It’s really a bit like elementary arithmetic, at least the material we covered in the undergrad course I took. I doubt you can use it for anything but logic programming or otherwise reasoning with machines.

It’s still interesting, though. After a while it really gets you thinking about representation, meaning, and whether 2 is a big enough number of logical values to assign to statements, or do you want to add quanitifers of uncertainty or even meaninglessness. There’s nothing in symbolic logic to explain language or refine your nonsense detector, though.

You might like these:

A Mathematician Reads the Newspaper
— John Allen Paulos

http://www.bcskeptics.info/resources/criticalthinking/index.html
— An idiosyncratic but interesting tutorial on argument, logical fallacies, and reasoning.

You might also enjoy just about anything for general audiences by the logician Raymond Smullyan. He’s funny.

Did you ever look at symbolic logic?

My impression is that symbolic logic does not give you a bullshit detector. It’s an attempt to replace the complex reality of reasoning with an extremely rigid set of typographical rules. For example, the Cyc project has been trying to duplicate common sense in a computer using predicate calculus (the main chunk of symbolic logic) for about 20 years now, with little or no success. People who master symbolic logic get good at working symbolic-logic problems, but the skill doesn’t carry over into other things. (Traditional logic is rather different, including a vocabulary of ideas about relevance, classification, etc.)

BTW, most “logic puzzles” of the kind that you find in puzzle books are called constraint satisfaction problems in math:
http://en.wikipedia.org/wiki/Constraint_satisfaction_problem
There are lots of completely systematic ways to solve them, which a computer can do. I don’t think they have much more to do with logical thinking than symbolic logic does.

Anyway, what did you find?