In many cases a person with dementia expresses herself with what she believes to be a very logical thought pattern that appears to a caregiver to be quite illogical. But if a person with dementia is expressing himself in a consistent but bizarre way, it might very much be indicative of a logic which — while unintelligible or not able to be decoded by a caregiver — has a consistency and repeatability that means that a person is communicating in a personally meaningful way.
A few thoughts in a mind model (AKA mind map) created by my own demented brain. The process of mind modeling is for me an alternate way of thinking and communicating that later permits me to translate the ideas and my (but possibly not your) logical network into words you might understand.
Please click on the image to expand it.