Definition:Decision Procedure

Let $$U$$ be a set of propositional formulas.

A decision procedure for $$U$$ is an algorithm which, given a propositional formula $$P$$, always terminates, returning the answer:
 * Yes if $$P \in U$$;
 * No if $$P \notin U$$.

Refutation Procedure
A decision procedure can work like this.

From Tautology and Contradiction, if $$P$$ is true then $$\neg P$$ is false and vice versa.

Suppose we wish to decide if $$P$$ is valid.

We apply the decision procedure to $$\neg P$$.

If it reports that $$\neg P$$ is satisfiable, then $$P$$ is not valid (although it may be satisfiable).

If it reports that $$\neg P$$ is unsatisfiable, then $$P$$ is valid.

Such a decision procedure is called a refutation procedure.