Our results highlight the basic roles played by negation (and in its weak form inequality) and recursion, and a crucial difference beWe study the complexity of the problem of answering queries using materialized views. This problem has attracted a lot of attention recently because of its relevance in data integration. Previous work considered only conjunctive view definitions. We examine the consequences of allowing more expressive view definition languages. The languages we consider for view definitions and user queries are: conjunctive queries with inequality, positive queries, datalog, and first-order logic. We show that the complexity of the problem depends on whether views are assumed to store all the tuples that satisfy the view definition, or only a subset of it. Finally, we apply the results to the view consistency and view self-maintainability problems which arise in data warehousing. tween open and closed world assumption in the view definition. The main focus of the paper is the study of the data complexity of the problem of answering queries using materialized views. More precisely, the problem is for a fixed view definition and a fixed query, given a view instance I and a tuple t, is t a certain answer, i.e. is t in the answer to the query on the database no matter which is the database yielding the view instance I. This articulation of the problem highlights the main parameters: (i) What are the database and the view models? (ii) What are the query and the view definition languages? (iii) Is yielding assuming an open or a closed world? In the present paper, we use the relational model for the database and the view model. However, our work strongly suggests moving towards an incomplete information model, e.g. conditional tables . Indeed, we will briefly show how these tables can be used for solving the problem in most solvable cases. For the query and view definition languages, we considerthe most popular formal query languages, namely conjunctive queries, conjunctive queries with inequality, positive queries, datalog, and first-order logic. We focus on certain answers, i.e. tuples that are in the answer for any database yielding this particular view instance.
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