Actually, mormons think they are very logical. I've seen many instances of people talking about how Brandon Sanderson being Mormon is why he's so thorough at world building.
As someone who has worked with and for Mormons, it's a special kind of hell. Usually some flavor of narcissist stunted at a middle-school level of inward development.
Professing to be a mormon is a logical decision if your culture is mormon.
Disinterest in pursuing a more empirical world view is not illogical if one would have to damage their relationship with those closest to them in its pursuit.
(Sorry about the pretentiousness of that (and this) sentence, I can't find a more vernacular way of expressing these ideas succinctly).
Most people don't actually know what logic is. I would ask him to define logic to see where he's coming from. Because most people either don't have a definition or if they do it's different than the one the person they're talking to has. But to do that, you'll also want a definition you could explain to someone else going into asking the question.
If they had the vocabulary, they probably would say that they live by heavyweight axioms like “Joseph Smith was a prophet of God” and “The Book of Mormon is true”. From my experience, it is possible to exercise logic with flawed axioms so long as you steer clear of a liberal arts education (my mistake, lol).
It's always so hard to read and understand when people start using them/they when referring to a single person. Please stop, it's okay to say him/her, nobody will die.