Calculational solutions to Smullyans logical puzzles

[Cross-posted to sci.math and sci.logic because this is about math & logic as well...]

Hello all,

For some time, I've been working on puzzles from books by Raymond Smullyan (The Lady Or The Tiger, To Mock a Mockingbird, What Is The Name Of This Book?).

I found that a lot of these puzzles suddenly become fairly easy when you use logical notations and calculational proofs. (I later found out that others had the same experience; see http://www.cs.cornell.edu/gries/Logic/Neatsolution.html). This post is just to share a little of that experience, by giving one example.

Logic is defined recursively by advice:

Logic is that thing which a

Psychologist will advise you to be careful in there. Logician will advise you to be careful out there. Philosopher will advise you that your system needs to be fixed. Engineer will advise you that you should avoid contact with scientists and philosophers.