Possible and Certain Answers for Queries over Order-Incomplete Data

Authors Antoine Amarilli, Mouhamadou Lamine Ba, Daniel Deutch, Pierre Senellart

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Antoine Amarilli
Mouhamadou Lamine Ba
Daniel Deutch
Pierre Senellart

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Antoine Amarilli, Mouhamadou Lamine Ba, Daniel Deutch, and Pierre Senellart. Possible and Certain Answers for Queries over Order-Incomplete Data. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


To combine and query ordered data from multiple sources, one needs to handle uncertainty about the possible orderings. Examples of such "order-incomplete" data include integrated event sequences such as log entries; lists of properties (e.g., hotels and restaurants) ranked by an unknown function reflecting relevance or customer ratings; and documents edited concurrently with an uncertain order on edits. This paper introduces a query language for order-incomplete data, based on the positive relational algebra with order-aware accumulation. We use partial orders to represent order-incomplete data, and study possible and certain answers for queries in this context. We show that these problems are respectively NP-complete and coNP-complete, but identify many tractable cases depending on the query operators or input partial orders.
  • certain answer
  • possible answer
  • partial order
  • uncertain data


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