TypeDb is a practical Datalog-based database system [1] (with a different syntax). TerminusDb is a project in a similar vein [2], but actually an RDF store at its core. If you want to experiment with the connections between Datalog, relational algebra, and SQL, check out the Datalog Educational System. And if you want to jump into the theory, Foundations of Databases (the "Alice book") is very thorough but relatively readable [4]! Oh, and there's a Google project, Logica, to do Datalog over Postgres databases [5].

[1]: https://typedb.com/ [2]: https://terminusdb.com/ [3]: http://www.fdi.ucm.es/profesor/fernan/des/ [4]: http://webdam.inria.fr/Alice/ [5]: https://github.com/evgskv/logica