[jrimclean]

Natural deduction for propositional logic? Simple rules, real math. There are lots of good problems of varying difficulty in Logic in Computer Science by Huth and Ryan.

Edit: Perhaps this doesn't qualify as a game per se, but I think it might be a fun activity to work through the proofs together.

[Jtsummers]

I don't see why that wouldn't be a game. As a kid (maybe not at 5, closer to 10?) my parents were giving me puzzle books that included puzzles based on deductive reasoning.

Clue is based on this form of logic. Or that's how I played it at least.

https://boardgamegeek.com/boardgamecategory/1039/deduction

More games of this form.