- Valid: always true regardless of the values of its variables, e.g.,
P OR NOT(P)..
Slightly more formally: A valid formula is one which is always true, no matter what truth values its variables may have.
- Satisfiable: Can be solved, i.e.,
false values can be assigned to its variables, in a way that the final outcome is true.
Slightly more formally: A satisfiable formula is one which can sometimes be true, i.e., there is some assignment of truth values to its variables that makes it true.
An example of an unsatisfiable formula is
P AND NOT(P)..
Why are satisfiability and validity treated together?
Because they are related:
To check that G is valid,
we can check that NOT(G) is not satisfiable.
If you want to read more about satisfiability and validity in an accesible way, check the chapter 3 of Mathematics for Computer Science by Lehman, Thomson and Meyer.