Mathematical Logic a formalized method of analyzing situations.
Boolean Algebra is a relation to this topic.
Charts or tables are used with particular symbols.
True, False, And, Or, Not, and other terms are used.

Logic Puzzles these are strategy puzzles. Where argument and reasoning are important. Any situation where Sherlock Holmes might be found.
Closely related to Recreational Math
Usually these puzzles are solved by making a grid and crossing out or filling in what you know.
One type iswhere you find out which person has which pet, living on which street. Or any similar situation.
There are also a few other types, which include:
Sudoko, and all of its relations
Paint by number puzzle, which is a grid with numbers, the numbers tell how many are next to each other in that row or column, there are several variants on this theme
There are other types as well, when I find good examples, I will add them

Some good books
To be Added

Additional information on these topics can be found on the following sites, as well as many others:
To be Added