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Datalog with Negation and Monotonicity

Authors Bas Ketsman , Christoph Koch

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  • 18 pages

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Bas Ketsman
  • École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
Christoph Koch
  • École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

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Bas Ketsman and Christoph Koch. Datalog with Negation and Monotonicity. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 19:1-19:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


Positive Datalog has several nice properties that are lost when the language is extended with negation. One example is that fixpoints of positive Datalog programs are robust w.r.t. the order in which facts are inserted, which facilitates efficient evaluation of such programs in distributed environments. A natural question to ask, given a (stratified) Datalog program with negation, is whether an equivalent positive Datalog program exists. In this context, it is known that positive Datalog can express only a strict subset of the monotone queries, yet the exact relationship between the positive and monotone fragments of semi-positive and stratified Datalog was previously left open. In this paper, we complete the picture by showing that monotone queries expressible in semi-positive Datalog exist which are not expressible in positive Datalog. To provide additional insight into this gap, we also characterize a large class of semi-positive Datalog programs for which the dichotomy `monotone if and only if rewritable to positive Datalog' holds. Finally, we give best-effort techniques to reduce the amount of negation that is exhibited by a program, even if the program is not monotone.

Subject Classification

ACM Subject Classification
  • Information systems → Relational database query languages
  • Theory of computation → Constraint and logic programming
  • Datalog
  • Monotonicity


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