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<Paper uid="W02-1711">
  <Title>A Proposal for Screening Inconsistencies in Ontologies based on Query Languages using WSD</Title>
  <Section position="3" start_page="0" end_page="3" type="metho">
    <SectionTitle>
2 Global-as-view approach
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    <Paragraph position="0"> In (Calvanese et al., 2001), global-as-view and local-as-view approaches are proposed for ontology integration. According to the global-as-view approach, the mapping between the global and the local ontologies is given by associating each term in the global ontology with a view.</Paragraph>
    <Paragraph position="1"> Let C be a term in the global ontology G, V a query language over the terms of the local ontologies, and M the mapping between the global and the local ontologies. Given that D is a local model for the ontology integration system and I a global interpretation for the system, the correspondence between C and V is specified as follows by referring to (Calvanese et al., 2001): *&lt;C,V,sound&gt; if all tuples satisfying V in D satisfy C in</Paragraph>
    <Paragraph position="3"> if no tuple other than those satisfying V in D satisfies C in I *&lt;C,V,exact&gt; if the set of tuples that satisfy C in I is exactly the set of tuples satisfying V in D. In the above notation, &amp;quot;I satisfies&amp;quot; means that I satisfies every correspondence in the mapping between the global ontology and the local ontologies wrt D. These correspondences are valid if the global ontology is assumed to be consistent; however, inconsistencies might occur when the term in the global ontology has more than one definition. We use the word &amp;quot;bass,&amp;quot; for example, which has at least two definitions, one, &amp;quot;a man whose singing voice is very low,&amp;quot; and another, &amp;quot;a kind of fish&amp;quot;(LDOCE, 1995). Each definition is represented in order with firstorder-language-like notation, as follows:</Paragraph>
    <Paragraph position="5"> Some concepts in the global ontology are described using the above two C(x)s. The following concept is represented with the first C(x) be-</Paragraph>
    <Paragraph position="7"> The concept C(x) in (1) can be represented with the DAML+OIL notation, as shown below.</Paragraph>
    <Paragraph position="8"> This concept is assumed to belong to one local ontology (for example, local-ont-1). In the representation, some parts in the representation, such as namespace prefixes and URIs, are omitted because they do not directly relate to this paperfs intention. In addition, the referenced resources and properties whose definitions are not in the representation are supposed to be defined implicitly.</Paragraph>
    <Paragraph position="9">  is formed, 'x' as a result of the global ontology becomes a set of instances for a new class, and the local ontology is revised by adding a subclass of the existing class. If such a new subclass were named &amp;quot;sub-bass,&amp;quot; it would be represented in this manner:  Let O be an ontology screening system. In this case, O obtains one concept &amp;quot;sub-bass,&amp;quot; i.e., &amp;quot;a bass singer working at an orchestra,&amp;quot; from the intersection between C(x) and isMemberOf(x,orchestra). The concept &amp;quot;subbass&amp;quot; is formed by combining the local and global ontologies. Considering this example, appropriate extensions of the intended concept in the global ontology are obtained and recognized only if the right sense of the concept in the local ontology is used. A different concept might be drawn from different senses from other local ontologies, but the high rate of co-occurrence between singer and orchestra led by WSD would play a crucial role in preventing another sense from being considered. Let's consider another example:</Paragraph>
    <Paragraph position="11"> In (2), x is likely the second sense of &amp;quot;bass.&amp;quot; For example, x is an extension of the bass class as a subclass of fish. WSD would justify it because the co-occurrence of &amp;quot;fish&amp;quot; and &amp;quot;river&amp;quot; is rather strong. The local ontology of &amp;quot;bass&amp;quot; from the second sense (local-ont-2) is represented with DAML+OIL, as shown below. It  is also revised when a new subclass from query (2) is added.</Paragraph>
    <Paragraph position="12">  According to (Calvanese et al., 2001), the following situations involving inconsistency or ambiguity occur as a result of the mapping of global and local ontologies: 1. There are no global models.</Paragraph>
    <Paragraph position="13"> This occurs when the data in the extension of the local ontologies do not satisfy the constraints for functional attributes.</Paragraph>
    <Paragraph position="14"> For example, in (Calvanese et al., 2001), a property &amp;quot;age&amp;quot; is considered. Since &amp;quot;age&amp;quot; is a function, the value as its range must be defined with only one value. However, the global ontology does not have a model concerning &amp;quot;age&amp;quot; any more if &amp;quot;age&amp;quot; has more  than one value from the constraint of the concepts in a local ontology.</Paragraph>
    <Paragraph position="15"> 2. There are several global models.</Paragraph>
    <Paragraph position="16">  This occurs when the data in the extension of the local ontologies do not satisfy the ISA relationships of the global ontology: i.e., several ways exist to add suitable instances to the elements of the global ontology in order to satisfy the constraints from a local ontology. For example, it is assumed that a &amp;quot;student&amp;quot; must be enrolled in a certain university. More than one university can be considered when the constraints in a local ontology do not mention which university each extension of &amp;quot;student&amp;quot; is enrolled in from the concept definitions of the local ontology. Such ambiguities depend on how precisely the concepts of a local ontology are defined. As a result, all interpretations for an intended ontology integration system within which a valid concept exists must be accepted as models because of the potential ambiguities present in local ontologies. null We propose two other solutions to the unsuitable situations described above; the first relates to yielding invalid extensions, and the second to forming wrong concept definitions as a result of WSD failure. For an explanation of the first situation, consider this example:  is assumed to be formed from concept C, which has the meaning of &amp;quot;bass as a singer.&amp;quot; The meaning of C  is &amp;quot;a bass that lives in a certain river.&amp;quot; Provided that &amp;quot;Ichiro&amp;quot; is an extension of C  , it could be said that Ichiro lives in a river. In an ontology hierarchy, there would be multiple inheritances around one term. Suppose &amp;quot;Ichiro&amp;quot; is also an extension of the class &amp;quot;man.&amp;quot; If the class &amp;quot;man&amp;quot; has a prop-erty called &amp;quot;isAddressOf,&amp;quot; which is defined as the same property of &amp;quot;livesIn,&amp;quot; &amp;quot;Ichiro&amp;quot; must have an instantiated address. When his address is &amp;quot;Tokyo,&amp;quot; an inconsistency arises because &amp;quot;Tokyo&amp;quot; and &amp;quot;river&amp;quot; are not classified in the same category. In addition, this inconsistency in terms of having an inappropriate value of properties is propagated towards lower sub-classes of the target class. This situation is expressed in Figure 1. We claim that a situation such as this should be solved using WSD because of the strong relationship between &amp;quot;fish&amp;quot;  would be assumed to be a concept referring to a subclass of person from the ordinary context. However, the ontology screening system might classify the concept C  into the wrong place in the global ontology if it takes the concept C as the second meaning of &amp;quot;bass,&amp;quot; i.e., a kind of fish. Deriving the related concepts in the global ontology on the basis of a wrong concept whose meaning is never intersectable with the right one causes an unexpected inconsistency over the global ontology. After C  is mistaken, the local ontology would result in a concept with the meaning &amp;quot;a bass whose hobby is swimming&amp;quot; in spite of the fact that a bass is a type of fish.</Paragraph>
    <Paragraph position="17">  The above situation has not yet been solved because the strength of the relationship between &amp;quot;fish&amp;quot; and &amp;quot;swimming&amp;quot; is rather high. In order to solve such problems, WSD should be applied to the property names as well as the property values: i.e., &amp;quot;hobby.&amp;quot;</Paragraph>
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