One of the most important lines of research in Description Logics (DLs) is concerned with the trade-off between expressive power and computational complexity of sound and complete reasoning. Research carried out in the past on this topic has shown that many DLs with efficient, i.e., worstcase polynomial time, reasoning algorithms lack the modeling power required for capturing conceptual models and basic ontology languages, while most DLs with sufficient modeling power suffer from inherently worst-case exponential time behavior of reasoning [1, 2]. Although the requirement of polynomially tractable reasoning might be less stringent when dealing with relatively small ontologies, we believe that the need of efficient reasoning algorithms is of paramount importance when the ontology system is to manage large amount of objects (e.g., from thousands to millions of instances). This is the case of several important applications where the use of ontologies is advocated nowadays. For example, in the Semantic Web, ontologies are often used to describe the relevant concepts of Web repositories, and such repositories may incorporate very large data sets, which constitute the instances of the concepts in the ontology. In such cases, two requirements emerge that are typically overlooked in DLs. First, the number of objects in the knowledge bases requires managing instances of concepts (i.e., ABoxes) in secondary storage. Second, significant queries to be posed to the knowledge base are more complex than the simple queries (i.e., concepts and roles) usually considered in DL research. Unfortunately, in these contexts, whenever the complexity of reasoning is exponential in the size of the instances (as for example in Fact1, Racer2 and in [3]), there is little hope for effective instance management and query answering algorithms. In [4] a new DL, called DL-Lite, was proposed specifically tailored to capture basic ontology languages, while keeping low complexity of reasoning. A DL-Lite knowledge base (KB) is constituted by two components: an intensional level (called TBox in DL jargon), used to model the concepts and the relations (roles) of the ontologies, and an exten-
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