investigative — to examine, study, or inquire into systematically; search or examine into the particulars of; examine in detail.
socratic — of or relating to Socrates or his philosophy, followers, etc., or to the Socratic method.
disquisitive — Relating to disquisition; fond of discussion or investigation; inquisitive.
fact-finding — a person who searches impartially for the facts or actualities of a subject or situation, especially one appointed to conduct an official investigation, as in a labor-management conflict.
investigatory — to examine, study, or inquire into systematically; search or examine into the particulars of; examine in detail.
snoopy — characterized by meddlesome curiosity; prying.