How would one make a good liars puzzle?

I’ve seen and made a few liars puzzles, and a recurring theme with liars puzzles is that they can be too easy, and can be dull, perhaps a bit repetitive. How can you come up with a Liars puzzle that is not too easy, but has interest and appeal?

In your answer you can, and are encouraged to make reference to previous liars puzzle, or even create one in order to support your reasoning.

Answer

If you're referring to Knights and Knaves type puzzles, the Wikipedia article on them suggests some variants that might produce some interesting complexity.

I find that a Liars mechanic can be very interesting when incorporated into other types of logic deduction puzzles, such as this Logic Grid puzzle I created earlier this year, in which a liars mechanic greatly increases the difficulty.

Liars mechanics can also increase complexity in Grid Deduction puzzles such as Sudoku. For example, here is a Slitherlink puzzle by Prasanna Seshadri, in which one clue from each row and column is lying, and must be different from its stated value. Similarly, here is a collection of Area 51 puzzles by Dave Millar, which is basically the same idea, but with several additional types of clues. A couple of Nikoli grid deduction puzzles have Liar mechanics built into their standard rules, including Yajisan-Kazusan and Usowan.

In fact, it's not uncommon for the World Puzzle and World Sudoku competitions to have an entire section devoted to this mechanic.

In any case, one way I might start to make a puzzle of this type would be to create a set of clues in which certain combinations produce a contradiction, constructing those combinations so that one can deduce previously uncertain clues or statements to be true.

For example, in the Logic Grid puzzle linked above, five people have lists of five clues each, one clue being false on each list. I created a circular chain of potential contradictions, which can be abstracted as follows:

A1-5, B1-5, C1-5 are all clues. Exactly one each of the A, B, and C clues is false. A1 conflicts with B2, B1 conflicts with C2, and C1 conflicts with A2. There are only two possibilities, all of the _1 clues are false or all of the _2 clues are false. Therefore all of the remaining A, B, and C clues must be true. Trenin finds this chain in his walkthrough in the section called Mary, Jeff, and Katie.