Logical System
2013
Reading
Colin Howson, [1997] Logic with trees Chapter 2
A central use for Trees is to produce a counter example to an invalid argument. To do this, you construct a tree with a complete open branch. You will be able to do this for invalid arguments (but not valid ones). Then you run up that branch assigning all atomic formulas True and all negations of atomic formulas False.
This software will let you try a few.