This riddle (from Amann and Escher) has been bothering me more than it should. What is going on here? I'm not sure I see how to translate this into the sort of propositional logic I can manipulate via the standard rules.
“The Simpsons are coming to visit this evening,” announced Maud Flanders. “The whole family — Homer, Marge and their three kids, Bart, Lisa and Maggie?” asked Ned Flanders dismayed. Maud, who never misses a chance to stimulate her husband’s logical thinking, replied, “I’ll explain it this way: If Homer comes then he will bring Marge too. At least one of the two children, Maggie and Lisa, are coming. Either Marge or Bart is coming, but not both. Either both Bart and Lisa are coming or neither is coming. And if Maggie comes, then Lisa and Homer are coming too. So now you know who is visiting this evening.” Who is coming to visit?
We know Homer is not coming, since if Homer comes, this implies Marge comes, which in turn implies Bart stays home, which in turn implies Lisa stays home, which in turn implies Maggie comes, which in turn implies Lisa comes, a contradiction.
Therefore Homer is not coming, which implies Maggie cannot come as well. Maggie not coming implies Lisa is coming, which implies Bart is coming, which implies Marge stays home.
Thus Bart and Lisa come but no one else does. (Each implication in the preceding argument is from a direct sentence in the problem).
Update
Translating into propositional logic might be overkill for this problem, but since you mentioned it, to translate into propositional logic, just define varibles $B, L, M_{ag}, H, M_{arg}$, representing the statements "Homer is coming", etc... and then translate the sentences as
$$H\implies M_{arg}$$ $$M_{ag}\vee L$$ $$M_{arg}\oplus B$$ $$B\Leftrightarrow L$$ $$M_{ag}\implies (L\wedge H)$$ (Here $\oplus$ is "exclusive or".)