Dementia, lying, denying, and forgetting

When you deprive somebody of his mind, he'll get dementia. This word is easy in various languages:

English: dementia
French: démence
Spanish: demencia
Italian: demenza

where the prefixes dé- and de- are considered privative, i.e. "marked as absence, removal, or loss", and the root, traced to Latin, means "mind". But things get slightly complicated if the root changes a little bit. The Latin word for "mind" can change to another word mentior or mentiri in infinitive, which means "to lie". According to Wiktionary, "[t]he meaning 'to lie' stems from a semantic shift 'to be inventive, have second thoughts' > 'to lie, conjure up'." The downstream reflexes all take this meaning:

French and Spanish: mentir, "to lie"
Italian: mentire, "to lie"

But we must not forget two words that take quite different meanings even though their prefix and the root remain almost the same:

French: démentir, "to deny (wrongdoing, scandal etc.)"
Italian: dimenticare, "to forget"

Démentir makes sense because when you remove or try to remove (dé-) a lie (the root, without the verb suffix), you're denying it. Dimenticare makes sense because if you lose (di-) your mind (the root, without the verb suffix), you forget something. But we still have to make a small effort to remember these two words because in Spanish you say negar, in Italian you say negare for "to deny", and in Spanish you say olvidar and in French you say oublier for "to forget", adding inconsistencies to this whole group of related words.