International Journal of Web & Semantic Technology (IJWest) Vol.1, Num.4, October 2010

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## 2.3 Notion Of Mismatch Between Two Ontologies

We focus on the following two types of mismatch between the client and server ontologies in this paper.

Specialization Mismatch(Type-1): **In this type of incompatibility the client recognizes a class** c2 as the specialization of another class c1 whereas the server recognizes c2 **as the specialization of** some other class c
′

1**. Our first example (Figure 1) is an instance of this type.**
Attribute Assignment Mismatch(Type-2): **A very common type of incompatibility arises where**
the client and the server both recognize classes c
′

1
, . . . , c′n as the specializations of another class c1, but the client associates an attribute α with the super class c1**, whereas the server associates**
α **with some of the sub classes** c
′

i
, . . . , c′j
, 0 < i, j ≤ n**. Since we view the mismatches from the**
query answering perspective, we use the notion of this conflict from the query perspective. If the set of variables that is used in a query q, is not available at server side, we denote that as **attribute**
level(Type-2) **mismatch. Our first example (Figure 2) is an instance of this type.**

## 3 Graph Model Of Ontology

While describing an ontology using OWL, the class and the attributes(modeled as properties in the context of OWL) are used to represent the meta-data. We use a graph based approach to model the meta-data that are described as classes and attributes in OWL. While using OWL, the properties are used to express the attributes. Therefore we use the term property and attribute interchangeably. We define the ontology graph as follows.

Definition 1. A graph model for an ontology O is G = (V, E) where, V **is the set of vertices and**
E is the set of directed edges. Each node vi ∈ V **represents a class in the OWL ontology and** vi is associated with a property list L(vi) **whose elements are the data properties of the class. The directed**
edges can be of the following types 32