Logic does not pertain to truth, it pertains to prejudice. In a physical sense, logic is backed by the presence of science; an incomplete set of skewed observations of reality as seen through hand made devices.
Truth is an unstable concept, but there is also, an 'is' as seen through a consciousness of unprejudiced observation. One cannot trust anything one hears as truth but merely opinion, even if what is heard supports ones beliefs. There is actually nothing discerning logic and belief apart, only, only words.
For instance, I cant tell you the truth, only my observations which may serve you to question your beliefs. Any truth you come across should come from inside you, from a place free of prejudice. If you dont do this, your mind is at the whim of the currents it chances to get caught in.