Gösta Grahne
ABSTRACT
The notion of representation systems describes structures that are algebraically closed under queries. It has recently been realized that representation systems are highly relevant also in the context of data exchange. We extend the notion of representation system to encompass data exchange mappings and their composition. Seen through this lens, two major classes of representation systems emerge, namely homomorphic data exchange systems and strong data exchange systems. The homomorphic "OWA" systems encompass the "classical" part of data exchange. Reasoning is modulo homomorphic equivalence (CQ-equivalence), and only unions of conjunctive queries and monotone data exchange mappings are supported.
We then develop some new technical tools that allow us to prove that there is a class of '"CWA" strong representation systems in which reasoning is modulo isomorphic equivalence. These systems are based on conditional tables, and they support first order queries and non-monotonic data exchange mappings specified by a large class of second order dependencies. We achieve this by showing that, under a CWA-interpretation, conditional tables are chaseable with the aforementioned class of second order dependencies, and that the class is closed under composition in the CWA-setting.
We also introduce a stricter notion of composability, and show that the class of (first order) source-to-target tuple generating dependencies is closed under the stricter notion of composability.
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Index Terms
- Representation systems for data exchange
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