Disjunctive Datalog is an extension of the logic programming language Datalog that allows disjunctions in the heads of rules. This extension enables disjunctive Datalog to express several NP-hard problems that are not known to be expressable in plain Datalog. Disjunctive Datalog has been applied in the context of reasoning about ontologies in the semantic web.[1] DLV is an implementation of disjunctive Datalog.
Syntax edit
A disjunctive Datalog program is a collection of rules. A rule is a clause of the form:[2]
where , ..., may be negated, and may include (in)equality constraints.
Semantics edit
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There are at least three ways to define the semantics of disjunctive Datalog:[3]
- Minimal model semantics
- Perfect model semantics
- Disjunctive stable model semantics, which generalizes the stable model semantics
Expressivity edit
This section needs expansion with: examples of programs expressing these problems. You can help by adding to it. (March 2023) |
Disjunctive Datalog can express several NP-complete and NP-hard problems, including the travelling salesman problem, graph coloring, maximum clique problem, and minimal vertex cover.[3] These problems are only expressible in Datalog if the polynomial hierarchy collapses.
Implementations edit
The DLV (DataLog with Disjunction, where the logical disjunction symbol V is used) system implements the disjunctive stable model semantics.[4]
See also edit
Sources edit
Notes edit
- ^ Kaminski, Mark; Nenov, Yavor; Grau, Bernardo Cuenca (2014-06-21). "Datalog Rewritability of Disjunctive Datalog Programs and its Applications to Ontology Reasoning". Proceedings of the AAAI Conference on Artificial Intelligence. 28 (1). arXiv:1404.3141. doi:10.1609/aaai.v28i1.8854. ISSN 2374-3468. S2CID 17098158.
- ^ Eiter, Gottlob & Mannila 1997, p. 370.
- ^ a b Eiter, Gottlob & Mannila 1997.
- ^ Alviano, Mario; Faber, Wolfgang; Leone, Nicola; Perri, Simona; Pfeifer, Gerald; Terracina, Giorgio (2011), "The Disjunctive Datalog System DLV", Datalog Reloaded, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 282–301, doi:10.1007/978-3-642-24206-9_17, ISBN 978-3-642-24205-2, retrieved 2023-08-04
References edit
- Eiter, Thomas; Gottlob, Georg; Mannila, Heikki (1997-09-01). "Disjunctive datalog". ACM Transactions on Database Systems. 22 (3): 364–418. doi:10.1145/261124.261126. ISSN 0362-5915. S2CID 8755376.