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    Chapter 2 MODELS FOR INCOMPLETE AND PROBABILISTIC INFORMATION

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    Keywords: We discuss, compare and relate some old and some new models for incomplete and probabilistic databases. We characterize the expressive power of c-tables over infinite domains and we introduce a new kind of result, algebraic completion, for studying less expressive models. By viewing probabilistic models as incompleteness models with additional probability information, we define completeness and closure under query languages of general probabilistic database models and we introduce a new such model, probabilistic c-tables, that is shown to be complete and closed under the relational algebra. We also identify fundamental connections between query answering with incomplete and probabilistic databases and data provenance. We show that the calculations for incomplete databases, probabilistic databases, bag semantics, lineage, and why-provenance are particular cases of the same general algorithms involving semi-rings. This further suggests a comprehensive provenance representation that uses semi-rings of polynomials. Finally, we show that for positive Boolean c-tables, containment of positive relational queries is the same as for standard set semantics. Incomplete databases, probabilistic databases, provenance, lineage, semi-rings 1.

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    Title : Chapter 2 MODELS FOR INCOMPLETE AND PROBABILISTIC INFORMATION
    Abstract : Keywords: We discuss, compare and relate some old and some new models for incomplete and probabilistic databases. We characterize the expressive power of c-tables over infinite domains and we introduce a new kind of result, algebraic completion, for studying less expressive models. By viewing probabilistic models as incompleteness models with additional probability information, we define completeness and closure under query languages of general probabilistic database models and we introduce a new such model, probabilistic c-tables, that is shown to be complete and closed under the relational algebra. We also identify fundamental connections between query answering with incomplete and probabilistic databases and data provenance. We show that the calculations for incomplete databases, probabilistic databases, bag semantics, lineage, and why-provenance are particular cases of the same general algorithms involving semi-rings. This further suggests a comprehensive provenance representation that uses semi-rings of polynomials. Finally, we show that for positive Boolean c-tables, containment of positive relational queries is the same as for standard set semantics. Incomplete databases, probabilistic databases, provenance, lineage, semi-rings 1.
    Subject : unspecified
    Area : Computer Science
    Language : English
    Affiliations
    Url : http://www.cs.ucdavis.edu/~green/papers/models-chapter.pdf
    Doi : 10.1.1.162.2806

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