The learning of recursive logic programs (i.e. the class of logic programs where at least one clause is recursive) from incomplete information, such as input/output examples, is a challenging subfield both of ILP (Inductive Logic Programming) and of the synthesis (in general) of logic programs from formal specifications. This is an extremely important class of logic programs, as the recent work on constructive induction shows that necessarily invented predicates have recursive programs, and it even turns out that their induction is much harder than the one of non-recursive programs. We call this "inductive program synthesis". We introduce a system called DIALOGS-II (Dialogue-based Inductive and Abductive LOgic Program Synthesizer-II) whose ancestor is DIALOGS. It is a schema-guided, interactive, and non-incremental synthesizer of recursive logic programs that takes the initiative and queries a (possibly naive) specifier for evidence in her/his conceptual language. It can be used by any learner (including itself) that detects, or merely conjectures, the necessity of invention of a new predicate. Moreover, due to its powerful codification of "recursion-theory" into program schemata and schematic constraints, it needs very little evidence and is very fast.