Premise: These are like the knight-knave puzzles; only now we are visiting insane asylums, where there are only patients and doctors. Moreover, each of them are either insane or sane. Sane inhabitants of an asylum are entirely accurate in their beliefs (they believe all and only true statements and disbelief all and only false ones), whereas insane inhabitants are totally inaccurate in their beliefs. Nonetheless they are all honest--whatever they say, they believe. You may reason as you like, but you must write down your reasoning.
Questions: You visit an asylum and ask an inhabitant “Are you a patient?” The inhabitant replies “I believe so.” Is anything necessarily wrong with this asylum?