Order dependencies in relational database due to Ginsburg and Hull are relationships between attributes with domains of ordered values. The basic notions in this paper are comparison systems and relational attribute models in Dedekind categories. A comparison system constitutes a formal structure of possible orders for attribute domains. A relational attribute model is a system of relations on an object (of tuples or records) in Dedekind categories, which can be constructed by a suitable relational interpretation of comparing symbols. Generalizing order dependencies as well as functional dependencies, the paper introduces extended order dependencies, and their satisfactory relations for relational attribute models in Dedekind category. Then we give a simple proof that a revised set of inference rules is sound and complete.
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