Querying Order-Incomplete Data

To combine ordered data originating from multiple sources, one needs a framework that can represent uncertainty about the possible orderings or, as we call it, order-incomplete data. Examples of such data are lists of properties (such as hotels and restaurants) ranked by an unknown function reflecting relevance or customer ratings; documents edited concurrently with uncertainty on the order of contributions; and the result of integrating event sequences such as sensor readouts or log entries. Our work extends the positive relational algebra to ordered and order-incomplete data, and introduces a set of axioms to guide the design of a bag semantics for the language. We introduce two simple such semantics, one of which is shown to be the most general for our set of axioms. We next design a strong representation system for them, based on partial orders interpreted through a possible worlds semantics. We study the expressiveness of our query language, connecting it to complexity measures on partial orders. We further introduce a top-k operator, and investigate the complexity of query evaluation, studied in the context of certain and possible answers. We last introduce a duplicate elimination operator to return to set semantics, and re-