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When is naive evaluation possible?

Published:22 June 2013Publication History

ABSTRACT

The term naive evaluation refers to evaluating queries over incomplete databases as if nulls were usual data values, i.e., to using the standard database query evaluation engine. Since the semantics of query answering over incomplete databases is that of certain answers, we would like to know when naive evaluation computes them: i.e., when certain answers can be found without inventing new specialized algorithms. For relational databases it is well known that unions of conjunctive queries possess this desirable property, and results on preservation of formulae under homomorphisms tell us that within relational calculus, this class cannot be extended under the open-world assumption.

Our goal here is twofold. First, we develop a general framework that allows us to determine, for a given semantics of incompleteness, classes of queries for which naive evaluation computes certain answers. Second, we apply this approach to a variety of semantics, showing that for many classes of queries beyond unions of conjunctive queries, naive evaluation makes perfect sense under assumptions different from open-world. Our key observations are: (1) naive evaluation is equivalent to monotonicity of queries with respect to a semantics-induced ordering, and (2) for most reasonable semantics, such monotonicity is captured by preservation under various types of homomorphisms. Using these results we find classes of queries for which naive evaluation works, e.g., positive first-order formulae for the closed-world semantics. Even more, we introduce a general relation-based framework for defining semantics of incompleteness, show how it can be used to capture many known semantics and to introduce new ones, and describe classes of first-order queries for which naive evaluation works under such semantics.

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        • Published in

          cover image ACM Conferences
          PODS '13: Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI symposium on Principles of database systems
          June 2013
          334 pages
          ISBN:9781450320665
          DOI:10.1145/2463664
          • General Chair:
          • Richard Hull,
          • Program Chair:
          • Wenfei Fan

          Copyright © 2013 ACM

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 22 June 2013

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          PODS '13 Paper Acceptance Rate24of97submissions,25%Overall Acceptance Rate476of1,835submissions,26%

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