Suppose I have the following problem:
$2$ kids are liars, $3$ can only say the truth.
Julia: "Jack is only a liar, if John is telling the truth
Jack: "If Joey doesn't lie, then either Julia or John do
Joey: "Jane lies, as does Julia or Jack.
John: "If Jack is telling the truth, then Julia or Joey do as well
Jane: "If you round up Julia, Joey, and John, you will have at least one liar." Who are the compulsive liars?
Now before giving this problem to somebody else, I have to make sure that I have given enough information for this problem to be solved, and that none of my information is contradictory. Is there a systematic way of constructing such problems and if so what branch of maths deals with this?