I haven't done this yet, but heard about it from my fellow math teacher at WIldcat Community FreeSchool. I think we can build on it somehow, and turn it into a logic game.
There is a puzzle in Alice in Puzzleland (by Raymond Smullyan) in which you encounter John, or perhaps his identical twin brother. You know that one of them always lies and the other always tells the truth, but not which is which. What one question (of just 3 words) can you ask to find out whether you're talking to John or his brother?
I think Sarah told the kids the answer-question. Then, wanting to help them see why it was so, she made little slips of paper that said John, Twin, Liar, Truth-teller, and had the kids pick two (a person and a status) and answer the question from lots of different perspectives. She said they had trouble staying in character when they got the Liar role. That got me thinking about trying to come up with lying games, which I imagine they'd love, mixed with components of this or other liar and truth-teller puzzles. I'll keep thinking about this, but wanted to share the idea before I forgot... ;>
I think we can make a "paradox builder" using "multiplication of predicates" - MariaD