which isthe union of the source ontologies The merged ontology captures all theknowledge from the original ontologies The challenge in ontologymerging is to ensure that all correspondences and differences betweenthe ontologies are reflected in the merged ontology

Summarizing, ontology mapping is mostly concerned with the sentation of correspondences between ontologies; ontology alignment isconcerned with the discovery of these correspondences; and ontologymerging is concerned with creating the union of ontologies, based oncorrespondences between the ontologies We provide an overview of themain approaches in ontology merging, ontology mapping, and ontologyalignment in Section 6.2

repre-After the survey we present a practical approach to ontology tion where we describe a language to specify ontology mappings, analignment method for semi-automatically discovering mappings, a gra-phical tool for browsing and creating mappings in a user friendly way, inSection 6.3

media-We conclude with a summary in Section 6.4

6.2 APPROACHES IN ONTOLOGY MEDIATION

In this section we give an overview of some of the major approaches inontology mediation, particularly focusing on ontology mapping, align-ment, and merging

An important issue in these approaches is the location and tion of the overlap and the mismatches between concepts, relations, andinstances in different ontologies In order to achieve a better under-standing of the mismatches which all these approaches are trying toovercome, we give an overview of the mismatches which might occurbetween different ontologies, based on the work by Klein (2001), inSection 6.2.1

We survey a number of representative approaches for ontology ping, ontology alignment, and ontology merging in Sections 6.2.2, 6.2.3,and 6.2.4, respectively For more elaborate and detailed surveys we referthe reader to References (Kalfoglou and Schorlemmer, 2003; Noy, 2004;Doan and Halevy, 2005; Shvaiko and Euzenat, 2005).

map-6.2.1 Ontology Mismatches

The two basic types of ontology mismatches are: (1) Conceptualizationmismatches, which are mismatches of different conceptualizations of thesame domain and (2) Explication mismatches, which are mismatches in theway a conceptualization is specified

Conceptualization mismatches fall in two categories A scope mismatchoccurs when two classes have some overlap in their extensions (the sets

of instances), but the extensions are not exactly the same (e.g., theconcepts Student and TaxPayer) There is a mismatch in the modelcoverage and granularity if there is a difference in (a) the part of the domainthat is covered by both ontologies (e.g., the ontologies of universityemployees and students) or (b) the level of detail with which the model iscovered (e.g., one ontology might have one concept Person whereasanother ontology distinguishes between YoungPerson, MiddleAged-Person, and OldPerson)

Explication mismatches fall in three categories There is (1) a mismatch

in the style of modeling if either (a) the paradigm used to specify a certainconcept (e.g., time) is different (e.g., intervals vs points in time) or (b) theway the concept is described differs (e.g., using subclasses vs attributes todistinguish groups of instances) There is a (2) terminological mismatchwhen two concepts are equivalent, but they are represented usingdifferent names (synonyms) or when the same name is used for differentconcepts (homonyms) Finally, an (3) encoding mismatch occurs whenvalues in different ontologies are encoded in a different way (e.g.,using kilometers vs miles for a distance measure)

6.2.2 Ontology Mapping

An ontology mapping is a (declarative) specification of the semanticoverlap between two ontologies; it is the output of the mapping process(see Figure 6.1) The correspondences between different entities of thetwo ontologies are typically expressed using some axioms formulated in

a specific mapping language The three main phases for any mappingprocess are: (1) mapping discovery, (2) mapping representation, and (3)mapping exploitation/execution In this section we survey a numberexisting approaches for ontology mapping, with a focus on the mappingrepresentation aspect

A common tendency among ontology mapping approaches is theexistence of an ontology of mappings (e.g., MAFRA (Maedche et al.,2002), RDFT (Omelayenko, 2002)), which constitutes the vocabulary forthe representation of mappings.

MAFRA (MApping FRAmework for distributed ontologies) (Maedche

et al., 2002) supports the interactive, incremental, and dynamic ontologymapping process, where the final purpose of such a process is to supportinstance transformation It addresses all the phases of the mappingprocess: lift & normalization (lifting the content of the ontologies toRDF-S and normalization of their vocabularies by eliminating syntacticaland lexical differences), similarity (computation of the similaritiesbetween ontology entities as a support for mapping discovery), semanticbridging (establishing correspondences between similar entities, in theform of so-called semantic bridges—defining the mapping), execution(exploiting the bridges/mapping for instance transformation), and post-processing (revisiting the mapping specification for improvements)

We will focus in the following on the representation of mappings usingsemantic bridges in MAFRA The semantic bridges are captured in theSemantic Bridging Ontology (SBO) SBO is a taxonomy of genericbridges; instances of these generic bridges, called concrete bridges, con-stitute the actual concrete mappings We give an overview of thedimensions along which a bridge can be described in MAFRA, followed

by a shallow description of the classes of SBO which allow one to expresssuch bridges

A bridge can be described along five dimensions:

1 Entity dimension: pertains to the entities related by a bridge whichmay be concepts (modeling classes of objects in the real world),relations, attributes, or extensional patterns (modeling the content ofinstances)

2 Cardinality dimension: pertains to the number of ontology entities atboth sides of the semantic bridge (usually 1:n or m:1; m:n is seldomrequired and it can be usually decomposed into m:1:n)

3 Structural dimension: pertains to the way elementary bridges may becombined into a more complex bridge (relations that may hold betweenbridges: specialization, alternatives, composition, abstraction)

4 Transformation dimension: describes how instances are transformed bymeans of an associated transformation function

input Mapping creation/ output

alignment

Mapping rules

Mapping O1

O2

Figure 6.1 Ontology mapping

5 Constraint dimension: allows one to express conditions upon whosefulfillment the bridge evaluation depends The transformation ruleassociated with the bridge is not executed unless these conditions hold.The abstract class SemanticBridge describes a generic bridge, uponwhich there are no restrictions regarding the entity types that the bridgeconnects or the cardinality For supporting composition, this class hasdefined a relation hasBridge The class SemanticBridgeAlt sup-ports the alternative modeling primitive by grouping several mutuallyexclusive semantic bridges The abstract class SemanticBridge isfurther specialized in the SBO according to the entity type: Relation-Bridge, ConceptBridge, and AttributeBridge Rule is a class fordescribing generic rules Condition and Transformation are itssubclasses which are responsible for describing the condition necessaryfor the execution of a bridge and the transformation function of a bridge,respectively The Service class maps the bridge parameters with thetransformation procedure arguments to procedures.

RDFT (Omelayenko, 2002) is a mapping meta-ontology for mappingXML DTDs to/and RDF schemas targeted towards business integrationtasks The business integration task in this context is seen as a service inte-gration task, where each enterprise is represented as a Web servicespecified in WSDL A conceptual model of WSDL was developedbased on RDF Schema extended with the temporal ontology PSL Serviceintegration is reduced to concept integration; RDFT contains mapping-specific concepts such as events, messages, vocabularies, and XML-specific parts of the conceptual model

The most important class of the meta-ontology is Bridge, whichenables one to specify correspondences between one entity and a set ofentities or vice versa, depending on the type of the bridge: one-to-many ormany-to-one The relation between the source and target components of abridge can be an EquivalentRelation (states the equivalencebetween the two components) or a VersionRelation (states that thetarget set of elements form a later version of the source set of elements,assuming identical domains for the two) This is specified via the bridgeproperty Relation Bridges can be categorized in:

RDFBridges, which are bridges between RDF Schema entities Thesecan be Class2Class or Property2Property bridges

XMLBridges, which are bridges between XML tags of the source/targetDTD and the target/source RDF Schema entities These can be Tag2-Class, Tag2Property, Class2Tag, or Property2Tag bridges

Event2Event bridges, which are bridges that connect two eventspertaining to different services They connect instances of the meta-class mediator:Event

Collections of bridges which serve a common purpose are grouped in amap When defined in such a way, as a set of bridges, mappings are said

to be declarative, while procedural mappings can be defined by means of

an XPath expression for the transformation of instance data

C-OWL Another perspective on ontology mapping is given by ContextOWL (C-OWL) (Bouquet et al., 2004), which is a language that extendsthe ontology language OWL (Dean and Schreiber, 2004) both syntacti-cally and semantically in order to allow for the representation ofcontextual ontologies The term contextual ontology refers to the fact thatthe contents of the ontology are kept local and they can be mapped withthe contents of other ontologies via explicit mappings (bridge rules) toallow for a controlled form of global visibility This is opposed to theOWL importing mechanism where a set of local models is globalized in aunique shared model

Bridge rules allow connecting entities (concepts, roles, or individuals)from different ontologies that subsume one another, are equivalent, aredisjoint or have some overlap A C-OWL mapping is a set of bridgesbetween two ontologies A set of OWL ontologies together with map-pings between each of them is called a context space

The local models semantics defined for C-OWL, as opposed to theOWL global semantics, considers that each context uses a local set ofmodels and a local domain of interpretation Thus, it is possible to haveontologies with contradicting axioms or unsatisfiable ontologies withoutthe entire context space being unsatisfiable

6.2.3 Ontology Alignment

Ontology alignment is the process of discovering similarities between twosource ontologies The result of a matching operation is a specification ofsimilarities between two ontologies Ontology alignment is generallydescribed as the application of the so-called Match operator (cf (Rahmand Bernstein, 2001)) The input of the operator is a number of ontology andthe output is a specification of the correspondences between the ontologies.There are many different algorithms which implement the matchoperator These algorithms can be generally classified along two dimen-sions On the one hand there is the distinction between schema-basedand instance-based matching A schema-based matcher takes differentaspects of the concepts and relations in the ontologies and uses somesimilarity measure to determine correspondence (e.g., (Noy and Musen,2000b)) An instance-based matcher takes the instances which belong tothe concepts in the different ontologies and compares these to discoversimilarity between the concepts (e.g., (Doan et al., 2004)) On the otherhand there is the distinction between element-level and structure-levelmatching An element-level matcher compares properties of the particu-lar concept or relation, such as the name, and uses these to findsimilarities (e.g., (Noy and Musen, 2000b)) A structure-level matchercompares the structure (e.g., the concept hierarchy) of the ontologies to