To add to this description, the Prolog-derived syntactic core of Datalog (the Horn clauses and facts) can be viewed as a combination of "unification" and mutually recursive rules to find a fixpoint over your data+query. It's essentially like solving simultaneous equations.

The Prolog-derived syntax is routinely extended because the core is typically too simplistic/inexpressive to be directly useful, e.g. see https://www.fdi.ucm.es/profesor/fernan/des/html/manual/manua...